1,1,114,0,0.400348," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c)^4,x, algorithm=""fricas"")","\frac{a \sinh\left(d x + c\right)^{5} + {\left(10 \, a \cosh\left(d x + c\right)^{2} - 7 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(3 \, {\left(a - 4 \, b\right)} d x - 8 \, b\right)} \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} - 3 \, {\left(7 \, a - 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a + 72 \, b\right)} \sinh\left(d x + c\right)}{64 \, d \cosh\left(d x + c\right)}"," ",0,"1/64*(a*sinh(d*x + c)^5 + (10*a*cosh(d*x + c)^2 - 7*a + 8*b)*sinh(d*x + c)^3 + 8*(3*(a - 4*b)*d*x - 8*b)*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 - 3*(7*a - 8*b)*cosh(d*x + c)^2 - 8*a + 72*b)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
2,1,85,0,0.440970," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c)^3,x, algorithm=""fricas"")","\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 4 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 4 \, a + 6 \, b\right)} \sinh\left(d x + c\right)^{2} - 9 \, a + 36 \, b}{24 \, d \cosh\left(d x + c\right)}"," ",0,"1/24*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 4*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 4*a + 6*b)*sinh(d*x + c)^2 - 9*a + 36*b)/(d*cosh(d*x + c))","B",0
3,1,67,0,0.405418," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c)^2,x, algorithm=""fricas"")","\frac{a \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a - 2 \, b\right)} d x - 2 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 8 \, b\right)} \sinh\left(d x + c\right)}{8 \, d \cosh\left(d x + c\right)}"," ",0,"1/8*(a*sinh(d*x + c)^3 - 4*((a - 2*b)*d*x - 2*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a - 8*b)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
4,1,38,0,0.427833," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c),x, algorithm=""fricas"")","\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a - 2 \, b}{2 \, d \cosh\left(d x + c\right)}"," ",0,"1/2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a - 2*b)/(d*cosh(d*x + c))","A",0
5,1,180,0,0.418343," ","integrate(csch(d*x+c)*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, b \cosh\left(d x + c\right) - {\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\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)} \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 + 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)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((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)*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
6,1,91,0,0.399980," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(a + b\right)} \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 + b)*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
7,1,924,0,0.430556," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 2 \, {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(5 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(5 \, {\left(a + 3 \, 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(a + 3 \, b\right)} \cosh\left(d x + c\right) - {\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{6} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 3 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{6} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 3 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(5 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, 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 + 3*b)*cosh(d*x + c)^5 + 10*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^4 + 2*(a + 3*b)*sinh(d*x + c)^5 + 4*(a - b)*cosh(d*x + c)^3 + 4*(5*(a + 3*b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^3 + 4*(5*(a + 3*b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(a + 3*b)*cosh(d*x + c) - ((a + 3*b)*cosh(d*x + c)^6 + 6*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + 3*b)*sinh(d*x + c)^6 - (a + 3*b)*cosh(d*x + c)^4 + (15*(a + 3*b)*cosh(d*x + c)^2 - a - 3*b)*sinh(d*x + c)^4 + 4*(5*(a + 3*b)*cosh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c)^2 + (15*(a + 3*b)*cosh(d*x + c)^4 - 6*(a + 3*b)*cosh(d*x + c)^2 - a - 3*b)*sinh(d*x + c)^2 + 2*(3*(a + 3*b)*cosh(d*x + c)^5 - 2*(a + 3*b)*cosh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + 3*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a + 3*b)*cosh(d*x + c)^6 + 6*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + 3*b)*sinh(d*x + c)^6 - (a + 3*b)*cosh(d*x + c)^4 + (15*(a + 3*b)*cosh(d*x + c)^2 - a - 3*b)*sinh(d*x + c)^4 + 4*(5*(a + 3*b)*cosh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c)^2 + (15*(a + 3*b)*cosh(d*x + c)^4 - 6*(a + 3*b)*cosh(d*x + c)^2 - a - 3*b)*sinh(d*x + c)^2 + 2*(3*(a + 3*b)*cosh(d*x + c)^5 - 2*(a + 3*b)*cosh(d*x + c)^3 - (a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + 3*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(5*(a + 3*b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a + 3*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
8,1,246,0,0.384106," ","integrate(csch(d*x+c)^4*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + a + 4 \, 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 - 2*b)*cosh(d*x + c)^2 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c) + (a - 2*b)*sinh(d*x + c)^2 + a + 4*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
9,1,342,0,0.416784," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, a^{2} \sinh\left(d x + c\right)^{7} + 3 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(3 \, {\left(3 \, a^{2} - 24 \, a b + 8 \, b^{2}\right)} d x - 48 \, a b + 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 24 \, {\left(3 \, {\left(3 \, a^{2} - 24 \, a b + 8 \, b^{2}\right)} d x - 48 \, a b + 32 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(105 \, a^{2} \cosh\left(d x + c\right)^{4} - 30 \, {\left(5 \, a^{2} - 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 63 \, a^{2} + 528 \, a b - 256 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 24 \, {\left(3 \, {\left(3 \, a^{2} - 24 \, a b + 8 \, b^{2}\right)} d x - 48 \, a b + 32 \, b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} - 5 \, {\left(5 \, a^{2} - 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - {\left(63 \, a^{2} - 528 \, a b + 256 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 15 \, a^{2} + 160 \, a b\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*sinh(d*x + c)^7 + 3*(21*a^2*cosh(d*x + c)^2 - 5*a^2 + 16*a*b)*sinh(d*x + c)^5 + 8*(3*(3*a^2 - 24*a*b + 8*b^2)*d*x - 48*a*b + 32*b^2)*cosh(d*x + c)^3 + 24*(3*(3*a^2 - 24*a*b + 8*b^2)*d*x - 48*a*b + 32*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (105*a^2*cosh(d*x + c)^4 - 30*(5*a^2 - 16*a*b)*cosh(d*x + c)^2 - 63*a^2 + 528*a*b - 256*b^2)*sinh(d*x + c)^3 + 24*(3*(3*a^2 - 24*a*b + 8*b^2)*d*x - 48*a*b + 32*b^2)*cosh(d*x + c) + 3*(7*a^2*cosh(d*x + c)^6 - 5*(5*a^2 - 16*a*b)*cosh(d*x + c)^4 - (63*a^2 - 528*a*b + 256*b^2)*cosh(d*x + c)^2 - 15*a^2 + 160*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
10,1,212,0,0.393725," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^3,x, algorithm=""fricas"")","\frac{a^{2} \cosh\left(d x + c\right)^{6} + a^{2} \sinh\left(d x + c\right)^{6} - 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 8 \, a b\right)} \sinh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} - 64 \, a b + 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 64 \, a b - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 26 \, a^{2} + 168 \, a b - 16 \, 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*cosh(d*x + c)^6 + a^2*sinh(d*x + c)^6 - 6*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 3*(5*a^2*cosh(d*x + c)^2 - 2*a^2 + 8*a*b)*sinh(d*x + c)^4 - 3*(11*a^2 - 64*a*b + 16*b^2)*cosh(d*x + c)^2 + 3*(5*a^2*cosh(d*x + c)^4 - 12*(a^2 - 4*a*b)*cosh(d*x + c)^2 - 11*a^2 + 64*a*b - 16*b^2)*sinh(d*x + c)^2 - 26*a^2 + 168*a*b - 16*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
11,1,252,0,0.409498," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} \sinh\left(d x + c\right)^{5} - 4 \, {\left(3 \, {\left(a^{2} - 4 \, a b\right)} d x - 12 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(3 \, {\left(a^{2} - 4 \, a b\right)} d x - 12 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(30 \, a^{2} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} - 48 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(3 \, {\left(a^{2} - 4 \, a b\right)} d x - 12 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{2} - 48 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 16 \, a b - 8 \, 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*sinh(d*x + c)^5 - 4*(3*(a^2 - 4*a*b)*d*x - 12*a*b + 2*b^2)*cosh(d*x + c)^3 - 12*(3*(a^2 - 4*a*b)*d*x - 12*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (30*a^2*cosh(d*x + c)^2 + 9*a^2 - 48*a*b + 8*b^2)*sinh(d*x + c)^3 - 12*(3*(a^2 - 4*a*b)*d*x - 12*a*b + 2*b^2)*cosh(d*x + c) + 3*(5*a^2*cosh(d*x + c)^4 + (9*a^2 - 48*a*b + 8*b^2)*cosh(d*x + c)^2 + 2*a^2 - 16*a*b - 8*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
12,1,133,0,0.402912," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c),x, algorithm=""fricas"")","\frac{3 \, a^{2} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} \sinh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + 9 \, a^{2} - 24 \, a b - 8 \, 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*cosh(d*x + c)^4 + 3*a^2*sinh(d*x + c)^4 + 12*(a^2 - 2*a*b)*cosh(d*x + c)^2 + 6*(3*a^2*cosh(d*x + c)^2 + 2*a^2 - 4*a*b)*sinh(d*x + c)^2 + 9*a^2 - 24*a*b - 8*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
13,1,1148,0,0.424940," ","integrate(csch(d*x+c)*(a+b*sech(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 + 5 \, 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 + 5 \, 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 + 5 \, 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({\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 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)} \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 + 5 \, 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 + 5*b^2)*cosh(d*x + c)^3 + 4*(15*(2*a*b + b^2)*cosh(d*x + c)^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^3 + 12*(5*(2*a*b + b^2)*cosh(d*x + c)^3 + (6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*a*b + b^2)*cosh(d*x + c) - 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))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 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))*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 + 5*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
14,1,284,0,0.415598," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(3 \, a^{2} + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 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} + {\left(9 \, a^{2} + 18 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(3 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b + 4 \, 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 + 6*a*b + 4*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 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 + (9*a^2 + 18*a*b + 8*b^2)*cosh(d*x + c) - 2*(3*(3*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a*b + 4*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
15,1,2930,0,0.452642," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 54 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{9} + 8 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(27 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(9 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(189 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(189 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(63 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(27 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{2} + 6 \, a b + 5 \, 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} + a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 6 \, a b + 5 \, b^{2} + 2 \, {\left(5 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{2} + 6 \, a b + 5 \, 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} + a^{2} + 6 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 6 \, a b + 5 \, b^{2} + 2 \, {\left(5 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + 5 \, 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(27 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(9 \, a^{2} + 6 \, a b - 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 18 \, a b + 15 \, b^{2}\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 + 6*a*b + 5*b^2)*cosh(d*x + c)^9 + 54*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^8 + 6*(a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^9 + 8*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 + 8*(27*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + 3*a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^7 + 56*(9*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + (3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(9*a^2 + 6*a*b - 11*b^2)*cosh(d*x + c)^5 + 4*(189*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 42*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + 9*a^2 + 6*a*b - 11*b^2)*sinh(d*x + c)^5 + 4*(189*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 + 70*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + 5*(9*a^2 + 6*a*b - 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 8*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + 8*(63*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 35*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 5*(9*a^2 + 6*a*b - 11*b^2)*cosh(d*x + c)^2 + 3*a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^3 + 8*(27*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 + 21*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 + 5*(9*a^2 + 6*a*b - 11*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c) - 3*((a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^10 + 10*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^10 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^8 + (45*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^8 + 8*(15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 2*(105*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 14*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b - 5*b^2)*sinh(d*x + c)^6 + 4*(63*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 + 14*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 - 3*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 2*(105*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 35*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 - 15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b - 5*b^2)*sinh(d*x + c)^4 + 8*(15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 + 7*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 - 5*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 - (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + (45*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^8 + 28*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 - 30*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 - 12*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2 + 2*(5*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^9 + 4*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 - 6*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 - 4*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^10 + 10*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^10 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^8 + (45*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^8 + 8*(15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 2*(105*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 14*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b - 5*b^2)*sinh(d*x + c)^6 + 4*(63*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 + 14*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 - 3*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 2*(105*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 35*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 - 15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b - 5*b^2)*sinh(d*x + c)^4 + 8*(15*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 + 7*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 - 5*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 - (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + (45*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^8 + 28*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 - 30*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 - 12*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2)*sinh(d*x + c)^2 + a^2 + 6*a*b + 5*b^2 + 2*(5*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^9 + 4*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^7 - 6*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^5 - 4*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^3 + (a^2 + 6*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(27*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^8 + 28*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^6 + 10*(9*a^2 + 6*a*b - 11*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 + 3*a^2 + 18*a*b + 15*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 + 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
16,1,408,0,0.399771," ","integrate(csch(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(a^{2} - 4 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 4 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 12 \, a b + 12 \, b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + 2 \, b^{2}\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)}}{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 - 4*a*b - 4*b^2)*cosh(d*x + c)^4 + 8*(a^2 + 2*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - 4*a*b - 4*b^2)*sinh(d*x + c)^4 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*(a^2 - 4*a*b - 4*b^2)*cosh(d*x + c)^2 + 2*a^2 + 4*a*b)*sinh(d*x + c)^2 + 3*a^2 + 12*a*b + 12*b^2 + 8*((a^2 + 2*a*b + 2*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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
17,1,727,0,0.452998," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^4,x, algorithm=""fricas"")","\frac{5 \, a^{3} \sinh\left(d x + c\right)^{9} + 15 \, {\left(12 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3} + 8 \, a^{2} b\right)} \sinh\left(d x + c\right)^{7} - 8 \, {\left(120 \, a^{2} b - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 40 \, {\left(120 \, a^{2} b - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(630 \, a^{3} \cosh\left(d x + c\right)^{4} - 150 \, a^{3} + 1560 \, a^{2} b - 1280 \, a b^{2} + 64 \, b^{3} - 315 \, {\left(a^{3} - 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} - 40 \, {\left(120 \, a^{2} b - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(84 \, a^{3} \cosh\left(d x + c\right)^{6} - 105 \, {\left(a^{3} - 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 62 \, a^{3} + 792 \, a^{2} b - 512 \, a b^{2} - 64 \, b^{3} - 4 \, {\left(75 \, a^{3} - 780 \, a^{2} b + 640 \, a b^{2} - 32 \, 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 - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(120 \, a^{2} b - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 80 \, {\left(120 \, a^{2} b - 160 \, a b^{2} + 8 \, b^{3} - 15 \, {\left(a^{3} - 12 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right) + 5 \, {\left(9 \, a^{3} \cosh\left(d x + c\right)^{8} - 21 \, {\left(a^{3} - 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(75 \, a^{3} - 780 \, a^{2} b + 640 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{3} + 504 \, a^{2} b - 256 \, a b^{2} + 128 \, b^{3} - 6 \, {\left(31 \, a^{3} - 396 \, a^{2} b + 256 \, a b^{2} + 32 \, 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*sinh(d*x + c)^9 + 15*(12*a^3*cosh(d*x + c)^2 - a^3 + 8*a^2*b)*sinh(d*x + c)^7 - 8*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^5 - 40*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)*sinh(d*x + c)^4 + (630*a^3*cosh(d*x + c)^4 - 150*a^3 + 1560*a^2*b - 1280*a*b^2 + 64*b^3 - 315*(a^3 - 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 - 40*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 5*(84*a^3*cosh(d*x + c)^6 - 105*(a^3 - 8*a^2*b)*cosh(d*x + c)^4 - 62*a^3 + 792*a^2*b - 512*a*b^2 - 64*b^3 - 4*(75*a^3 - 780*a^2*b + 640*a*b^2 - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 - 40*(2*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 3*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 - 80*(120*a^2*b - 160*a*b^2 + 8*b^3 - 15*(a^3 - 12*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c) + 5*(9*a^3*cosh(d*x + c)^8 - 21*(a^3 - 8*a^2*b)*cosh(d*x + c)^6 - 2*(75*a^3 - 780*a^2*b + 640*a*b^2 - 32*b^3)*cosh(d*x + c)^4 - 36*a^3 + 504*a^2*b - 256*a*b^2 + 128*b^3 - 6*(31*a^3 - 396*a^2*b + 256*a*b^2 + 32*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
18,1,403,0,0.414867," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} \cosh\left(d x + c\right)^{8} + 5 \, a^{3} \sinh\left(d x + c\right)^{8} - 20 \, {\left(a^{3} - 9 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3} + 9 \, a^{2} b\right)} \sinh\left(d x + c\right)^{6} - 20 \, {\left(11 \, a^{3} - 90 \, a^{2} b + 36 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(35 \, a^{3} \cosh\left(d x + c\right)^{4} - 22 \, a^{3} + 180 \, a^{2} b - 72 \, a b^{2} - 30 \, {\left(a^{3} - 9 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 425 \, a^{3} + 3960 \, a^{2} b - 1200 \, a b^{2} + 64 \, b^{3} - 20 \, {\left(31 \, a^{3} - 279 \, a^{2} b + 96 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} - 9 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 31 \, a^{3} + 279 \, a^{2} b - 96 \, a b^{2} - 16 \, b^{3} - 6 \, {\left(11 \, a^{3} - 90 \, a^{2} b + 36 \, a b^{2}\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*cosh(d*x + c)^8 + 5*a^3*sinh(d*x + c)^8 - 20*(a^3 - 9*a^2*b)*cosh(d*x + c)^6 + 20*(7*a^3*cosh(d*x + c)^2 - a^3 + 9*a^2*b)*sinh(d*x + c)^6 - 20*(11*a^3 - 90*a^2*b + 36*a*b^2)*cosh(d*x + c)^4 + 10*(35*a^3*cosh(d*x + c)^4 - 22*a^3 + 180*a^2*b - 72*a*b^2 - 30*(a^3 - 9*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 425*a^3 + 3960*a^2*b - 1200*a*b^2 + 64*b^3 - 20*(31*a^3 - 279*a^2*b + 96*a*b^2 + 16*b^3)*cosh(d*x + c)^2 + 20*(7*a^3*cosh(d*x + c)^6 - 15*(a^3 - 9*a^2*b)*cosh(d*x + c)^4 - 31*a^3 + 279*a^2*b - 96*a*b^2 - 16*b^3 - 6*(11*a^3 - 90*a^2*b + 36*a*b^2)*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
19,1,595,0,0.429355," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^2,x, algorithm=""fricas"")","\frac{15 \, a^{3} \sinh\left(d x + c\right)^{7} + 4 \, {\left(90 \, a^{2} b - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(90 \, a^{2} b - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(315 \, a^{3} \cosh\left(d x + c\right)^{2} + 75 \, a^{3} - 360 \, a^{2} b + 120 \, a b^{2} + 16 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(90 \, a^{2} b - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(105 \, a^{3} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} - 216 \, a^{2} b - 24 \, a b^{2} + 16 \, b^{3} + 2 \, {\left(75 \, a^{3} - 360 \, a^{2} b + 120 \, a b^{2} + 16 \, 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 - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(90 \, a^{2} b - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 40 \, {\left(90 \, a^{2} b - 30 \, a b^{2} - 4 \, b^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right) + 5 \, {\left(21 \, a^{3} \cosh\left(d x + c\right)^{6} + {\left(75 \, a^{3} - 360 \, a^{2} b + 120 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} - 144 \, a^{2} b - 48 \, a b^{2} - 64 \, b^{3} + 3 \, {\left(27 \, a^{3} - 216 \, a^{2} b - 24 \, a b^{2} + 16 \, 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*sinh(d*x + c)^7 + 4*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c)^5 + 20*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c)*sinh(d*x + c)^4 + (315*a^3*cosh(d*x + c)^2 + 75*a^3 - 360*a^2*b + 120*a*b^2 + 16*b^3)*sinh(d*x + c)^5 + 20*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c)^3 + 5*(105*a^3*cosh(d*x + c)^4 + 27*a^3 - 216*a^2*b - 24*a*b^2 + 16*b^3 + 2*(75*a^3 - 360*a^2*b + 120*a*b^2 + 16*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 20*(2*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c)^3 + 3*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 40*(90*a^2*b - 30*a*b^2 - 4*b^3 - 15*(a^3 - 6*a^2*b)*d*x)*cosh(d*x + c) + 5*(21*a^3*cosh(d*x + c)^6 + (75*a^3 - 360*a^2*b + 120*a*b^2 + 16*b^3)*cosh(d*x + c)^4 + 15*a^3 - 144*a^2*b - 48*a*b^2 - 64*b^3 + 3*(27*a^3 - 216*a^2*b - 24*a*b^2 + 16*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
20,1,276,0,0.393924," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c),x, algorithm=""fricas"")","\frac{5 \, a^{3} \cosh\left(d x + c\right)^{6} + 5 \, a^{3} \sinh\left(d x + c\right)^{6} + 30 \, {\left(a^{3} - 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} - 4 \, a^{2} b\right)} \sinh\left(d x + c\right)^{4} + 50 \, a^{3} - 180 \, a^{2} b - 80 \, a b^{2} - 32 \, b^{3} + 5 \, {\left(15 \, a^{3} - 48 \, a^{2} b - 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} - 48 \, a^{2} b - 16 \, a b^{2} + 36 \, {\left(a^{3} - 2 \, a^{2} b\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*cosh(d*x + c)^6 + 5*a^3*sinh(d*x + c)^6 + 30*(a^3 - 2*a^2*b)*cosh(d*x + c)^4 + 15*(5*a^3*cosh(d*x + c)^2 + 2*a^3 - 4*a^2*b)*sinh(d*x + c)^4 + 50*a^3 - 180*a^2*b - 80*a*b^2 - 32*b^3 + 5*(15*a^3 - 48*a^2*b - 16*a*b^2)*cosh(d*x + c)^2 + 5*(15*a^3*cosh(d*x + c)^4 + 15*a^3 - 48*a^2*b - 16*a*b^2 + 36*(a^3 - 2*a^2*b)*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
21,1,3443,0,0.444836," ","integrate(csch(d*x+c)*(a+b*sech(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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 40 \, {\left(9 \, a^{2} b + 12 \, a b^{2} + 4 \, 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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(135 \, a^{2} b + 195 \, a b^{2} + 89 \, 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 + 195 \, a b^{2} + 89 \, b^{3} + 210 \, {\left(9 \, 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)^{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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(135 \, a^{2} b + 195 \, a b^{2} + 89 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(9 \, a^{2} b + 12 \, a b^{2} + 4 \, 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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} + {\left(135 \, a^{2} b + 195 \, a b^{2} + 89 \, 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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(135 \, a^{2} b + 195 \, a b^{2} + 89 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, 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(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) - 15 \, {\left({\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} + 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} + 9 \, {\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} + 40 \, {\left(3 \, {\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)^{7} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(21 \, {\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} + 14 \, {\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} + 4 \, {\left(63 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\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} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\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)^{4} + 40 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\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)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\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} + 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)^{2} + 10 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\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(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 15 \, {\left({\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} + 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} + 9 \, {\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} + 40 \, {\left(3 \, {\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)^{7} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(21 \, {\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} + 14 \, {\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} + 4 \, {\left(63 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\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} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\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)^{4} + 40 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\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)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\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} + 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)^{2} + 10 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\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(\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 + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(135 \, a^{2} b + 195 \, a b^{2} + 89 \, 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 + 12 \, a b^{2} + 4 \, 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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^7 + 40*(9*a^2*b + 12*a*b^2 + 4*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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(135*a^2*b + 195*a*b^2 + 89*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 + 195*a*b^2 + 89*b^3 + 210*(9*a^2*b + 12*a*b^2 + 4*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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + (135*a^2*b + 195*a*b^2 + 89*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 40*(9*a^2*b + 12*a*b^2 + 4*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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 9*a^2*b + 12*a*b^2 + 4*b^3 + (135*a^2*b + 195*a*b^2 + 89*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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + (135*a^2*b + 195*a*b^2 + 89*b^3)*cosh(d*x + c)^3 + 3*(9*a^2*b + 12*a*b^2 + 4*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 + 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 + 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 + 9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 40*(3*(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)^7 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 10*(21*(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 + 14*(a^3 + 3*a^2*b + 3*a*b^2 + 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 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 10*(21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 35*(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)^4 + 40*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 7*(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)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 5*(9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 30*(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 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 10*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 4*(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(cosh(d*x + c) + sinh(d*x + c) + 1) + 15*((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 + 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 + 9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 40*(3*(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)^7 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 10*(21*(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 + 14*(a^3 + 3*a^2*b + 3*a*b^2 + 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 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 10*(21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 35*(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)^4 + 40*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 7*(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)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 5*(9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 30*(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 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 10*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 4*(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(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 + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 2*(135*a^2*b + 195*a*b^2 + 89*b^3)*cosh(d*x + c)^4 + 9*a^2*b + 9*a*b^2 + 3*b^3 + 12*(9*a^2*b + 12*a*b^2 + 4*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
22,1,622,0,0.469858," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(5 \, a^{3} + 15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + {\left(25 \, a^{3} + 75 \, a^{2} b + 80 \, a b^{2} + 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(45 \, a^{2} b + 80 \, a b^{2} + 32 \, b^{3} + 10 \, {\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(10 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(25 \, a^{3} + 75 \, a^{2} b + 80 \, a b^{2} + 32 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 14 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right) - {\left(5 \, {\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{2} b + 60 \, a b^{2} + 40 \, b^{3} + 3 \, {\left(45 \, a^{2} b + 80 \, a b^{2} + 32 \, 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 + 15*a^2*b + 20*a*b^2 + 8*b^3)*cosh(d*x + c)^5 + 5*(5*a^3 + 15*a^2*b + 20*a*b^2 + 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^2*b + 20*a*b^2 + 8*b^3)*sinh(d*x + c)^5 + (25*a^3 + 75*a^2*b + 80*a*b^2 + 32*b^3)*cosh(d*x + c)^3 - (45*a^2*b + 80*a*b^2 + 32*b^3 + 10*(15*a^2*b + 20*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (10*(5*a^3 + 15*a^2*b + 20*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + 3*(25*a^3 + 75*a^2*b + 80*a*b^2 + 32*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^3 + 15*a^2*b + 14*a*b^2 + 4*b^3)*cosh(d*x + c) - (5*(15*a^2*b + 20*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 30*a^2*b + 60*a*b^2 + 40*b^3 + 3*(45*a^2*b + 80*a*b^2 + 32*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
23,1,6717,0,0.595619," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{30 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 390 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + 30 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{13} + 20 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 20 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3} + 117 \, {\left(a^{3} + 9 \, 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)^{11} + 220 \, {\left(39 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 6 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(10725 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 225 \, a^{3} + 585 \, a^{2} b + 495 \, a b^{2} + 231 \, b^{3} + 550 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 6 \, {\left(6435 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 550 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 825 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3} + 27 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 63 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(6435 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1540 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3} + 28 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(10725 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 3300 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(2145 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 825 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 126 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{3} + 225 \, a^{2} b + 375 \, a b^{2} + 175 \, b^{3} + 15 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(585 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 275 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 54 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right) - 15 \, {\left({\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + {\left(3 \, a^{3} + 27 \, a^{2} b + 45 \, a b^{2} + 21 \, b^{3} + 91 \, {\left(a^{3} + 9 \, 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)^{12} + 4 \, {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} + 198 \, {\left(a^{3} + 9 \, 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)^{10} + 2 \, {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 330 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1485 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 45 \, a^{2} b - 75 \, a b^{2} - 35 \, b^{3} + 45 \, {\left(a^{3} + 9 \, 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)^{8} + 8 \, {\left(429 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 297 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2772 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 45 \, a^{2} b - 75 \, a b^{2} - 35 \, b^{3} - 140 \, {\left(a^{3} + 9 \, 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)^{6} + 2 \, {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1188 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1485 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} - 75 \, {\left(a^{3} + 9 \, 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} + 4 \, {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 165 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 198 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 27 \, a^{2} b + 45 \, a b^{2} + 21 \, b^{3} + 6 \, {\left(a^{3} + 9 \, 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)^{2} + 2 \, {\left(7 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 18 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 15 \, {\left({\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + {\left(3 \, a^{3} + 27 \, a^{2} b + 45 \, a b^{2} + 21 \, b^{3} + 91 \, {\left(a^{3} + 9 \, 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)^{12} + 4 \, {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} + 198 \, {\left(a^{3} + 9 \, 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)^{10} + 2 \, {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 330 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1485 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 45 \, a^{2} b - 75 \, a b^{2} - 35 \, b^{3} + 45 \, {\left(a^{3} + 9 \, 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)^{8} + 8 \, {\left(429 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 297 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2772 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 45 \, a^{2} b - 75 \, a b^{2} - 35 \, b^{3} - 140 \, {\left(a^{3} + 9 \, 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)^{6} + 2 \, {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1188 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1485 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} - 75 \, {\left(a^{3} + 9 \, 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} + 4 \, {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 165 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 198 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 27 \, a^{2} b + 45 \, a b^{2} + 21 \, b^{3} + 6 \, {\left(a^{3} + 9 \, 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)^{2} + 2 \, {\left(7 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 18 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(195 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 110 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 27 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(75 \, a^{3} + 135 \, a^{2} b - 15 \, a b^{2} - 103 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(75 \, a^{3} + 195 \, a^{2} b + 165 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 135 \, a^{2} b + 225 \, a b^{2} + 105 \, b^{3} + 30 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 75 \, a b^{2} + 35 \, 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 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^13 + 390*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)*sinh(d*x + c)^12 + 30*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*sinh(d*x + c)^13 + 20*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 20*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3 + 117*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 220*(39*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + (9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 6*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^9 + 2*(10725*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + 225*a^3 + 585*a^2*b + 495*a*b^2 + 231*b^3 + 550*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 6*(6435*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 550*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 9*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 8*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^7 + 8*(6435*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 825*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3 + 27*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 8*(6435*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 + 1155*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 63*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^3 + 7*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^5 + 6*(6435*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + 1540*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 126*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^4 + 75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3 + 28*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(10725*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 + 3300*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 378*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^5 + 140*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^3 + 15*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 20*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 4*(2145*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + 825*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 126*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^6 + 70*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^4 + 45*a^3 + 225*a^2*b + 375*a*b^2 + 175*b^3 + 15*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(585*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^11 + 275*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 54*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^7 + 42*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^5 + 15*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^3 + 15*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 30*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c) - 15*((a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^14 + 14*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)*sinh(d*x + c)^13 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*sinh(d*x + c)^14 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^12 + (3*a^3 + 27*a^2*b + 45*a*b^2 + 21*b^3 + 91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 9*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + (1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 + 198*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 330*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + (3003*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 1485*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 - 5*a^3 - 45*a^2*b - 75*a*b^2 - 35*b^3 + 45*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 + 297*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + (3003*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + 2772*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 210*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 - 5*a^3 - 45*a^2*b - 75*a*b^2 - 35*b^3 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 + 1188*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 + 126*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 - 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + (1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + 1485*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + 210*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 - 350*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 - 75*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^11 + 165*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 + 30*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 - 70*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 - 25*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2 + (91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^12 + 198*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + 45*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 - 75*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + 3*a^3 + 27*a^2*b + 45*a*b^2 + 21*b^3 + 6*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^13 + 18*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^11 + 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 - 20*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 - 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 2*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 15*((a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^14 + 14*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)*sinh(d*x + c)^13 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*sinh(d*x + c)^14 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^12 + (3*a^3 + 27*a^2*b + 45*a*b^2 + 21*b^3 + 91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 9*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + (1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 + 198*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 330*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + (3003*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 1485*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 - 5*a^3 - 45*a^2*b - 75*a*b^2 - 35*b^3 + 45*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 + 297*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + (3003*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + 2772*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 210*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 - 5*a^3 - 45*a^2*b - 75*a*b^2 - 35*b^3 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 + 1188*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 + 126*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 - 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + (1001*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + 1485*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 + 210*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 - 350*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 - 75*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^11 + 165*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 + 30*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 - 70*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 - 25*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + (a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2 + (91*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^12 + 198*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^10 + 45*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^8 - 140*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 - 75*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + 3*a^3 + 27*a^2*b + 45*a*b^2 + 21*b^3 + 6*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^13 + 18*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^11 + 5*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^9 - 20*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^7 - 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^5 + 2*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(195*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^12 + 110*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 27*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^8 + 28*(75*a^3 + 135*a^2*b - 15*a*b^2 - 103*b^3)*cosh(d*x + c)^6 + 15*(75*a^3 + 195*a^2*b + 165*a*b^2 + 77*b^3)*cosh(d*x + c)^4 + 15*a^3 + 135*a^2*b + 225*a*b^2 + 105*b^3 + 30*(9*a^3 + 45*a^2*b + 75*a*b^2 + 35*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
24,1,955,0,0.586603," ","integrate(csch(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(5 \, a^{3} - 30 \, a^{2} b - 60 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 30 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{3} - 30 \, a^{2} b - 60 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(15 \, a^{3} - 60 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(30 \, a^{3} - 120 \, a b^{2} - 64 \, b^{3} + 15 \, {\left(5 \, a^{3} - 30 \, a^{2} b - 60 \, a b^{2} - 32 \, 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^{2} b + 30 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 15 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 50 \, a^{3} + 240 \, a^{2} b + 360 \, a b^{2} + 192 \, b^{3} + {\left(75 \, a^{3} + 270 \, a^{2} b + 300 \, a b^{2} + 64 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{3} - 30 \, a^{2} b - 60 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 270 \, a^{2} b + 300 \, a b^{2} + 64 \, b^{3} + 12 \, {\left(15 \, a^{3} - 60 \, a b^{2} - 32 \, 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^{2} b + 30 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(5 \, a^{3} + 15 \, a^{2} b + 15 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(25 \, a^{3} + 75 \, a^{2} b + 30 \, a b^{2} - 32 \, 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 - 30*a^2*b - 60*a*b^2 - 32*b^3)*cosh(d*x + c)^6 + 12*(5*a^3 + 15*a^2*b + 30*a*b^2 + 16*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^3 - 30*a^2*b - 60*a*b^2 - 32*b^3)*sinh(d*x + c)^6 + 2*(15*a^3 - 60*a*b^2 - 32*b^3)*cosh(d*x + c)^4 + (30*a^3 - 120*a*b^2 - 64*b^3 + 15*(5*a^3 - 30*a^2*b - 60*a*b^2 - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(5*a^3 + 15*a^2*b + 30*a*b^2 + 16*b^3)*cosh(d*x + c)^3 + 4*(5*a^3 + 15*a^2*b + 15*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 50*a^3 + 240*a^2*b + 360*a*b^2 + 192*b^3 + (75*a^3 + 270*a^2*b + 300*a*b^2 + 64*b^3)*cosh(d*x + c)^2 + (15*(5*a^3 - 30*a^2*b - 60*a*b^2 - 32*b^3)*cosh(d*x + c)^4 + 75*a^3 + 270*a^2*b + 300*a*b^2 + 64*b^3 + 12*(15*a^3 - 60*a*b^2 - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(5*a^3 + 15*a^2*b + 30*a*b^2 + 16*b^3)*cosh(d*x + c)^5 + 8*(5*a^3 + 15*a^2*b + 15*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (25*a^3 + 75*a^2*b + 30*a*b^2 - 32*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
25,1,1681,0,0.593240," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \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 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 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}\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \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 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 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}\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) - a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} + 12 \, a b + 8 \, 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(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 8*(3*a^2 + 12*a*b + 8*b^2)*d*x*cosh(d*x + c)^4 - 8*(a^2 + a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 - 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 + 4*(3*a^2 + 12*a*b + 8*b^2)*d*x - 60*(a^2 + a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 4*(3*a^2 + 12*a*b + 8*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*cosh(d*x + c)^6 + 12*(3*a^2 + 12*a*b + 8*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 + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a + b)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4)*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - a^2 + 8*(a^2*cosh(d*x + c)^7 + 4*(3*a^2 + 12*a*b + 8*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*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4), 1/64*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 8*(3*a^2 + 12*a*b + 8*b^2)*d*x*cosh(d*x + c)^4 - 8*(a^2 + a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 - 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 + 4*(3*a^2 + 12*a*b + 8*b^2)*d*x - 60*(a^2 + a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 4*(3*a^2 + 12*a*b + 8*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*cosh(d*x + c)^6 + 12*(3*a^2 + 12*a*b + 8*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 + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a + b)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4)*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) - a^2 + 8*(a^2*cosh(d*x + c)^7 + 4*(3*a^2 + 12*a*b + 8*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*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4)]","B",0
26,1,1246,0,0.491785," ","integrate(sinh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{a \cosh\left(d x + c\right)^{6} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a \sinh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 4 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 4 \, b\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 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}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 6 \, {\left(a \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{24 \, {\left(a^{2} d \cosh\left(d x + c\right)^{3} + 3 \, a^{2} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{a \cosh\left(d x + c\right)^{6} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a \sinh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 4 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 4 \, b\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 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}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 24 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 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}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 6 \, {\left(a \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{24 \, {\left(a^{2} d \cosh\left(d x + c\right)^{3} + 3 \, a^{2} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*(a*cosh(d*x + c)^6 + 6*a*cosh(d*x + c)*sinh(d*x + c)^5 + a*sinh(d*x + c)^6 - 3*(3*a + 4*b)*cosh(d*x + c)^4 + 3*(5*a*cosh(d*x + c)^2 - 3*a - 4*b)*sinh(d*x + c)^4 + 4*(5*a*cosh(d*x + c)^3 - 3*(3*a + 4*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a + 4*b)*cosh(d*x + c)^2 + 3*(5*a*cosh(d*x + c)^4 - 6*(3*a + 4*b)*cosh(d*x + c)^2 - 3*a - 4*b)*sinh(d*x + c)^2 + 12*((a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a + b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a + b)*sinh(d*x + c)^3)*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 6*(a*cosh(d*x + c)^5 - 2*(3*a + 4*b)*cosh(d*x + c)^3 - (3*a + 4*b)*cosh(d*x + c))*sinh(d*x + c) + a)/(a^2*d*cosh(d*x + c)^3 + 3*a^2*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*d*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*d*sinh(d*x + c)^3), 1/24*(a*cosh(d*x + c)^6 + 6*a*cosh(d*x + c)*sinh(d*x + c)^5 + a*sinh(d*x + c)^6 - 3*(3*a + 4*b)*cosh(d*x + c)^4 + 3*(5*a*cosh(d*x + c)^2 - 3*a - 4*b)*sinh(d*x + c)^4 + 4*(5*a*cosh(d*x + c)^3 - 3*(3*a + 4*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a + 4*b)*cosh(d*x + c)^2 + 3*(5*a*cosh(d*x + c)^4 - 6*(3*a + 4*b)*cosh(d*x + c)^2 - 3*a - 4*b)*sinh(d*x + c)^2 - 24*((a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a + b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a + b)*sinh(d*x + c)^3)*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) + 24*((a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a + b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a + b)*sinh(d*x + c)^3)*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 6*(a*cosh(d*x + c)^5 - 2*(3*a + 4*b)*cosh(d*x + c)^3 - (3*a + 4*b)*cosh(d*x + c))*sinh(d*x + c) + a)/(a^2*d*cosh(d*x + c)^3 + 3*a^2*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*d*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*d*sinh(d*x + c)^3)]","B",0
27,1,805,0,0.482892," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a + 2 \, b\right)} d x \cosh\left(d x + c\right)^{2} - 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 \, {\left(2 \, {\left(a + 2 \, b\right)} d x - 3 \, a \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \sqrt{a b + b^{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}\right)} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(2 \, {\left(a + 2 \, b\right)} d x \cosh\left(d x + c\right) - a \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + a}{8 \, {\left(a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left(a + 2 \, b\right)} d x \cosh\left(d x + c\right)^{2} - 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 \, {\left(2 \, {\left(a + 2 \, b\right)} d x - 3 \, a \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 8 \, \sqrt{-a b - b^{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}\right)} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(2 \, {\left(a + 2 \, b\right)} d x \cosh\left(d x + c\right) - a \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + a}{8 \, {\left(a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/8*(4*(a + 2*b)*d*x*cosh(d*x + c)^2 - a*cosh(d*x + c)^4 - 4*a*cosh(d*x + c)*sinh(d*x + c)^3 - a*sinh(d*x + c)^4 + 2*(2*(a + 2*b)*d*x - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*sqrt(a*b + b^2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(2*(a + 2*b)*d*x*cosh(d*x + c) - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2), -1/8*(4*(a + 2*b)*d*x*cosh(d*x + c)^2 - a*cosh(d*x + c)^4 - 4*a*cosh(d*x + c)*sinh(d*x + c)^3 - a*sinh(d*x + c)^4 + 2*(2*(a + 2*b)*d*x - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 8*sqrt(-a*b - b^2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(2*(a + 2*b)*d*x*cosh(d*x + c) - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2)]","B",0
28,1,595,0,0.511955," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right)\right)}}, \frac{2 \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 2 \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{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(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*(sqrt(-b/a)*(cosh(d*x + c) + sinh(d*x + c))*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)/(a*d*cosh(d*x + c) + a*d*sinh(d*x + c)), 1/2*(2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - 2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)/(a*d*cosh(d*x + c) + a*d*sinh(d*x + c))]","B",0
29,1,533,0,0.507253," ","integrate(csch(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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 \, {\left(a + b\right)} d}, -\frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{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)}{{\left(a + b\right)} d}\right]"," ",0,"[1/2*(sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 2*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*log(cosh(d*x + c) + sinh(d*x + c) - 1))/((a + b)*d), -(sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + log(cosh(d*x + c) + sinh(d*x + c) + 1) - log(cosh(d*x + c) + sinh(d*x + c) - 1))/((a + b)*d)]","B",0
30,1,588,0,0.557329," ","integrate(csch(d*x+c)^2/(a+b*sech(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 + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4}{2 \, {\left({\left(a + b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a + b\right)} 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 + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 2}{{\left(a + b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a + b\right)} 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 + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4)/((a + b)*d*cosh(d*x + c)^2 + 2*(a + b)*d*cosh(d*x + c)*sinh(d*x + c) + (a + b)*d*sinh(d*x + c)^2 - (a + b)*d), ((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - 2)/((a + b)*d*cosh(d*x + c)^2 + 2*(a + b)*d*cosh(d*x + c)*sinh(d*x + c) + (a + b)*d*sinh(d*x + c)^2 - (a + b)*d)]","B",0
31,1,1881,0,0.464185," ","integrate(csch(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \sinh\left(d x + c\right)^{3} - {\left(\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} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) - 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} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 2 \, {\left(a + b\right)} \cosh\left(d x + c\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \sinh\left(d x + c\right)^{3} + 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} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, b}\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} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 2 \, {\left(a + b\right)} \cosh\left(d x + c\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\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)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/2*(2*(a + b)*cosh(d*x + c)^3 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a + b)*sinh(d*x + c)^3 - (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)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*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) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 2*(a + b)*cosh(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)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((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(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^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^4 - 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d + 4*((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 - (a^2 + 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -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*(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)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/b) - 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)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 2*(a + b)*cosh(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)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((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(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^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^4 - 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d + 4*((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 - (a^2 + 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
32,1,1753,0,0.523890," ","integrate(csch(d*x+c)^4/(a+b*sech(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 \, a \cosh\left(d x + c\right)^{2} + 24 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a \cosh\left(d x + c\right)^{6} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a \sinh\left(d x + c\right)^{6} - 3 \, a \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a \cosh\left(d x + c\right)^{5} - 2 \, a \cosh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - a\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 48 \, {\left(b \cosh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 8 \, a + 4 \, b}{6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{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 \, a \cosh\left(d x + c\right)^{2} + 12 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a \cosh\left(d x + c\right)^{6} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a \sinh\left(d x + c\right)^{6} - 3 \, a \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a \cosh\left(d x + c\right)^{5} - 2 \, a \cosh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - a\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 24 \, {\left(b \cosh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, a + 2 \, b}{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\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*cosh(d*x + c)^2 + 24*(3*b*cosh(d*x + c)^2 + a)*sinh(d*x + c)^2 - 3*(a*cosh(d*x + c)^6 + 6*a*cosh(d*x + c)*sinh(d*x + c)^5 + a*sinh(d*x + c)^6 - 3*a*cosh(d*x + c)^4 + 3*(5*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^4 + 4*(5*a*cosh(d*x + c)^3 - 3*a*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a*cosh(d*x + c)^2 + 3*(5*a*cosh(d*x + c)^4 - 6*a*cosh(d*x + c)^2 + a)*sinh(d*x + c)^2 + 6*(a*cosh(d*x + c)^5 - 2*a*cosh(d*x + c)^3 + a*cosh(d*x + c))*sinh(d*x + c) - a)*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 48*(b*cosh(d*x + c)^3 + a*cosh(d*x + c))*sinh(d*x + c) - 8*a + 4*b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^6 - 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 4*(5*(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))*sinh(d*x + c)^3 + 3*(5*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 - 6*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d + 6*((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^5 - 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -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*cosh(d*x + c)^2 + 12*(3*b*cosh(d*x + c)^2 + a)*sinh(d*x + c)^2 + 3*(a*cosh(d*x + c)^6 + 6*a*cosh(d*x + c)*sinh(d*x + c)^5 + a*sinh(d*x + c)^6 - 3*a*cosh(d*x + c)^4 + 3*(5*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^4 + 4*(5*a*cosh(d*x + c)^3 - 3*a*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a*cosh(d*x + c)^2 + 3*(5*a*cosh(d*x + c)^4 - 6*a*cosh(d*x + c)^2 + a)*sinh(d*x + c)^2 + 6*(a*cosh(d*x + c)^5 - 2*a*cosh(d*x + c)^3 + a*cosh(d*x + c))*sinh(d*x + c) - a)*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 24*(b*cosh(d*x + c)^3 + a*cosh(d*x + c))*sinh(d*x + c) - 4*a + 2*b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^6 - 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 4*(5*(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))*sinh(d*x + c)^3 + 3*(5*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^4 - 6*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d)*sinh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d + 6*((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^5 - 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
33,1,5169,0,0.561648," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3} - 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} - 64 \, a^{2} b - 64 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x - 270 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, a^{3} \cosh\left(d x + c\right)^{5} - 90 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 16 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{2} b + 48 \, a b^{2} + 32 \, b^{3} + 12 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x - 7 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{3} \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x + 240 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{3} \cosh\left(d x + c\right)^{9} - 180 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 80 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} + 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 120 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 6 \, a^{2} b + 3 \, {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 48 \, {\left({\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\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)^{3} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 24 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(a^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} d \sinh\left(d x + c\right)^{8} + a^{5} d \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, a^{5} d \cosh\left(d x + c\right)^{4} + a^{5} d + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{5} + a^{5} d \cosh\left(d x + c\right) + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{6} + 3 \, a^{5} d \cosh\left(d x + c\right)^{2} + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{5} d \cosh\left(d x + c\right)^{7} + a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3} - 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} - 64 \, a^{2} b - 64 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x - 270 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, a^{3} \cosh\left(d x + c\right)^{5} - 90 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 16 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{2} b + 48 \, a b^{2} + 32 \, b^{3} + 12 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x - 7 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{3} \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x + 240 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{3} \cosh\left(d x + c\right)^{9} - 180 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 80 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} + 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 120 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 6 \, a^{2} b + 3 \, {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 96 \, {\left({\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 4 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\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)^{3} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(15 \, a^{3} + 64 \, a^{2} b + 64 \, a b^{2} - 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 24 \, {\left(4 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(a^{3} + 10 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{3} + 128 \, a^{2} b + 128 \, a b^{2} + 24 \, {\left(a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(a^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} d \sinh\left(d x + c\right)^{8} + a^{5} d \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, a^{5} d \cosh\left(d x + c\right)^{4} + a^{5} d + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{5} + a^{5} d \cosh\left(d x + c\right) + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, a^{5} d \cosh\left(d x + c\right)^{6} + 3 \, a^{5} d \cosh\left(d x + c\right)^{2} + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{5} d \cosh\left(d x + c\right)^{7} + a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/64*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 - 6*(a^3 + 2*a^2*b)*cosh(d*x + c)^10 + 6*(11*a^3*cosh(d*x + c)^2 - a^3 - 2*a^2*b)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 - 3*(a^3 + 2*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 - (15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^8 + (495*a^3*cosh(d*x + c)^4 - 15*a^3 - 64*a^2*b - 64*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x - 270*(a^3 + 2*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*a^3*cosh(d*x + c)^5 - 90*(a^3 + 2*a^2*b)*cosh(d*x + c)^3 - (15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 16*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^6 + 4*(231*a^3*cosh(d*x + c)^6 - 315*(a^3 + 2*a^2*b)*cosh(d*x + c)^4 + 16*a^2*b + 48*a*b^2 + 32*b^3 + 12*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x - 7*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*a^3*cosh(d*x + c)^7 - 189*(a^3 + 2*a^2*b)*cosh(d*x + c)^5 - 7*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 12*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^4 + (495*a^3*cosh(d*x + c)^8 - 1260*(a^3 + 2*a^2*b)*cosh(d*x + c)^6 - 70*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^4 + 15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x + 240*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*a^3*cosh(d*x + c)^9 - 180*(a^3 + 2*a^2*b)*cosh(d*x + c)^7 - 14*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^5 + 80*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 + 6*(a^3 + 2*a^2*b)*cosh(d*x + c)^2 + 2*(33*a^3*cosh(d*x + c)^10 - 135*(a^3 + 2*a^2*b)*cosh(d*x + c)^8 - 14*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^6 + 120*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^4 + 3*a^3 + 6*a^2*b + 3*(15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 48*((a^2 + 2*a*b)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b)*sinh(d*x + c)^8 + 2*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^6 + 2*(14*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 3*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^2 + 2*a*b)*cosh(d*x + c)^4 + (70*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 30*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^4 + 4*(14*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 10*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 15*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 3*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^5 + (a^2 + 2*a*b)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(3*a^3*cosh(d*x + c)^11 - 15*(a^3 + 2*a^2*b)*cosh(d*x + c)^9 - 2*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^7 + 24*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^5 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^8 + 8*a^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*d*sinh(d*x + c)^8 + a^5*d*cosh(d*x + c)^4 + 2*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + 2*(14*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^6 + 4*(14*a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (70*a^5*d*cosh(d*x + c)^4 + a^5*d + 30*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a^5*d*cosh(d*x + c)^5 + a^5*d*cosh(d*x + c) + 10*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 2*(14*a^5*d*cosh(d*x + c)^6 + 3*a^5*d*cosh(d*x + c)^2 + 15*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 4*(2*a^5*d*cosh(d*x + c)^7 + a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5)*sinh(d*x + c)), 1/64*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 - 6*(a^3 + 2*a^2*b)*cosh(d*x + c)^10 + 6*(11*a^3*cosh(d*x + c)^2 - a^3 - 2*a^2*b)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 - 3*(a^3 + 2*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 - (15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^8 + (495*a^3*cosh(d*x + c)^4 - 15*a^3 - 64*a^2*b - 64*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x - 270*(a^3 + 2*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*a^3*cosh(d*x + c)^5 - 90*(a^3 + 2*a^2*b)*cosh(d*x + c)^3 - (15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 16*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^6 + 4*(231*a^3*cosh(d*x + c)^6 - 315*(a^3 + 2*a^2*b)*cosh(d*x + c)^4 + 16*a^2*b + 48*a*b^2 + 32*b^3 + 12*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x - 7*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*a^3*cosh(d*x + c)^7 - 189*(a^3 + 2*a^2*b)*cosh(d*x + c)^5 - 7*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 12*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^4 + (495*a^3*cosh(d*x + c)^8 - 1260*(a^3 + 2*a^2*b)*cosh(d*x + c)^6 - 70*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^4 + 15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x + 240*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*a^3*cosh(d*x + c)^9 - 180*(a^3 + 2*a^2*b)*cosh(d*x + c)^7 - 14*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^5 + 80*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 + 6*(a^3 + 2*a^2*b)*cosh(d*x + c)^2 + 2*(33*a^3*cosh(d*x + c)^10 - 135*(a^3 + 2*a^2*b)*cosh(d*x + c)^8 - 14*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^6 + 120*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^4 + 3*a^3 + 6*a^2*b + 3*(15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 96*((a^2 + 2*a*b)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b)*sinh(d*x + c)^8 + 2*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^6 + 2*(14*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 3*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^2 + 2*a*b)*cosh(d*x + c)^4 + (70*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 30*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^4 + 4*(14*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 10*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 15*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 3*(a^2 + 4*a*b + 4*b^2)*cosh(d*x + c)^5 + (a^2 + 2*a*b)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(3*a^3*cosh(d*x + c)^11 - 15*(a^3 + 2*a^2*b)*cosh(d*x + c)^9 - 2*(15*a^3 + 64*a^2*b + 64*a*b^2 - 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^7 + 24*(4*a^2*b + 12*a*b^2 + 8*b^3 + 3*(a^3 + 10*a^2*b + 24*a*b^2 + 16*b^3)*d*x)*cosh(d*x + c)^5 + (15*a^3 + 128*a^2*b + 128*a*b^2 + 24*(a^3 + 8*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^8 + 8*a^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*d*sinh(d*x + c)^8 + a^5*d*cosh(d*x + c)^4 + 2*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + 2*(14*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^6 + 4*(14*a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (70*a^5*d*cosh(d*x + c)^4 + a^5*d + 30*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a^5*d*cosh(d*x + c)^5 + a^5*d*cosh(d*x + c) + 10*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 2*(14*a^5*d*cosh(d*x + c)^6 + 3*a^5*d*cosh(d*x + c)^2 + 15*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 4*(2*a^5*d*cosh(d*x + c)^7 + a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5)*sinh(d*x + c))]","B",0
34,1,3804,0,0.485576," ","integrate(sinh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{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} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, a^{2} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} - 20 \, a b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{2} \cosh\left(d x + c\right)^{4} - 14 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} - 66 \, a b - 60 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} - 66 \, a b - 60 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, a^{2} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, a^{2} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} - 20 \, a b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 22 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(a^{4} d \cosh\left(d x + c\right)^{7} + 7 \, a^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{4} d \sinh\left(d x + c\right)^{7} + a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{4} d \cosh\left(d x + c\right)^{4} + a^{4} d + 20 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, a^{4} d \cosh\left(d x + c\right)^{5} + 3 \, a^{4} d \cosh\left(d x + c\right) + 20 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, a^{4} d \cosh\left(d x + c\right)^{6} + 3 \, a^{4} d \cosh\left(d x + c\right)^{2} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}, \frac{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} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, a^{2} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} - 20 \, a b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{2} \cosh\left(d x + c\right)^{4} - 14 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} - 66 \, a b - 60 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} - 66 \, a b - 60 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, a^{2} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, a^{2} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} - 20 \, a b\right)} \sinh\left(d x + c\right)^{2} - 12 \, {\left({\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 22 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 12 \, {\left({\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 22 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(13 \, a^{2} + 66 \, a b + 60 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} + 20 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(a^{4} d \cosh\left(d x + c\right)^{7} + 7 \, a^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{4} d \sinh\left(d x + c\right)^{7} + a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{4} d \cosh\left(d x + c\right)^{4} + a^{4} d + 20 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, a^{4} d \cosh\left(d x + c\right)^{5} + 3 \, a^{4} d \cosh\left(d x + c\right) + 20 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, a^{4} d \cosh\left(d x + c\right)^{6} + 3 \, a^{4} d \cosh\left(d x + c\right)^{2} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*(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 - (7*a^2 + 20*a*b)*cosh(d*x + c)^8 + (45*a^2*cosh(d*x + c)^2 - 7*a^2 - 20*a*b)*sinh(d*x + c)^8 + 8*(15*a^2*cosh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^6 + 2*(105*a^2*cosh(d*x + c)^4 - 14*(7*a^2 + 20*a*b)*cosh(d*x + c)^2 - 13*a^2 - 66*a*b - 60*b^2)*sinh(d*x + c)^6 + 4*(63*a^2*cosh(d*x + c)^5 - 14*(7*a^2 + 20*a*b)*cosh(d*x + c)^3 - 3*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^4 + 2*(105*a^2*cosh(d*x + c)^6 - 35*(7*a^2 + 20*a*b)*cosh(d*x + c)^4 - 15*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^2 - 13*a^2 - 66*a*b - 60*b^2)*sinh(d*x + c)^4 + 8*(15*a^2*cosh(d*x + c)^7 - 7*(7*a^2 + 20*a*b)*cosh(d*x + c)^5 - 5*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^3 - (13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c)^2 + (45*a^2*cosh(d*x + c)^8 - 28*(7*a^2 + 20*a*b)*cosh(d*x + c)^6 - 30*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^4 - 12*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^2 - 7*a^2 - 20*a*b)*sinh(d*x + c)^2 + 6*((3*a^2 + 5*a*b)*cosh(d*x + c)^7 + 7*(3*a^2 + 5*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + 5*a*b)*sinh(d*x + c)^7 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^2 + 6*a^2 + 22*a*b + 20*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + 5*a*b)*cosh(d*x + c)^3 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + 5*a*b)*cosh(d*x + c)^3 + (35*(3*a^2 + 5*a*b)*cosh(d*x + c)^4 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^2 + 3*a^2 + 5*a*b)*sinh(d*x + c)^3 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^5 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + 5*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + a^2 + 2*(5*a^2*cosh(d*x + c)^9 - 4*(7*a^2 + 20*a*b)*cosh(d*x + c)^7 - 6*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^5 - 4*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^4*d*cosh(d*x + c)^7 + 7*a^4*d*cosh(d*x + c)*sinh(d*x + c)^6 + a^4*d*sinh(d*x + c)^7 + a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^5 + (21*a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d)*sinh(d*x + c)^5 + 5*(7*a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^4*d*cosh(d*x + c)^4 + a^4*d + 20*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*a^4*d*cosh(d*x + c)^5 + 3*a^4*d*cosh(d*x + c) + 20*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (7*a^4*d*cosh(d*x + c)^6 + 3*a^4*d*cosh(d*x + c)^2 + 10*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)), 1/24*(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 - (7*a^2 + 20*a*b)*cosh(d*x + c)^8 + (45*a^2*cosh(d*x + c)^2 - 7*a^2 - 20*a*b)*sinh(d*x + c)^8 + 8*(15*a^2*cosh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^6 + 2*(105*a^2*cosh(d*x + c)^4 - 14*(7*a^2 + 20*a*b)*cosh(d*x + c)^2 - 13*a^2 - 66*a*b - 60*b^2)*sinh(d*x + c)^6 + 4*(63*a^2*cosh(d*x + c)^5 - 14*(7*a^2 + 20*a*b)*cosh(d*x + c)^3 - 3*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^4 + 2*(105*a^2*cosh(d*x + c)^6 - 35*(7*a^2 + 20*a*b)*cosh(d*x + c)^4 - 15*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^2 - 13*a^2 - 66*a*b - 60*b^2)*sinh(d*x + c)^4 + 8*(15*a^2*cosh(d*x + c)^7 - 7*(7*a^2 + 20*a*b)*cosh(d*x + c)^5 - 5*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^3 - (13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c)^2 + (45*a^2*cosh(d*x + c)^8 - 28*(7*a^2 + 20*a*b)*cosh(d*x + c)^6 - 30*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^4 - 12*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^2 - 7*a^2 - 20*a*b)*sinh(d*x + c)^2 - 12*((3*a^2 + 5*a*b)*cosh(d*x + c)^7 + 7*(3*a^2 + 5*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + 5*a*b)*sinh(d*x + c)^7 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^2 + 6*a^2 + 22*a*b + 20*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + 5*a*b)*cosh(d*x + c)^3 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + 5*a*b)*cosh(d*x + c)^3 + (35*(3*a^2 + 5*a*b)*cosh(d*x + c)^4 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^2 + 3*a^2 + 5*a*b)*sinh(d*x + c)^3 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^5 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + 5*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) + 12*((3*a^2 + 5*a*b)*cosh(d*x + c)^7 + 7*(3*a^2 + 5*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + 5*a*b)*sinh(d*x + c)^7 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^2 + 6*a^2 + 22*a*b + 20*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + 5*a*b)*cosh(d*x + c)^3 + 2*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + 5*a*b)*cosh(d*x + c)^3 + (35*(3*a^2 + 5*a*b)*cosh(d*x + c)^4 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^2 + 3*a^2 + 5*a*b)*sinh(d*x + c)^3 + (21*(3*a^2 + 5*a*b)*cosh(d*x + c)^5 + 20*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + 5*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + 5*a*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + a^2 + 2*(5*a^2*cosh(d*x + c)^9 - 4*(7*a^2 + 20*a*b)*cosh(d*x + c)^7 - 6*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^5 - 4*(13*a^2 + 66*a*b + 60*b^2)*cosh(d*x + c)^3 - (7*a^2 + 20*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^4*d*cosh(d*x + c)^7 + 7*a^4*d*cosh(d*x + c)*sinh(d*x + c)^6 + a^4*d*sinh(d*x + c)^7 + a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^5 + (21*a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d)*sinh(d*x + c)^5 + 5*(7*a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^4*d*cosh(d*x + c)^4 + a^4*d + 20*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*a^4*d*cosh(d*x + c)^5 + 3*a^4*d*cosh(d*x + c) + 20*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (7*a^4*d*cosh(d*x + c)^6 + 3*a^4*d*cosh(d*x + c)^2 + 10*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^4)*sinh(d*x + c))]","B",0
35,1,2925,0,0.501564," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x - 15 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 4 \, a b\right)} d x - 24 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 20 \, a b + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - a^{2} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{4} d \sinh\left(d x + c\right)^{6} + a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} d \cosh\left(d x + c\right)^{4} + a^{4} d + 12 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{4} d \cosh\left(d x + c\right)^{5} + a^{4} d \cosh\left(d x + c\right) + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x - 15 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a^{2} \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 4 \, a b\right)} d x - 24 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 6 \, a b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 20 \, a b + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - a^{2} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} + 6 \, a b + 8 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} + 4 \, a b\right)} d x + a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{4} d \sinh\left(d x + c\right)^{6} + a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} d \cosh\left(d x + c\right)^{4} + a^{4} d + 12 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{4} d \cosh\left(d x + c\right)^{5} + a^{4} d \cosh\left(d x + c\right) + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/8*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 - 2*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^6 + 2*(14*a^2*cosh(d*x + c)^2 - 2*(a^2 + 4*a*b)*d*x + a^2 + 2*a*b)*sinh(d*x + c)^6 + 4*(14*a^2*cosh(d*x + c)^3 - 3*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 - 4*(a^2 + 6*a*b + 8*b^2)*d*x - 15*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 - 5*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^3 - 4*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^2 + 4*a*b)*d*x + a^2 + 6*a*b)*cosh(d*x + c)^2 + 2*(14*a^2*cosh(d*x + c)^6 - 15*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^4 - 2*(a^2 + 4*a*b)*d*x - 24*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b)*sinh(d*x + c)^2 + 2*((3*a^2 + 4*a*b)*cosh(d*x + c)^6 + 6*(3*a^2 + 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^2 + 4*a*b)*sinh(d*x + c)^6 + 2*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^4 + (15*(3*a^2 + 4*a*b)*cosh(d*x + c)^2 + 6*a^2 + 20*a*b + 16*b^2)*sinh(d*x + c)^4 + 4*(5*(3*a^2 + 4*a*b)*cosh(d*x + c)^3 + 2*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 4*a*b)*cosh(d*x + c)^2 + (15*(3*a^2 + 4*a*b)*cosh(d*x + c)^4 + 12*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^2 + 3*a^2 + 4*a*b)*sinh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b)*cosh(d*x + c)^5 + 4*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^3 + (3*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - a^2 + 4*(2*a^2*cosh(d*x + c)^7 - 3*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^5 - 8*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^3 - (2*(a^2 + 4*a*b)*d*x + a^2 + 6*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^4*d*cosh(d*x + c)^6 + 6*a^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a^4*d*sinh(d*x + c)^6 + a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^4 + (15*a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d)*sinh(d*x + c)^4 + 4*(5*a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4*d*cosh(d*x + c)^4 + a^4*d + 12*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*a^4*d*cosh(d*x + c)^5 + a^4*d*cosh(d*x + c) + 4*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)), 1/8*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 - 2*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^6 + 2*(14*a^2*cosh(d*x + c)^2 - 2*(a^2 + 4*a*b)*d*x + a^2 + 2*a*b)*sinh(d*x + c)^6 + 4*(14*a^2*cosh(d*x + c)^3 - 3*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 - 4*(a^2 + 6*a*b + 8*b^2)*d*x - 15*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 - 5*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^3 - 4*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^2 + 4*a*b)*d*x + a^2 + 6*a*b)*cosh(d*x + c)^2 + 2*(14*a^2*cosh(d*x + c)^6 - 15*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^4 - 2*(a^2 + 4*a*b)*d*x - 24*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^2 - a^2 - 6*a*b)*sinh(d*x + c)^2 + 4*((3*a^2 + 4*a*b)*cosh(d*x + c)^6 + 6*(3*a^2 + 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^2 + 4*a*b)*sinh(d*x + c)^6 + 2*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^4 + (15*(3*a^2 + 4*a*b)*cosh(d*x + c)^2 + 6*a^2 + 20*a*b + 16*b^2)*sinh(d*x + c)^4 + 4*(5*(3*a^2 + 4*a*b)*cosh(d*x + c)^3 + 2*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 4*a*b)*cosh(d*x + c)^2 + (15*(3*a^2 + 4*a*b)*cosh(d*x + c)^4 + 12*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^2 + 3*a^2 + 4*a*b)*sinh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b)*cosh(d*x + c)^5 + 4*(3*a^2 + 10*a*b + 8*b^2)*cosh(d*x + c)^3 + (3*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - a^2 + 4*(2*a^2*cosh(d*x + c)^7 - 3*(2*(a^2 + 4*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^5 - 8*((a^2 + 6*a*b + 8*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^3 - (2*(a^2 + 4*a*b)*d*x + a^2 + 6*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^4*d*cosh(d*x + c)^6 + 6*a^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a^4*d*sinh(d*x + c)^6 + a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^4 + (15*a^4*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b)*d)*sinh(d*x + c)^4 + 4*(5*a^4*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4*d*cosh(d*x + c)^4 + a^4*d + 12*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*a^4*d*cosh(d*x + c)^5 + a^4*d*cosh(d*x + c) + 4*(a^4 + 2*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c))]","B",0
36,1,1780,0,0.544445," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a \cosh\left(d x + c\right)^{6} + 12 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, a \sinh\left(d x + c\right)^{6} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, a \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)^{3} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, a \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} + 3 \, {\left(a \cosh\left(d x + c\right)^{5} + 5 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{5} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \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} + a \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 12 \, {\left(a \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) + 2 \, a}{4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{5} + 5 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} d \sinh\left(d x + c\right)^{5} + a^{3} d \cosh\left(d x + c\right) + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{4} + a^{3} d + 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a \cosh\left(d x + c\right)^{6} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a \sinh\left(d x + c\right)^{6} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a \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)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a \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} + 3 \, {\left(a \cosh\left(d x + c\right)^{5} + 5 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{5} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \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} + a \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 3 \, {\left(a \cosh\left(d x + c\right)^{5} + 5 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{5} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \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} + a \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 6 \, {\left(a \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 \, {\left(a^{3} d \cosh\left(d x + c\right)^{5} + 5 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} d \sinh\left(d x + c\right)^{5} + a^{3} d \cosh\left(d x + c\right) + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{3} d \cosh\left(d x + c\right)^{4} + a^{3} d + 6 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(2*a*cosh(d*x + c)^6 + 12*a*cosh(d*x + c)*sinh(d*x + c)^5 + 2*a*sinh(d*x + c)^6 + 6*(a + 2*b)*cosh(d*x + c)^4 + 6*(5*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^4 + 8*(5*a*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(a + 2*b)*cosh(d*x + c)^2 + 6*(5*a*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 3*(a*cosh(d*x + c)^5 + 5*a*cosh(d*x + c)*sinh(d*x + c)^4 + a*sinh(d*x + c)^5 + 2*(a + 2*b)*cosh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + a*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 12*(a*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) + 2*a)/(a^3*d*cosh(d*x + c)^5 + 5*a^3*d*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*d*sinh(d*x + c)^5 + a^3*d*cosh(d*x + c) + 2*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^3 + 2*(5*a^3*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b)*d)*sinh(d*x + c)^3 + 2*(5*a^3*d*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^3*d*cosh(d*x + c)^4 + a^3*d + 6*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/2*(a*cosh(d*x + c)^6 + 6*a*cosh(d*x + c)*sinh(d*x + c)^5 + a*sinh(d*x + c)^6 + 3*(a + 2*b)*cosh(d*x + c)^4 + 3*(5*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^4 + 4*(5*a*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c)^2 + 3*(5*a*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 3*(a*cosh(d*x + c)^5 + 5*a*cosh(d*x + c)*sinh(d*x + c)^4 + a*sinh(d*x + c)^5 + 2*(a + 2*b)*cosh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + a*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - 3*(a*cosh(d*x + c)^5 + 5*a*cosh(d*x + c)*sinh(d*x + c)^4 + a*sinh(d*x + c)^5 + 2*(a + 2*b)*cosh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + a*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 6*(a*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)/(a^3*d*cosh(d*x + c)^5 + 5*a^3*d*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*d*sinh(d*x + c)^5 + a^3*d*cosh(d*x + c) + 2*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^3 + 2*(5*a^3*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b)*d)*sinh(d*x + c)^3 + 2*(5*a^3*d*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^3*d*cosh(d*x + c)^4 + a^3*d + 6*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
37,1,2376,0,0.580485," ","integrate(csch(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + a b + 4 \, {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 4 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\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^{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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + a b + 4 \, {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + a b + 4 \, {\left({\left(3 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(a b + b^{2}\right)} \cosh\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\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^{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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a*b + b^2)*cosh(d*x + c)^3 + 12*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a*b + b^2)*sinh(d*x + c)^3 - ((3*a^2 + a*b)*cosh(d*x + c)^4 + 4*(3*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + a*b)*sinh(d*x + c)^4 + 2*(3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + a*b)*cosh(d*x + c)^2 + 3*a^2 + 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + a*b + 4*((3*a^2 + a*b)*cosh(d*x + c)^3 + (3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(a*b + b^2)*cosh(d*x + c) + 4*(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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 4*(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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(3*(a*b + b^2)*cosh(d*x + c)^2 + a*b + b^2)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a*b + b^2)*cosh(d*x + c)^3 + 6*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a*b + b^2)*sinh(d*x + c)^3 + ((3*a^2 + a*b)*cosh(d*x + c)^4 + 4*(3*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + a*b)*sinh(d*x + c)^4 + 2*(3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + a*b)*cosh(d*x + c)^2 + 3*a^2 + 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + a*b + 4*((3*a^2 + a*b)*cosh(d*x + c)^3 + (3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - ((3*a^2 + a*b)*cosh(d*x + c)^4 + 4*(3*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + a*b)*sinh(d*x + c)^4 + 2*(3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + a*b)*cosh(d*x + c)^2 + 3*a^2 + 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + a*b + 4*((3*a^2 + a*b)*cosh(d*x + c)^3 + (3*a^2 + 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 2*(a*b + b^2)*cosh(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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*(a*b + b^2)*cosh(d*x + c)^2 + a*b + b^2)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
38,1,2407,0,0.622878," ","integrate(csch(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(3 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - 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} + {\left(a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} \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(15 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\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)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, a^{2} - 4 \, a b + 16 \, {\left({\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 4 \, a b - 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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - 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} + {\left(a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} \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(15 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\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)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, a^{2} - 2 \, a b + 8 \, {\left({\left(2 \, a^{2} + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 4 \, a b - 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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^4 + 16*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(2*a^2 + a*b + 2*b^2)*sinh(d*x + c)^4 + 8*(2*a^2 + 4*a*b - b^2)*cosh(d*x + c)^2 + 8*(3*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^2 + 2*a^2 + 4*a*b - b^2)*sinh(d*x + c)^2 - 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 + (a^2 + 4*a*b)*cosh(d*x + c)^4 + (15*a^2*cosh(d*x + c)^2 + a^2 + 4*a*b)*sinh(d*x + c)^4 + 4*(5*a^2*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 + (15*a^2*cosh(d*x + c)^4 + 6*(a^2 + 4*a*b)*cosh(d*x + c)^2 - a^2 - 4*a*b)*sinh(d*x + c)^2 - a^2 + 2*(3*a^2*cosh(d*x + c)^5 + 2*(a^2 + 4*a*b)*cosh(d*x + c)^3 - (a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*a^2 - 4*a*b + 16*((2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^3 + (2*a^2 + 4*a*b - 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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d)*sinh(d*x + c)^4 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c)^2 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c)^3 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^4 + 8*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(2*a^2 + a*b + 2*b^2)*sinh(d*x + c)^4 + 4*(2*a^2 + 4*a*b - b^2)*cosh(d*x + c)^2 + 4*(3*(2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^2 + 2*a^2 + 4*a*b - b^2)*sinh(d*x + c)^2 - 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 + (a^2 + 4*a*b)*cosh(d*x + c)^4 + (15*a^2*cosh(d*x + c)^2 + a^2 + 4*a*b)*sinh(d*x + c)^4 + 4*(5*a^2*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 + (15*a^2*cosh(d*x + c)^4 + 6*(a^2 + 4*a*b)*cosh(d*x + c)^2 - a^2 - 4*a*b)*sinh(d*x + c)^2 - a^2 + 2*(3*a^2*cosh(d*x + c)^5 + 2*(a^2 + 4*a*b)*cosh(d*x + c)^3 - (a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*a^2 - 2*a*b + 8*((2*a^2 + a*b + 2*b^2)*cosh(d*x + c)^3 + (2*a^2 + 4*a*b - 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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d)*sinh(d*x + c)^4 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c)^2 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*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 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c)^3 - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
39,1,6878,0,0.733111," ","integrate(csch(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 11 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - a b + 8 \, {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, 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{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 3 \, a b + 8 \, {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b - 3 \, 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 - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 3 \, a b + 8 \, {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b - 3 \, 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 - 3 \, 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} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\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)^{8} + 8 \, {\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)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\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^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\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^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\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^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d\right)} \sinh\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)^{2} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\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^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\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 + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 11 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - a b + 8 \, {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, 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(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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 11 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - a b + 8 \, {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} + 11 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, 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(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 3 \, a b + 8 \, {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b - 3 \, 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 - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a b - 3 \, 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} - 3 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b - 3 \, 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 - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 3 \, a b + 8 \, {\left({\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b - 3 \, 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 - 3 \, 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} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\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)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\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^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\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^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\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^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d\right)} \sinh\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)^{2} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\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^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\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 + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a^2 - b^2)*cosh(d*x + c)^7 + 28*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2 - b^2)*sinh(d*x + c)^7 + 4*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^5 + 4*(21*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^5 + 20*(7*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 + 4*(35*(a^2 - b^2)*cosh(d*x + c)^4 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^3 + 4*(21*(a^2 - b^2)*cosh(d*x + c)^5 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^2 - a*b)*cosh(d*x + c)^8 + 8*(3*a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 - a*b)*sinh(d*x + c)^8 + 4*(3*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^3 + 3*(3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 - a*b)*cosh(d*x + c)^4 + 30*(3*a*b - b^2)*cosh(d*x + c)^2 - 3*a^2 - 11*a*b + 4*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^5 + 10*(3*a*b - b^2)*cosh(d*x + c)^3 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^6 + 15*(3*a*b - b^2)*cosh(d*x + c)^4 - 3*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^2 + 3*a^2 - a*b + 8*((3*a^2 - a*b)*cosh(d*x + c)^7 + 3*(3*a*b - b^2)*cosh(d*x + c)^5 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^3 + (3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(a^2 - b^2)*cosh(d*x + c) - 2*((a^2 - 3*a*b)*cosh(d*x + c)^8 + 8*(a^2 - 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 - 3*a*b)*sinh(d*x + c)^8 + 4*(a*b - 3*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^3 + 3*(a*b - 3*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 - 3*a*b)*cosh(d*x + c)^4 + 30*(a*b - 3*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^5 + 10*(a*b - 3*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 - 3*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^6 + 15*(a*b - 3*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 - 3*a*b + 8*((a^2 - 3*a*b)*cosh(d*x + c)^7 + 3*(a*b - 3*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 + (a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*((a^2 - 3*a*b)*cosh(d*x + c)^8 + 8*(a^2 - 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 - 3*a*b)*sinh(d*x + c)^8 + 4*(a*b - 3*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^3 + 3*(a*b - 3*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 - 3*a*b)*cosh(d*x + c)^4 + 30*(a*b - 3*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^5 + 10*(a*b - 3*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 - 3*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^6 + 15*(a*b - 3*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 - 3*a*b + 8*((a^2 - 3*a*b)*cosh(d*x + c)^7 + 3*(a*b - 3*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 + (a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(7*(a^2 - b^2)*cosh(d*x + c)^6 + 5*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^8 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d)*sinh(d*x + c)^6 - 2*(a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 30*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d)*sinh(d*x + c)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^5 + 10*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^3 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^6 + 15*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^4 - 3*(a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^7 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^5 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a^2 - b^2)*cosh(d*x + c)^7 + 14*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2 - b^2)*sinh(d*x + c)^7 + 2*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^5 + 2*(21*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^5 + 10*(7*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 + 2*(35*(a^2 - b^2)*cosh(d*x + c)^4 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^3 + 2*(21*(a^2 - b^2)*cosh(d*x + c)^5 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - ((3*a^2 - a*b)*cosh(d*x + c)^8 + 8*(3*a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 - a*b)*sinh(d*x + c)^8 + 4*(3*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^3 + 3*(3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 - a*b)*cosh(d*x + c)^4 + 30*(3*a*b - b^2)*cosh(d*x + c)^2 - 3*a^2 - 11*a*b + 4*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^5 + 10*(3*a*b - b^2)*cosh(d*x + c)^3 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^6 + 15*(3*a*b - b^2)*cosh(d*x + c)^4 - 3*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^2 + 3*a^2 - a*b + 8*((3*a^2 - a*b)*cosh(d*x + c)^7 + 3*(3*a*b - b^2)*cosh(d*x + c)^5 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^3 + (3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) + ((3*a^2 - a*b)*cosh(d*x + c)^8 + 8*(3*a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 - a*b)*sinh(d*x + c)^8 + 4*(3*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^3 + 3*(3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 - a*b)*cosh(d*x + c)^4 + 30*(3*a*b - b^2)*cosh(d*x + c)^2 - 3*a^2 - 11*a*b + 4*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 - a*b)*cosh(d*x + c)^5 + 10*(3*a*b - b^2)*cosh(d*x + c)^3 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 - a*b)*cosh(d*x + c)^6 + 15*(3*a*b - b^2)*cosh(d*x + c)^4 - 3*(3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^2 + 3*a*b - b^2)*sinh(d*x + c)^2 + 3*a^2 - a*b + 8*((3*a^2 - a*b)*cosh(d*x + c)^7 + 3*(3*a*b - b^2)*cosh(d*x + c)^5 - (3*a^2 + 11*a*b - 4*b^2)*cosh(d*x + c)^3 + (3*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 2*(a^2 - b^2)*cosh(d*x + c) - ((a^2 - 3*a*b)*cosh(d*x + c)^8 + 8*(a^2 - 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 - 3*a*b)*sinh(d*x + c)^8 + 4*(a*b - 3*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^3 + 3*(a*b - 3*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 - 3*a*b)*cosh(d*x + c)^4 + 30*(a*b - 3*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^5 + 10*(a*b - 3*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 - 3*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^6 + 15*(a*b - 3*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 - 3*a*b + 8*((a^2 - 3*a*b)*cosh(d*x + c)^7 + 3*(a*b - 3*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 + (a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^2 - 3*a*b)*cosh(d*x + c)^8 + 8*(a^2 - 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 - 3*a*b)*sinh(d*x + c)^8 + 4*(a*b - 3*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^3 + 3*(a*b - 3*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 - 3*a*b)*cosh(d*x + c)^4 + 30*(a*b - 3*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 - 3*a*b)*cosh(d*x + c)^5 + 10*(a*b - 3*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 - 3*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 - 3*a*b)*cosh(d*x + c)^6 + 15*(a*b - 3*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 + a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 - 3*a*b + 8*((a^2 - 3*a*b)*cosh(d*x + c)^7 + 3*(a*b - 3*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 + (a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(a^2 - b^2)*cosh(d*x + c)^6 + 5*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^8 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d)*sinh(d*x + c)^6 - 2*(a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 30*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d)*sinh(d*x + c)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^5 + 10*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^3 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^6 + 15*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^4 - 3*(a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^7 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^5 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*cosh(d*x + c)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
40,1,6143,0,0.525101," ","integrate(csch(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 48 \, {\left(14 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(105 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 45 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{10} - {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 14 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 16 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, a b + 2 \, {\left(5 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 14 \, a b + 8 \, 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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 16 \, a^{2} + 44 \, a b + 16 \, {\left(6 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\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)^{9} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\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 - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\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 - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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 + 2 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{6 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(14 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(105 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 45 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{10} - {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 14 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 16 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, a b + 2 \, {\left(5 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(3 \, a^{2} - 14 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 16 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 14 \, a b + 8 \, 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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 8 \, a^{2} + 22 \, a b + 8 \, {\left(6 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\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)^{9} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\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 - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\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 - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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 + 2 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/12*(12*(3*a*b - 2*b^2)*cosh(d*x + c)^8 + 96*(3*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(3*a*b - 2*b^2)*sinh(d*x + c)^8 + 24*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^6 + 24*(14*(3*a*b - 2*b^2)*cosh(d*x + c)^2 + 2*a^2 + 3*a*b + 11*b^2)*sinh(d*x + c)^6 + 48*(14*(3*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^4 + 8*(105*(3*a*b - 2*b^2)*cosh(d*x + c)^4 + 45*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^2 + 10*a^2 + 22*a*b - 33*b^2)*sinh(d*x + c)^4 + 32*(21*(3*a*b - 2*b^2)*cosh(d*x + c)^5 + 15*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^3 + (10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(2*a^2 - 9*a*b + 19*b^2)*cosh(d*x + c)^2 + 8*(42*(3*a*b - 2*b^2)*cosh(d*x + c)^6 + 45*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^4 + 6*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^2 + 2*a^2 - 9*a*b + 19*b^2)*sinh(d*x + c)^2 + 3*((3*a^2 - 2*a*b)*cosh(d*x + c)^10 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^9 + (3*a^2 - 2*a*b)*sinh(d*x + c)^10 - (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^8 + (45*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 - 3*a^2 + 14*a*b - 8*b^2)*sinh(d*x + c)^8 + 8*(15*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 - (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^6 + 2*(105*(3*a^2 - 2*a*b)*cosh(d*x + c)^4 - 14*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 16*a*b + 12*b^2)*sinh(d*x + c)^6 + 4*(63*(3*a^2 - 2*a*b)*cosh(d*x + c)^5 - 14*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(105*(3*a^2 - 2*a*b)*cosh(d*x + c)^6 - 35*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^4 - 15*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b - 12*b^2)*sinh(d*x + c)^4 + 8*(15*(3*a^2 - 2*a*b)*cosh(d*x + c)^7 - 7*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^5 - 5*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^3 + (3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^2 + (45*(3*a^2 - 2*a*b)*cosh(d*x + c)^8 - 28*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^6 - 30*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^2 + 3*a^2 - 14*a*b + 8*b^2)*sinh(d*x + c)^2 - 3*a^2 + 2*a*b + 2*(5*(3*a^2 - 2*a*b)*cosh(d*x + c)^9 - 4*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^7 - 6*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^5 + 4*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^3 + (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 16*a^2 + 44*a*b + 16*(6*(3*a*b - 2*b^2)*cosh(d*x + c)^7 + 9*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^5 + 2*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^3 + (2*a^2 - 9*a*b + 19*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)^10 + 10*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^10 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^8 + (45*(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 - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d)*sinh(d*x + c)^8 - 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^6 + 8*(15*(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 - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 - 14*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^2 - (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d)*sinh(d*x + c)^6 + 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^5 - 14*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^3 - 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^6 - 35*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^4 - 15*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^2 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d)*sinh(d*x + c)^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^7 - 7*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^5 - 5*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^3 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^8 - 28*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^6 - 30*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^4 + 12*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^2 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d)*sinh(d*x + c)^2 - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 2*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^9 - 4*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^7 - 6*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^5 + 4*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^3 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/6*(6*(3*a*b - 2*b^2)*cosh(d*x + c)^8 + 48*(3*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(3*a*b - 2*b^2)*sinh(d*x + c)^8 + 12*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^6 + 12*(14*(3*a*b - 2*b^2)*cosh(d*x + c)^2 + 2*a^2 + 3*a*b + 11*b^2)*sinh(d*x + c)^6 + 24*(14*(3*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^4 + 4*(105*(3*a*b - 2*b^2)*cosh(d*x + c)^4 + 45*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^2 + 10*a^2 + 22*a*b - 33*b^2)*sinh(d*x + c)^4 + 16*(21*(3*a*b - 2*b^2)*cosh(d*x + c)^5 + 15*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^3 + (10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^2 - 9*a*b + 19*b^2)*cosh(d*x + c)^2 + 4*(42*(3*a*b - 2*b^2)*cosh(d*x + c)^6 + 45*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^4 + 6*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^2 + 2*a^2 - 9*a*b + 19*b^2)*sinh(d*x + c)^2 + 3*((3*a^2 - 2*a*b)*cosh(d*x + c)^10 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^9 + (3*a^2 - 2*a*b)*sinh(d*x + c)^10 - (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^8 + (45*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 - 3*a^2 + 14*a*b - 8*b^2)*sinh(d*x + c)^8 + 8*(15*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 - (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^6 + 2*(105*(3*a^2 - 2*a*b)*cosh(d*x + c)^4 - 14*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 16*a*b + 12*b^2)*sinh(d*x + c)^6 + 4*(63*(3*a^2 - 2*a*b)*cosh(d*x + c)^5 - 14*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(105*(3*a^2 - 2*a*b)*cosh(d*x + c)^6 - 35*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^4 - 15*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b - 12*b^2)*sinh(d*x + c)^4 + 8*(15*(3*a^2 - 2*a*b)*cosh(d*x + c)^7 - 7*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^5 - 5*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^3 + (3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^2 + (45*(3*a^2 - 2*a*b)*cosh(d*x + c)^8 - 28*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^6 - 30*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^2 + 3*a^2 - 14*a*b + 8*b^2)*sinh(d*x + c)^2 - 3*a^2 + 2*a*b + 2*(5*(3*a^2 - 2*a*b)*cosh(d*x + c)^9 - 4*(3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c)^7 - 6*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^5 + 4*(3*a^2 + 16*a*b - 12*b^2)*cosh(d*x + c)^3 + (3*a^2 - 14*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - 8*a^2 + 22*a*b + 8*(6*(3*a*b - 2*b^2)*cosh(d*x + c)^7 + 9*(2*a^2 + 3*a*b + 11*b^2)*cosh(d*x + c)^5 + 2*(10*a^2 + 22*a*b - 33*b^2)*cosh(d*x + c)^3 + (2*a^2 - 9*a*b + 19*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)^10 + 10*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^10 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^8 + (45*(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 - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d)*sinh(d*x + c)^8 - 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^6 + 8*(15*(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 - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 - 14*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^2 - (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d)*sinh(d*x + c)^6 + 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^5 - 14*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^3 - 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^6 - 35*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^4 - 15*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^2 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d)*sinh(d*x + c)^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^7 - 7*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^5 - 5*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^3 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^8 - 28*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^6 - 30*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^4 + 12*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^2 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d)*sinh(d*x + c)^2 - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 2*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^9 - 4*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c)^7 - 6*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^5 + 4*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*cosh(d*x + c)^3 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
41,1,12353,0,0.637070," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{a^{4} \cosh\left(d x + c\right)^{16} + 16 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a^{4} \sinh\left(d x + c\right)^{16} - 4 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{14} + 4 \, {\left(30 \, a^{4} \cosh\left(d x + c\right)^{2} - a^{4} - 4 \, a^{3} b\right)} \sinh\left(d x + c\right)^{14} + 56 \, {\left(10 \, a^{4} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 2 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(910 \, a^{4} \cosh\left(d x + c\right)^{4} - 13 \, a^{4} - 72 \, a^{3} b - 88 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(546 \, a^{4} \cosh\left(d x + c\right)^{5} - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 4 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2002 \, a^{4} \cosh\left(d x + c\right)^{6} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 24 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x - 33 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(1430 \, a^{4} \cosh\left(d x + c\right)^{7} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} - 55 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 16 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, a^{4} \cosh\left(d x + c\right)^{8} - 6006 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 216 \, a^{3} b + 912 \, a^{2} b^{2} + 1472 \, a b^{3} + 896 \, b^{4} + 24 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x - 90 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, a^{4} \cosh\left(d x + c\right)^{9} - 858 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2002 \, a^{4} \cosh\left(d x + c\right)^{10} - 3003 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} - 462 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(546 \, a^{4} \cosh\left(d x + c\right)^{11} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{9} - 198 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(910 \, a^{4} \cosh\left(d x + c\right)^{12} - 2002 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 420 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 560 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x + 30 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} + 8 \, {\left(70 \, a^{4} \cosh\left(d x + c\right)^{13} - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{11} - 55 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 60 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(30 \, a^{4} \cosh\left(d x + c\right)^{14} - 91 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{12} - 33 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 3 \, {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(10 \, a^{4} + 60 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 33 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} + 200 \, a^{3} b + 496 \, a^{2} b^{2} + 576 \, a b^{3} + 256 \, b^{4} + 180 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3} + 14 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2} + 60 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(2 \, a^{4} \cosh\left(d x + c\right)^{15} - 7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{13} - 3 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(a^{7} d \cosh\left(d x + c\right)^{12} + 12 \, a^{7} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{7} d \sinh\left(d x + c\right)^{12} + a^{7} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{10} + 2 \, {\left(33 \, a^{7} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 2 \, a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, a^{7} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(495 \, a^{7} d \cosh\left(d x + c\right)^{4} + 180 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{7} d \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(231 \, a^{7} d \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{7} d \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(495 \, a^{7} d \cosh\left(d x + c\right)^{8} + a^{7} d + 840 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 60 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{7} d \cosh\left(d x + c\right)^{9} + a^{7} d \cosh\left(d x + c\right) + 120 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, a^{7} d \cosh\left(d x + c\right)^{10} + 3 \, a^{7} d \cosh\left(d x + c\right)^{2} + 90 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{7} d \cosh\left(d x + c\right)^{11} + a^{7} d \cosh\left(d x + c\right)^{3} + 10 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a^{4} \cosh\left(d x + c\right)^{16} + 16 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a^{4} \sinh\left(d x + c\right)^{16} - 4 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{14} + 4 \, {\left(30 \, a^{4} \cosh\left(d x + c\right)^{2} - a^{4} - 4 \, a^{3} b\right)} \sinh\left(d x + c\right)^{14} + 56 \, {\left(10 \, a^{4} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 2 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(910 \, a^{4} \cosh\left(d x + c\right)^{4} - 13 \, a^{4} - 72 \, a^{3} b - 88 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(546 \, a^{4} \cosh\left(d x + c\right)^{5} - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 4 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2002 \, a^{4} \cosh\left(d x + c\right)^{6} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 24 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x - 33 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(1430 \, a^{4} \cosh\left(d x + c\right)^{7} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} - 55 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 16 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, a^{4} \cosh\left(d x + c\right)^{8} - 6006 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 216 \, a^{3} b + 912 \, a^{2} b^{2} + 1472 \, a b^{3} + 896 \, b^{4} + 24 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x - 90 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, a^{4} \cosh\left(d x + c\right)^{9} - 858 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2002 \, a^{4} \cosh\left(d x + c\right)^{10} - 3003 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} - 462 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(546 \, a^{4} \cosh\left(d x + c\right)^{11} - 1001 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{9} - 198 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(910 \, a^{4} \cosh\left(d x + c\right)^{12} - 2002 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 420 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 560 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x + 30 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} + 8 \, {\left(70 \, a^{4} \cosh\left(d x + c\right)^{13} - 182 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{11} - 55 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 60 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(30 \, a^{4} \cosh\left(d x + c\right)^{14} - 91 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{12} - 33 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 3 \, {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left({\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(10 \, a^{4} + 60 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 33 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} + 200 \, a^{3} b + 496 \, a^{2} b^{2} + 576 \, a b^{3} + 256 \, b^{4} + 180 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3} + 14 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2} + 60 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(15 \, a^{4} + 100 \, a^{3} b + 248 \, a^{2} b^{2} + 288 \, a b^{3} + 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{4} + 30 \, a^{3} b + 56 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(5 \, a^{4} + 20 \, a^{3} b + 16 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 8 \, {\left(2 \, a^{4} \cosh\left(d x + c\right)^{15} - 7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{13} - 3 \, {\left(13 \, a^{4} + 72 \, a^{3} b + 88 \, a^{2} b^{2} - 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(9 \, a^{4} + 24 \, a^{3} b - 16 \, a^{2} b^{2} - 32 \, a b^{3} - 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(27 \, a^{3} b + 114 \, a^{2} b^{2} + 184 \, a b^{3} + 112 \, b^{4} + 3 \, {\left(3 \, a^{4} + 44 \, a^{3} b + 152 \, a^{2} b^{2} + 224 \, a b^{3} + 128 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(9 \, a^{4} + 168 \, a^{3} b + 496 \, a^{2} b^{2} + 416 \, a b^{3} + 24 \, {\left(a^{4} + 14 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(13 \, a^{4} + 144 \, a^{3} b + 200 \, a^{2} b^{2} + 12 \, {\left(a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(a^{7} d \cosh\left(d x + c\right)^{12} + 12 \, a^{7} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{7} d \sinh\left(d x + c\right)^{12} + a^{7} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{10} + 2 \, {\left(33 \, a^{7} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 2 \, a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, a^{7} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(495 \, a^{7} d \cosh\left(d x + c\right)^{4} + 180 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{7} d \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(231 \, a^{7} d \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a^{7} d \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(495 \, a^{7} d \cosh\left(d x + c\right)^{8} + a^{7} d + 840 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 60 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{7} d \cosh\left(d x + c\right)^{9} + a^{7} d \cosh\left(d x + c\right) + 120 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, a^{7} d \cosh\left(d x + c\right)^{10} + 3 \, a^{7} d \cosh\left(d x + c\right)^{2} + 90 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{7} d \cosh\left(d x + c\right)^{11} + a^{7} d \cosh\left(d x + c\right)^{3} + 10 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 8 \, a^{6} b + 8 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 2 \, a^{6} b\right)} d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/64*(a^4*cosh(d*x + c)^16 + 16*a^4*cosh(d*x + c)*sinh(d*x + c)^15 + a^4*sinh(d*x + c)^16 - 4*(a^4 + 4*a^3*b)*cosh(d*x + c)^14 + 4*(30*a^4*cosh(d*x + c)^2 - a^4 - 4*a^3*b)*sinh(d*x + c)^14 + 56*(10*a^4*cosh(d*x + c)^3 - (a^4 + 4*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^13 - 2*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^12 + 2*(910*a^4*cosh(d*x + c)^4 - 13*a^4 - 72*a^3*b - 88*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(546*a^4*cosh(d*x + c)^5 - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^3 - 3*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^11 - 4*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^10 + 4*(2002*a^4*cosh(d*x + c)^6 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^4 - 9*a^4 - 24*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x - 33*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 8*(1430*a^4*cosh(d*x + c)^7 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^5 - 55*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^3 - 5*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 16*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^8 + 2*(6435*a^4*cosh(d*x + c)^8 - 6006*(a^4 + 4*a^3*b)*cosh(d*x + c)^6 - 495*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 216*a^3*b + 912*a^2*b^2 + 1472*a*b^3 + 896*b^4 + 24*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x - 90*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*a^4*cosh(d*x + c)^9 - 858*(a^4 + 4*a^3*b)*cosh(d*x + c)^7 - 99*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^5 - 30*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^3 + 8*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^6 + 4*(2002*a^4*cosh(d*x + c)^10 - 3003*(a^4 + 4*a^3*b)*cosh(d*x + c)^8 - 462*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^6 - 210*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^4 + 9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(546*a^4*cosh(d*x + c)^11 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^9 - 198*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^7 - 126*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^5 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^3 + 3*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 2*(910*a^4*cosh(d*x + c)^12 - 2002*(a^4 + 4*a^3*b)*cosh(d*x + c)^10 - 495*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^8 - 420*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^6 + 560*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^4 + 13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x + 30*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 + 8*(70*a^4*cosh(d*x + c)^13 - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^11 - 55*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^9 - 60*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^7 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^5 + 10*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^3 + (13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 4*a^3*b)*cosh(d*x + c)^2 + 4*(30*a^4*cosh(d*x + c)^14 - 91*(a^4 + 4*a^3*b)*cosh(d*x + c)^12 - 33*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^10 - 45*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^8 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^6 + 15*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 3*(13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^12 + 12*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*sinh(d*x + c)^12 + 4*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^10 + 2*(10*a^4 + 60*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 33*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^3 + 2*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^8 + (495*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^4 + 30*a^4 + 200*a^3*b + 496*a^2*b^2 + 576*a*b^3 + 256*b^4 + 180*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^5 + 60*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + 2*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^6 + 4*(231*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^6 + 210*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3 + 14*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^7 + 126*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^5 + 14*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^3 + 3*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^4 + (495*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^8 + 840*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^6 + 140*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^4 + 5*a^4 + 20*a^3*b + 16*a^2*b^2 + 60*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^9 + 120*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^7 + 28*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^5 + 20*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(33*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^10 + 90*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^8 + 28*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^6 + 30*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 3*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^11 + 10*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^9 + 4*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^7 + 6*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^5 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(2*a^4*cosh(d*x + c)^15 - 7*(a^4 + 4*a^3*b)*cosh(d*x + c)^13 - 3*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^11 - 5*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^9 + 16*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^7 + 3*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^5 + (13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (a^4 + 4*a^3*b)*cosh(d*x + c))*sinh(d*x + c))/(a^7*d*cosh(d*x + c)^12 + 12*a^7*d*cosh(d*x + c)*sinh(d*x + c)^11 + a^7*d*sinh(d*x + c)^12 + a^7*d*cosh(d*x + c)^4 + 4*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^10 + 2*(33*a^7*d*cosh(d*x + c)^2 + 2*(a^7 + 2*a^6*b)*d)*sinh(d*x + c)^10 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^8 + 20*(11*a^7*d*cosh(d*x + c)^3 + 2*(a^7 + 2*a^6*b)*d*cosh(d*x + c))*sinh(d*x + c)^9 + (495*a^7*d*cosh(d*x + c)^4 + 180*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^2 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d)*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^6 + 8*(99*a^7*d*cosh(d*x + c)^5 + 60*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^3 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*a^7*d*cosh(d*x + c)^6 + 210*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b)*d)*sinh(d*x + c)^6 + 8*(99*a^7*d*cosh(d*x + c)^7 + 126*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (495*a^7*d*cosh(d*x + c)^8 + a^7*d + 840*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^6 + 140*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^4 + 60*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*a^7*d*cosh(d*x + c)^9 + a^7*d*cosh(d*x + c) + 120*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^7 + 28*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^5 + 20*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 2*(33*a^7*d*cosh(d*x + c)^10 + 3*a^7*d*cosh(d*x + c)^2 + 90*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^6 + 30*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 4*(3*a^7*d*cosh(d*x + c)^11 + a^7*d*cosh(d*x + c)^3 + 10*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^7 + 6*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^5)*sinh(d*x + c)), 1/64*(a^4*cosh(d*x + c)^16 + 16*a^4*cosh(d*x + c)*sinh(d*x + c)^15 + a^4*sinh(d*x + c)^16 - 4*(a^4 + 4*a^3*b)*cosh(d*x + c)^14 + 4*(30*a^4*cosh(d*x + c)^2 - a^4 - 4*a^3*b)*sinh(d*x + c)^14 + 56*(10*a^4*cosh(d*x + c)^3 - (a^4 + 4*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^13 - 2*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^12 + 2*(910*a^4*cosh(d*x + c)^4 - 13*a^4 - 72*a^3*b - 88*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(546*a^4*cosh(d*x + c)^5 - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^3 - 3*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^11 - 4*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^10 + 4*(2002*a^4*cosh(d*x + c)^6 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^4 - 9*a^4 - 24*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x - 33*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 8*(1430*a^4*cosh(d*x + c)^7 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^5 - 55*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^3 - 5*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 16*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^8 + 2*(6435*a^4*cosh(d*x + c)^8 - 6006*(a^4 + 4*a^3*b)*cosh(d*x + c)^6 - 495*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 216*a^3*b + 912*a^2*b^2 + 1472*a*b^3 + 896*b^4 + 24*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x - 90*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*a^4*cosh(d*x + c)^9 - 858*(a^4 + 4*a^3*b)*cosh(d*x + c)^7 - 99*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^5 - 30*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^3 + 8*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^6 + 4*(2002*a^4*cosh(d*x + c)^10 - 3003*(a^4 + 4*a^3*b)*cosh(d*x + c)^8 - 462*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^6 - 210*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^4 + 9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(546*a^4*cosh(d*x + c)^11 - 1001*(a^4 + 4*a^3*b)*cosh(d*x + c)^9 - 198*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^7 - 126*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^5 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^3 + 3*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 2*(910*a^4*cosh(d*x + c)^12 - 2002*(a^4 + 4*a^3*b)*cosh(d*x + c)^10 - 495*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^8 - 420*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^6 + 560*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^4 + 13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x + 30*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 + 8*(70*a^4*cosh(d*x + c)^13 - 182*(a^4 + 4*a^3*b)*cosh(d*x + c)^11 - 55*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^9 - 60*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^7 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^5 + 10*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^3 + (13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 4*a^3*b)*cosh(d*x + c)^2 + 4*(30*a^4*cosh(d*x + c)^14 - 91*(a^4 + 4*a^3*b)*cosh(d*x + c)^12 - 33*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^10 - 45*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^8 + 112*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^6 + 15*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 3*(13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 24*((5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^12 + 12*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*sinh(d*x + c)^12 + 4*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^10 + 2*(10*a^4 + 60*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 33*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^3 + 2*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^8 + (495*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^4 + 30*a^4 + 200*a^3*b + 496*a^2*b^2 + 576*a*b^3 + 256*b^4 + 180*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^5 + 60*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + 2*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^6 + 4*(231*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^6 + 210*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3 + 14*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^7 + 126*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^5 + 14*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^3 + 3*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^4 + (495*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^8 + 840*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^6 + 140*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^4 + 5*a^4 + 20*a^3*b + 16*a^2*b^2 + 60*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^9 + 120*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^7 + 28*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^5 + 20*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(33*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^10 + 90*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^8 + 28*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^6 + 30*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 3*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^11 + 10*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^9 + 4*(15*a^4 + 100*a^3*b + 248*a^2*b^2 + 288*a*b^3 + 128*b^4)*cosh(d*x + c)^7 + 6*(5*a^4 + 30*a^3*b + 56*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^5 + (5*a^4 + 20*a^3*b + 16*a^2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 8*(2*a^4*cosh(d*x + c)^15 - 7*(a^4 + 4*a^3*b)*cosh(d*x + c)^13 - 3*(13*a^4 + 72*a^3*b + 88*a^2*b^2 - 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^11 - 5*(9*a^4 + 24*a^3*b - 16*a^2*b^2 - 32*a*b^3 - 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^9 + 16*(27*a^3*b + 114*a^2*b^2 + 184*a*b^3 + 112*b^4 + 3*(3*a^4 + 44*a^3*b + 152*a^2*b^2 + 224*a*b^3 + 128*b^4)*d*x)*cosh(d*x + c)^7 + 3*(9*a^4 + 168*a^3*b + 496*a^2*b^2 + 416*a*b^3 + 24*(a^4 + 14*a^3*b + 40*a^2*b^2 + 32*a*b^3)*d*x)*cosh(d*x + c)^5 + (13*a^4 + 144*a^3*b + 200*a^2*b^2 + 12*(a^4 + 12*a^3*b + 16*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (a^4 + 4*a^3*b)*cosh(d*x + c))*sinh(d*x + c))/(a^7*d*cosh(d*x + c)^12 + 12*a^7*d*cosh(d*x + c)*sinh(d*x + c)^11 + a^7*d*sinh(d*x + c)^12 + a^7*d*cosh(d*x + c)^4 + 4*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^10 + 2*(33*a^7*d*cosh(d*x + c)^2 + 2*(a^7 + 2*a^6*b)*d)*sinh(d*x + c)^10 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^8 + 20*(11*a^7*d*cosh(d*x + c)^3 + 2*(a^7 + 2*a^6*b)*d*cosh(d*x + c))*sinh(d*x + c)^9 + (495*a^7*d*cosh(d*x + c)^4 + 180*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^2 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d)*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^6 + 8*(99*a^7*d*cosh(d*x + c)^5 + 60*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^3 + 2*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*a^7*d*cosh(d*x + c)^6 + 210*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b)*d)*sinh(d*x + c)^6 + 8*(99*a^7*d*cosh(d*x + c)^7 + 126*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (495*a^7*d*cosh(d*x + c)^8 + a^7*d + 840*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^6 + 140*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^4 + 60*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*a^7*d*cosh(d*x + c)^9 + a^7*d*cosh(d*x + c) + 120*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^7 + 28*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^5 + 20*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 2*(33*a^7*d*cosh(d*x + c)^10 + 3*a^7*d*cosh(d*x + c)^2 + 90*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^6 + 30*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 4*(3*a^7*d*cosh(d*x + c)^11 + a^7*d*cosh(d*x + c)^3 + 10*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 8*a^6*b + 8*a^5*b^2)*d*cosh(d*x + c)^7 + 6*(a^7 + 2*a^6*b)*d*cosh(d*x + c)^5)*sinh(d*x + c))]","B",0
42,1,8667,0,0.563993," ","integrate(sinh(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, a^{3} \cosh\left(d x + c\right)^{14} + 28 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 2 \, a^{3} \sinh\left(d x + c\right)^{14} - 2 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{2} - 5 \, a^{3} - 28 \, a^{2} b\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 2 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{4} - 39 \, a^{3} - 290 \, a^{2} b - 350 \, a b^{2} - 66 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{5} - 110 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 10 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(3003 \, a^{3} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 85 \, a^{3} - 730 \, a^{2} b - 1410 \, a b^{2} - 840 \, b^{3} - 45 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{7} - 99 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 10 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(3003 \, a^{3} \cosh\left(d x + c\right)^{8} - 924 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 85 \, a^{3} - 730 \, a^{2} b - 1410 \, a b^{2} - 840 \, b^{3} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{9} - 396 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{10} - 495 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 210 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 39 \, a^{3} - 290 \, a^{2} b - 350 \, a b^{2} - 75 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{11} - 55 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 30 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, a^{3} - 2 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 28 \, a^{2} b - 6 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left({\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{11} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(12 \, a^{3} + 52 \, a^{2} b + 56 \, a b^{2} + 55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3} + 72 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 14 \, {\left(33 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} + 26 \, a^{2} b + 28 \, a b^{2} + 21 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 336 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 7 \, a^{2} b + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 144 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 36 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{13} - 6 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(a^{6} d \cosh\left(d x + c\right)^{11} + 11 \, a^{6} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{6} d \sinh\left(d x + c\right)^{11} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{9} + a^{6} d \cosh\left(d x + c\right)^{3} + {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{4} + 72 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(33 \, a^{6} d \cosh\left(d x + c\right)^{5} + 24 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(231 \, a^{6} d \cosh\left(d x + c\right)^{6} + 252 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{4} + 21 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{6} + 2 \, a^{5} b\right)} d\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{5} + 35 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 10 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{8} + 336 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{6} + a^{6} d + 70 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 40 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{9} + 144 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{7} + 3 \, a^{6} d \cosh\left(d x + c\right) + 42 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 40 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, a^{6} d \cosh\left(d x + c\right)^{10} + 36 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{8} + 3 \, a^{6} d \cosh\left(d x + c\right)^{2} + 14 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 20 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a^{3} \cosh\left(d x + c\right)^{14} + 14 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + a^{3} \sinh\left(d x + c\right)^{14} - {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + {\left(91 \, a^{3} \cosh\left(d x + c\right)^{2} - 5 \, a^{3} - 28 \, a^{2} b\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{4} - 39 \, a^{3} - 290 \, a^{2} b - 350 \, a b^{2} - 66 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{5} - 110 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, a^{3} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 85 \, a^{3} - 730 \, a^{2} b - 1410 \, a b^{2} - 840 \, b^{3} - 45 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{7} - 99 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, a^{3} \cosh\left(d x + c\right)^{8} - 924 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 85 \, a^{3} - 730 \, a^{2} b - 1410 \, a b^{2} - 840 \, b^{3} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{9} - 396 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, a^{3} \cosh\left(d x + c\right)^{10} - 495 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 210 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 39 \, a^{3} - 290 \, a^{2} b - 350 \, a b^{2} - 75 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, a^{3} \cosh\left(d x + c\right)^{11} - 55 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 30 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, a^{3} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 28 \, a^{2} b - 6 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left({\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{11} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(12 \, a^{3} + 52 \, a^{2} b + 56 \, a b^{2} + 55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3} + 72 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 14 \, {\left(33 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} + 26 \, a^{2} b + 28 \, a b^{2} + 21 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 336 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 7 \, a^{2} b + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 144 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 36 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 15 \, {\left({\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{11} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(12 \, a^{3} + 52 \, a^{2} b + 56 \, a b^{2} + 55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3} + 72 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 14 \, {\left(33 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} + 26 \, a^{2} b + 28 \, a b^{2} + 21 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(165 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 336 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 7 \, a^{2} b + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 144 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 36 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(9 \, a^{3} + 45 \, a^{2} b + 80 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(3 \, a^{3} + 13 \, a^{2} b + 14 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} + 7 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{13} - 6 \, {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(17 \, a^{3} + 146 \, a^{2} b + 282 \, a b^{2} + 168 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(39 \, a^{3} + 290 \, a^{2} b + 350 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{3} + 28 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(a^{6} d \cosh\left(d x + c\right)^{11} + 11 \, a^{6} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{6} d \sinh\left(d x + c\right)^{11} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{9} + a^{6} d \cosh\left(d x + c\right)^{3} + {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{4} + 72 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(33 \, a^{6} d \cosh\left(d x + c\right)^{5} + 24 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(231 \, a^{6} d \cosh\left(d x + c\right)^{6} + 252 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{4} + 21 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{6} + 2 \, a^{5} b\right)} d\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{5} + 35 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 10 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(165 \, a^{6} d \cosh\left(d x + c\right)^{8} + 336 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{6} + a^{6} d + 70 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 40 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, a^{6} d \cosh\left(d x + c\right)^{9} + 144 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{7} + 3 \, a^{6} d \cosh\left(d x + c\right) + 42 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 40 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, a^{6} d \cosh\left(d x + c\right)^{10} + 36 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{8} + 3 \, a^{6} d \cosh\left(d x + c\right)^{2} + 14 \, {\left(3 \, a^{6} + 8 \, a^{5} b + 8 \, a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 20 \, {\left(a^{6} + 2 \, a^{5} b\right)} d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/48*(2*a^3*cosh(d*x + c)^14 + 28*a^3*cosh(d*x + c)*sinh(d*x + c)^13 + 2*a^3*sinh(d*x + c)^14 - 2*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^12 + 2*(91*a^3*cosh(d*x + c)^2 - 5*a^3 - 28*a^2*b)*sinh(d*x + c)^12 + 8*(91*a^3*cosh(d*x + c)^3 - 3*(5*a^3 + 28*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^11 - 2*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^10 + 2*(1001*a^3*cosh(d*x + c)^4 - 39*a^3 - 290*a^2*b - 350*a*b^2 - 66*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(1001*a^3*cosh(d*x + c)^5 - 110*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^3 - 5*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 10*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^8 + 2*(3003*a^3*cosh(d*x + c)^6 - 495*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^4 - 85*a^3 - 730*a^2*b - 1410*a*b^2 - 840*b^3 - 45*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(429*a^3*cosh(d*x + c)^7 - 99*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^5 - 15*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^3 - 5*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 10*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^6 + 2*(3003*a^3*cosh(d*x + c)^8 - 924*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^6 - 210*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^4 - 85*a^3 - 730*a^2*b - 1410*a*b^2 - 840*b^3 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(1001*a^3*cosh(d*x + c)^9 - 396*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^7 - 126*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^5 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^3 - 15*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^4 + 2*(1001*a^3*cosh(d*x + c)^10 - 495*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^8 - 210*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^6 - 350*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^4 - 39*a^3 - 290*a^2*b - 350*a*b^2 - 75*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(91*a^3*cosh(d*x + c)^11 - 55*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^9 - 30*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^7 - 70*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^5 - 25*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^3 - (39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*a^3 - 2*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^2 + 2*(91*a^3*cosh(d*x + c)^12 - 66*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^10 - 45*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^8 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^6 - 75*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^4 - 5*a^3 - 28*a^2*b - 6*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 15*((3*a^3 + 7*a^2*b)*cosh(d*x + c)^11 + 11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^10 + (3*a^3 + 7*a^2*b)*sinh(d*x + c)^11 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^9 + (12*a^3 + 52*a^2*b + 56*a*b^2 + 55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + 12*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^7 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^4 + 9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3 + 72*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 14*(33*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^5 + 24*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + (9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 2*(231*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^6 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 6*a^3 + 26*a^2*b + 28*a*b^2 + 21*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^7 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 35*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^3 + 10*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + (165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^8 + 336*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^6 + 70*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^4 + 3*a^3 + 7*a^2*b + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^9 + 144*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^7 + 42*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^5 + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^10 + 36*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^8 + 14*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^6 + 20*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(7*a^3*cosh(d*x + c)^13 - 6*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^11 - 5*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^9 - 20*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^7 - 15*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^5 - 2*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^3 - (5*a^3 + 28*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(a^6*d*cosh(d*x + c)^11 + 11*a^6*d*cosh(d*x + c)*sinh(d*x + c)^10 + a^6*d*sinh(d*x + c)^11 + 4*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^9 + a^6*d*cosh(d*x + c)^3 + (55*a^6*d*cosh(d*x + c)^2 + 4*(a^6 + 2*a^5*b)*d)*sinh(d*x + c)^9 + 2*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^7 + 3*(55*a^6*d*cosh(d*x + c)^3 + 12*(a^6 + 2*a^5*b)*d*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(165*a^6*d*cosh(d*x + c)^4 + 72*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^2 + (3*a^6 + 8*a^5*b + 8*a^4*b^2)*d)*sinh(d*x + c)^7 + 4*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^5 + 14*(33*a^6*d*cosh(d*x + c)^5 + 24*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^3 + (3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(231*a^6*d*cosh(d*x + c)^6 + 252*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^4 + 21*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^2 + 2*(a^6 + 2*a^5*b)*d)*sinh(d*x + c)^5 + 2*(165*a^6*d*cosh(d*x + c)^7 + 252*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^5 + 35*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^3 + 10*(a^6 + 2*a^5*b)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (165*a^6*d*cosh(d*x + c)^8 + 336*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^6 + a^6*d + 70*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^4 + 40*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*a^6*d*cosh(d*x + c)^9 + 144*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^7 + 3*a^6*d*cosh(d*x + c) + 42*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^5 + 40*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (11*a^6*d*cosh(d*x + c)^10 + 36*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^8 + 3*a^6*d*cosh(d*x + c)^2 + 14*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^6 + 20*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^4)*sinh(d*x + c)), 1/24*(a^3*cosh(d*x + c)^14 + 14*a^3*cosh(d*x + c)*sinh(d*x + c)^13 + a^3*sinh(d*x + c)^14 - (5*a^3 + 28*a^2*b)*cosh(d*x + c)^12 + (91*a^3*cosh(d*x + c)^2 - 5*a^3 - 28*a^2*b)*sinh(d*x + c)^12 + 4*(91*a^3*cosh(d*x + c)^3 - 3*(5*a^3 + 28*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^11 - (39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^10 + (1001*a^3*cosh(d*x + c)^4 - 39*a^3 - 290*a^2*b - 350*a*b^2 - 66*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*a^3*cosh(d*x + c)^5 - 110*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^3 - 5*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^8 + (3003*a^3*cosh(d*x + c)^6 - 495*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^4 - 85*a^3 - 730*a^2*b - 1410*a*b^2 - 840*b^3 - 45*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*a^3*cosh(d*x + c)^7 - 99*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^5 - 15*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^3 - 5*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^6 + (3003*a^3*cosh(d*x + c)^8 - 924*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^6 - 210*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^4 - 85*a^3 - 730*a^2*b - 1410*a*b^2 - 840*b^3 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*a^3*cosh(d*x + c)^9 - 396*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^7 - 126*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^5 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^3 - 15*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - (39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^4 + (1001*a^3*cosh(d*x + c)^10 - 495*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^8 - 210*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^6 - 350*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^4 - 39*a^3 - 290*a^2*b - 350*a*b^2 - 75*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*a^3*cosh(d*x + c)^11 - 55*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^9 - 30*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^7 - 70*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^5 - 25*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^3 - (39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - (5*a^3 + 28*a^2*b)*cosh(d*x + c)^2 + (91*a^3*cosh(d*x + c)^12 - 66*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^10 - 45*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^8 - 140*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^6 - 75*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^4 - 5*a^3 - 28*a^2*b - 6*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*((3*a^3 + 7*a^2*b)*cosh(d*x + c)^11 + 11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^10 + (3*a^3 + 7*a^2*b)*sinh(d*x + c)^11 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^9 + (12*a^3 + 52*a^2*b + 56*a*b^2 + 55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + 12*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^7 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^4 + 9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3 + 72*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 14*(33*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^5 + 24*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + (9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 2*(231*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^6 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 6*a^3 + 26*a^2*b + 28*a*b^2 + 21*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^7 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 35*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^3 + 10*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + (165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^8 + 336*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^6 + 70*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^4 + 3*a^3 + 7*a^2*b + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^9 + 144*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^7 + 42*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^5 + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^10 + 36*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^8 + 14*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^6 + 20*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) + 15*((3*a^3 + 7*a^2*b)*cosh(d*x + c)^11 + 11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^10 + (3*a^3 + 7*a^2*b)*sinh(d*x + c)^11 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^9 + (12*a^3 + 52*a^2*b + 56*a*b^2 + 55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + 12*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^7 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^4 + 9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3 + 72*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 14*(33*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^5 + 24*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + (9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 2*(231*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^6 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 6*a^3 + 26*a^2*b + 28*a*b^2 + 21*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^7 + 252*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^5 + 35*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^3 + 10*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^3 + 7*a^2*b)*cosh(d*x + c)^3 + (165*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^8 + 336*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^6 + 70*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^4 + 3*a^3 + 7*a^2*b + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^9 + 144*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^7 + 42*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^5 + 40*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^3 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (11*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^10 + 36*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^8 + 14*(9*a^3 + 45*a^2*b + 80*a*b^2 + 56*b^3)*cosh(d*x + c)^6 + 20*(3*a^3 + 13*a^2*b + 14*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 + 7*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 2*(7*a^3*cosh(d*x + c)^13 - 6*(5*a^3 + 28*a^2*b)*cosh(d*x + c)^11 - 5*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^9 - 20*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^7 - 15*(17*a^3 + 146*a^2*b + 282*a*b^2 + 168*b^3)*cosh(d*x + c)^5 - 2*(39*a^3 + 290*a^2*b + 350*a*b^2)*cosh(d*x + c)^3 - (5*a^3 + 28*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(a^6*d*cosh(d*x + c)^11 + 11*a^6*d*cosh(d*x + c)*sinh(d*x + c)^10 + a^6*d*sinh(d*x + c)^11 + 4*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^9 + a^6*d*cosh(d*x + c)^3 + (55*a^6*d*cosh(d*x + c)^2 + 4*(a^6 + 2*a^5*b)*d)*sinh(d*x + c)^9 + 2*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^7 + 3*(55*a^6*d*cosh(d*x + c)^3 + 12*(a^6 + 2*a^5*b)*d*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(165*a^6*d*cosh(d*x + c)^4 + 72*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^2 + (3*a^6 + 8*a^5*b + 8*a^4*b^2)*d)*sinh(d*x + c)^7 + 4*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^5 + 14*(33*a^6*d*cosh(d*x + c)^5 + 24*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^3 + (3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(231*a^6*d*cosh(d*x + c)^6 + 252*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^4 + 21*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^2 + 2*(a^6 + 2*a^5*b)*d)*sinh(d*x + c)^5 + 2*(165*a^6*d*cosh(d*x + c)^7 + 252*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^5 + 35*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^3 + 10*(a^6 + 2*a^5*b)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (165*a^6*d*cosh(d*x + c)^8 + 336*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^6 + a^6*d + 70*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^4 + 40*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*a^6*d*cosh(d*x + c)^9 + 144*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^7 + 3*a^6*d*cosh(d*x + c) + 42*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^5 + 40*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (11*a^6*d*cosh(d*x + c)^10 + 36*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^8 + 3*a^6*d*cosh(d*x + c)^2 + 14*(3*a^6 + 8*a^5*b + 8*a^4*b^2)*d*cosh(d*x + c)^6 + 20*(a^6 + 2*a^5*b)*d*cosh(d*x + c)^4)*sinh(d*x + c))]","B",0
43,1,9730,0,0.596216," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{4} + a^{3} b\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x + 33 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(495 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x + 180 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} 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^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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 + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(462 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b - 102 \, a^{2} b^{2} - 152 \, a b^{3} - 80 \, b^{4} - 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + a^{3} b\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{4} - 75 \, a^{3} b - 192 \, a^{2} b^{2} - 128 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x - 30 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, a^{4} - 2 \, a^{3} b + 8 \, {\left(55 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + 15 \, a^{3} b + 14 \, a^{2} b^{2} + 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{4} - 15 \, a^{3} b - 14 \, a^{2} b^{2} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x - 3 \, {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(60 \, a^{4} + 280 \, a^{3} b + 416 \, a^{2} b^{2} + 192 \, a b^{3} + 45 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4} + 56 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} + 140 \, a^{3} b + 208 \, a^{2} b^{2} + 96 \, a b^{3} + 15 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, 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} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2} + 24 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{4} + 15 \, a^{3} b + 14 \, a^{2} b^{2} + 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, 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} + a^{6} b\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + a^{6} b\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{4} + a^{3} b\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x + 33 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x + 180 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\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} + a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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 + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(462 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b - 102 \, a^{2} b^{2} - 152 \, a b^{3} - 80 \, b^{4} - 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + a^{3} b\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{4} - 75 \, a^{3} b - 192 \, a^{2} b^{2} - 128 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x - 30 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} - a^{3} b + 4 \, {\left(55 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + 15 \, a^{3} b + 14 \, a^{2} b^{2} + 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{4} - 15 \, a^{3} b - 14 \, a^{2} b^{2} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x - 3 \, {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, 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} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(60 \, a^{4} + 280 \, a^{3} b + 416 \, a^{2} b^{2} + 192 \, a b^{3} + 45 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4} + 56 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} + 140 \, a^{3} b + 208 \, a^{2} b^{2} + 96 \, a b^{3} + 15 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, 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} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2} + 24 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(45 \, a^{4} + 240 \, a^{3} b + 512 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(15 \, a^{4} + 70 \, a^{3} b + 104 \, a^{2} b^{2} + 48 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 24 \, a^{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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} - {\left(a^{4} + 7 \, a^{3} b + 6 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 3 \, a^{3} b - 32 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(27 \, a^{3} b + 102 \, a^{2} b^{2} + 152 \, a b^{3} + 80 \, b^{4} + 4 \, {\left(3 \, a^{4} + 29 \, a^{3} b + 82 \, a^{2} b^{2} + 104 \, a b^{3} + 48 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{4} + 75 \, a^{3} b + 192 \, a^{2} b^{2} + 128 \, a b^{3} + 16 \, {\left(a^{4} + 9 \, a^{3} b + 20 \, a^{2} b^{2} + 12 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{4} + 15 \, a^{3} b + 14 \, a^{2} b^{2} + 2 \, {\left(a^{4} + 7 \, a^{3} b + 6 \, 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} + a^{6} b\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + a^{6} b\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + a^{6} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{7} + 11 \, a^{6} b + 16 \, a^{5} b^{2} + 8 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + a^{6} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(2*(a^4 + a^3*b)*cosh(d*x + c)^12 + 24*(a^4 + a^3*b)*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^4 + a^3*b)*sinh(d*x + c)^12 + 8*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^10 + 4*(2*a^4 + 6*a^3*b + 4*a^2*b^2 - 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x + 33*(a^4 + a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(11*(a^4 + a^3*b)*cosh(d*x + c)^3 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^8 + 2*(495*(a^4 + a^3*b)*cosh(d*x + c)^4 + 5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x + 180*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^4 + a^3*b)*cosh(d*x + c)^5 + 60*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^6 + 4*(462*(a^4 + a^3*b)*cosh(d*x + c)^6 + 420*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^4 - 27*a^3*b - 102*a^2*b^2 - 152*a*b^3 - 80*b^4 - 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(198*(a^4 + a^3*b)*cosh(d*x + c)^7 + 252*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^5 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^3 - 3*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^4 + a^3*b)*cosh(d*x + c)^8 + 840*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^6 + 70*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^4 - 5*a^4 - 75*a^3*b - 192*a^2*b^2 - 128*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x - 30*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 2*a^4 - 2*a^3*b + 8*(55*(a^4 + a^3*b)*cosh(d*x + c)^9 + 120*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^7 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^5 - 10*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^3 - (5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^4 + 15*a^3*b + 14*a^2*b^2 + 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^4 + a^3*b)*cosh(d*x + c)^10 + 90*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^8 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^6 - 15*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^4 - 2*a^4 - 15*a^3*b - 14*a^2*b^2 - 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x - 3*(5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^10 + 10*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*sinh(d*x + c)^10 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^8 + (60*a^4 + 280*a^3*b + 416*a^2*b^2 + 192*a*b^3 + 45*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^3 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^6 + 2*(105*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4 + 56*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^5 + 56*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^3 + 3*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^4 + 2*(105*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^6 + 140*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^4 + 30*a^4 + 140*a^3*b + 208*a^2*b^2 + 96*a*b^3 + 15*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^7 + 28*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^5 + 5*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^3 + 2*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^2 + (45*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^8 + 112*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^6 + 30*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 24*a^2*b^2 + 24*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^9 + 16*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^7 + 6*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^5 + 8*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(a^4 + a^3*b)*cosh(d*x + c)^11 + 10*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^9 + 2*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^7 - 3*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^5 - (5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^4 + 15*a^3*b + 14*a^2*b^2 + 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + a^6*b)*d*cosh(d*x + c)^10 + 10*(a^7 + a^6*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + a^6*b)*d*sinh(d*x + c)^10 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^8 + (45*(a^7 + a^6*b)*d*cosh(d*x + c)^2 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d)*sinh(d*x + c)^8 + 2*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + a^6*b)*d*cosh(d*x + c)^3 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + a^6*b)*d*cosh(d*x + c)^4 + 56*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^2 + (3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d)*sinh(d*x + c)^6 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + a^6*b)*d*cosh(d*x + c)^5 + 56*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^3 + 3*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + a^6*b)*d*cosh(d*x + c)^6 + 140*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^4 + 15*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^2 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2)*d)*sinh(d*x + c)^4 + (a^7 + a^6*b)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + a^6*b)*d*cosh(d*x + c)^7 + 28*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^5 + 5*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^3 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + a^6*b)*d*cosh(d*x + c)^8 + 112*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^6 + 30*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^4 + 24*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + a^6*b)*d)*sinh(d*x + c)^2 + 2*(5*(a^7 + a^6*b)*d*cosh(d*x + c)^9 + 16*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^7 + 6*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^5 + 8*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^3 + (a^7 + a^6*b)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^4 + a^3*b)*cosh(d*x + c)^12 + 12*(a^4 + a^3*b)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^4 + a^3*b)*sinh(d*x + c)^12 + 4*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^10 + 2*(2*a^4 + 6*a^3*b + 4*a^2*b^2 - 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x + 33*(a^4 + a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^4 + a^3*b)*cosh(d*x + c)^3 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + (5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^8 + (495*(a^4 + a^3*b)*cosh(d*x + c)^4 + 5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x + 180*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^4 + a^3*b)*cosh(d*x + c)^5 + 60*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^6 + 2*(462*(a^4 + a^3*b)*cosh(d*x + c)^6 + 420*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^4 - 27*a^3*b - 102*a^2*b^2 - 152*a*b^3 - 80*b^4 - 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(198*(a^4 + a^3*b)*cosh(d*x + c)^7 + 252*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^5 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^3 - 3*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - (5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^4 + (495*(a^4 + a^3*b)*cosh(d*x + c)^8 + 840*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^6 + 70*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^4 - 5*a^4 - 75*a^3*b - 192*a^2*b^2 - 128*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x - 30*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 - a^3*b + 4*(55*(a^4 + a^3*b)*cosh(d*x + c)^9 + 120*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^7 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^5 - 10*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^3 - (5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^4 + 15*a^3*b + 14*a^2*b^2 + 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^2 + 2*(33*(a^4 + a^3*b)*cosh(d*x + c)^10 + 90*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^8 + 14*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^6 - 15*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^4 - 2*a^4 - 15*a^3*b - 14*a^2*b^2 - 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x - 3*(5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^10 + 10*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*sinh(d*x + c)^10 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^8 + (60*a^4 + 280*a^3*b + 416*a^2*b^2 + 192*a*b^3 + 45*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^3 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^6 + 2*(105*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4 + 56*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^5 + 56*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^3 + 3*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^4 + 2*(105*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^6 + 140*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^4 + 30*a^4 + 140*a^3*b + 208*a^2*b^2 + 96*a*b^3 + 15*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^7 + 28*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^5 + 5*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^3 + 2*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^2 + (45*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^8 + 112*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^6 + 30*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 24*a^2*b^2 + 24*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c)^9 + 16*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^7 + 6*(45*a^4 + 240*a^3*b + 512*a^2*b^2 + 512*a*b^3 + 192*b^4)*cosh(d*x + c)^5 + 8*(15*a^4 + 70*a^3*b + 104*a^2*b^2 + 48*a*b^3)*cosh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 24*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(3*(a^4 + a^3*b)*cosh(d*x + c)^11 + 10*(a^4 + 3*a^3*b + 2*a^2*b^2 - (a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c)^9 + 2*(5*a^4 + 3*a^3*b - 32*a^2*b^2 - 32*a*b^3 - 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^7 - 3*(27*a^3*b + 102*a^2*b^2 + 152*a*b^3 + 80*b^4 + 4*(3*a^4 + 29*a^3*b + 82*a^2*b^2 + 104*a*b^3 + 48*b^4)*d*x)*cosh(d*x + c)^5 - (5*a^4 + 75*a^3*b + 192*a^2*b^2 + 128*a*b^3 + 16*(a^4 + 9*a^3*b + 20*a^2*b^2 + 12*a*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^4 + 15*a^3*b + 14*a^2*b^2 + 2*(a^4 + 7*a^3*b + 6*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + a^6*b)*d*cosh(d*x + c)^10 + 10*(a^7 + a^6*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + a^6*b)*d*sinh(d*x + c)^10 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^8 + (45*(a^7 + a^6*b)*d*cosh(d*x + c)^2 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d)*sinh(d*x + c)^8 + 2*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + a^6*b)*d*cosh(d*x + c)^3 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + a^6*b)*d*cosh(d*x + c)^4 + 56*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^2 + (3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d)*sinh(d*x + c)^6 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + a^6*b)*d*cosh(d*x + c)^5 + 56*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^3 + 3*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + a^6*b)*d*cosh(d*x + c)^6 + 140*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^4 + 15*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^2 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2)*d)*sinh(d*x + c)^4 + (a^7 + a^6*b)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + a^6*b)*d*cosh(d*x + c)^7 + 28*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^5 + 5*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^3 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + a^6*b)*d*cosh(d*x + c)^8 + 112*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^6 + 30*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^4 + 24*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + a^6*b)*d)*sinh(d*x + c)^2 + 2*(5*(a^7 + a^6*b)*d*cosh(d*x + c)^9 + 16*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^7 + 6*(3*a^7 + 11*a^6*b + 16*a^5*b^2 + 8*a^4*b^3)*d*cosh(d*x + c)^5 + 8*(a^7 + 3*a^6*b + 2*a^5*b^2)*d*cosh(d*x + c)^3 + (a^7 + a^6*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
44,1,4829,0,0.513811," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} \cosh\left(d x + c\right)^{10} + 80 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, a^{2} \sinh\left(d x + c\right)^{10} + 20 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{8} + 20 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{8} + 160 \, {\left(6 \, a^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(84 \, a^{2} \cosh\left(d x + c\right)^{4} + 28 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(252 \, a^{2} \cosh\left(d x + c\right)^{5} + 140 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(84 \, a^{2} \cosh\left(d x + c\right)^{6} + 70 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 80 \, {\left(12 \, a^{2} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 20 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, a^{2} \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)^{6} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right) + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, a^{2} + 40 \, {\left(2 \, a^{2} \cosh\left(d x + c\right)^{9} + 4 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{5} d \cosh\left(d x + c\right)^{9} + 9 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{5} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{7} + a^{5} d \cosh\left(d x + c\right) + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a^{5} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, a^{5} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a^{5} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, a^{5} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + a^{5} d + 10 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{4 \, a^{2} \cosh\left(d x + c\right)^{10} + 40 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 4 \, a^{2} \sinh\left(d x + c\right)^{10} + 10 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{8} + 10 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{8} + 80 \, {\left(6 \, a^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(84 \, a^{2} \cosh\left(d x + c\right)^{4} + 28 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(252 \, a^{2} \cosh\left(d x + c\right)^{5} + 140 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(84 \, a^{2} \cosh\left(d x + c\right)^{6} + 70 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(12 \, a^{2} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 10 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, a^{2} \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)^{6} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right) + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, a^{2} \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)^{6} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right) + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, a^{2} + 20 \, {\left(2 \, a^{2} \cosh\left(d x + c\right)^{9} + 4 \, {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{5} d \cosh\left(d x + c\right)^{9} + 9 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{5} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{7} + a^{5} d \cosh\left(d x + c\right) + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a^{5} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, a^{5} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a^{5} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, a^{5} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{5} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + a^{5} d + 10 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(8*a^2*cosh(d*x + c)^10 + 80*a^2*cosh(d*x + c)*sinh(d*x + c)^9 + 8*a^2*sinh(d*x + c)^10 + 20*(2*a^2 + 5*a*b)*cosh(d*x + c)^8 + 20*(18*a^2*cosh(d*x + c)^2 + 2*a^2 + 5*a*b)*sinh(d*x + c)^8 + 160*(6*a^2*cosh(d*x + c)^3 + (2*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^6 + 20*(84*a^2*cosh(d*x + c)^4 + 28*(2*a^2 + 5*a*b)*cosh(d*x + c)^2 + 4*a^2 + 15*a*b + 12*b^2)*sinh(d*x + c)^6 + 8*(252*a^2*cosh(d*x + c)^5 + 140*(2*a^2 + 5*a*b)*cosh(d*x + c)^3 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^4 + 20*(84*a^2*cosh(d*x + c)^6 + 70*(2*a^2 + 5*a*b)*cosh(d*x + c)^4 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^2 + 4*a^2 + 15*a*b + 12*b^2)*sinh(d*x + c)^4 + 80*(12*a^2*cosh(d*x + c)^7 + 14*(2*a^2 + 5*a*b)*cosh(d*x + c)^5 + 5*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^3 + (4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 20*(2*a^2 + 5*a*b)*cosh(d*x + c)^2 + 20*(18*a^2*cosh(d*x + c)^8 + 28*(2*a^2 + 5*a*b)*cosh(d*x + c)^6 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^4 + 6*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^2 + 2*a^2 + 5*a*b)*sinh(d*x + c)^2 + 15*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 4*(9*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^7 + 28*(3*a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^4 + 42*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^5 + 70*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 4*(21*a^2*cosh(d*x + c)^6 + 35*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^3 + a^2*cosh(d*x + c) + 4*(9*a^2*cosh(d*x + c)^7 + 21*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 + 28*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 12*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2)*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*a^2 + 40*(2*a^2*cosh(d*x + c)^9 + 4*(2*a^2 + 5*a*b)*cosh(d*x + c)^7 + 3*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^5 + 2*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^3 + (2*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^9 + 9*a^5*d*cosh(d*x + c)*sinh(d*x + c)^8 + a^5*d*sinh(d*x + c)^9 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^7 + 4*(9*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^7 + a^5*d*cosh(d*x + c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^5 + 28*(3*a^5*d*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*a^5*d*cosh(d*x + c)^4 + 42*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d)*sinh(d*x + c)^5 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + 2*(63*a^5*d*cosh(d*x + c)^5 + 70*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*a^5*d*cosh(d*x + c)^6 + 35*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^3 + 4*(9*a^5*d*cosh(d*x + c)^7 + 21*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^5*d*cosh(d*x + c)^8 + 28*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + a^5*d + 10*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^4 + 12*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/8*(4*a^2*cosh(d*x + c)^10 + 40*a^2*cosh(d*x + c)*sinh(d*x + c)^9 + 4*a^2*sinh(d*x + c)^10 + 10*(2*a^2 + 5*a*b)*cosh(d*x + c)^8 + 10*(18*a^2*cosh(d*x + c)^2 + 2*a^2 + 5*a*b)*sinh(d*x + c)^8 + 80*(6*a^2*cosh(d*x + c)^3 + (2*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^6 + 10*(84*a^2*cosh(d*x + c)^4 + 28*(2*a^2 + 5*a*b)*cosh(d*x + c)^2 + 4*a^2 + 15*a*b + 12*b^2)*sinh(d*x + c)^6 + 4*(252*a^2*cosh(d*x + c)^5 + 140*(2*a^2 + 5*a*b)*cosh(d*x + c)^3 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^4 + 10*(84*a^2*cosh(d*x + c)^6 + 70*(2*a^2 + 5*a*b)*cosh(d*x + c)^4 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^2 + 4*a^2 + 15*a*b + 12*b^2)*sinh(d*x + c)^4 + 40*(12*a^2*cosh(d*x + c)^7 + 14*(2*a^2 + 5*a*b)*cosh(d*x + c)^5 + 5*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^3 + (4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 10*(2*a^2 + 5*a*b)*cosh(d*x + c)^2 + 10*(18*a^2*cosh(d*x + c)^8 + 28*(2*a^2 + 5*a*b)*cosh(d*x + c)^6 + 15*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^4 + 6*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^2 + 2*a^2 + 5*a*b)*sinh(d*x + c)^2 + 15*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 4*(9*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^7 + 28*(3*a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^4 + 42*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^5 + 70*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 4*(21*a^2*cosh(d*x + c)^6 + 35*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^3 + a^2*cosh(d*x + c) + 4*(9*a^2*cosh(d*x + c)^7 + 21*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 + 28*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 12*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - 15*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 4*(9*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^7 + 28*(3*a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^4 + 42*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^5 + 2*(63*a^2*cosh(d*x + c)^5 + 70*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^3 + 4*(21*a^2*cosh(d*x + c)^6 + 35*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^3 + a^2*cosh(d*x + c) + 4*(9*a^2*cosh(d*x + c)^7 + 21*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 5*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 + 28*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 10*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 12*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2)*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 4*a^2 + 20*(2*a^2*cosh(d*x + c)^9 + 4*(2*a^2 + 5*a*b)*cosh(d*x + c)^7 + 3*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^5 + 2*(4*a^2 + 15*a*b + 12*b^2)*cosh(d*x + c)^3 + (2*a^2 + 5*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^9 + 9*a^5*d*cosh(d*x + c)*sinh(d*x + c)^8 + a^5*d*sinh(d*x + c)^9 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^7 + 4*(9*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^7 + a^5*d*cosh(d*x + c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^5 + 28*(3*a^5*d*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*a^5*d*cosh(d*x + c)^4 + 42*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d)*sinh(d*x + c)^5 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + 2*(63*a^5*d*cosh(d*x + c)^5 + 70*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*a^5*d*cosh(d*x + c)^6 + 35*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^3 + 4*(9*a^5*d*cosh(d*x + c)^7 + 21*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5 + 5*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^5*d*cosh(d*x + c)^8 + 28*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + a^5*d + 10*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^4 + 12*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
45,1,8742,0,0.637251," ","integrate(csch(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4} + 21 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, 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 + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4} + 10 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{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 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} + a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) + 16 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} 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) - 16 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} 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) + 4 \, {\left(7 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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 + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4} + 21 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, 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 + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4} + 10 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a 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(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} + {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - {\left({\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, 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} + 10 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 150 \, a^{3} b + 209 \, a^{2} b^{2} + 104 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 40 \, a^{3} b + 23 \, a^{2} b^{2} + 6 \, a 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(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} 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) - 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} 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(7 \, {\left(9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} b + 14 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, {\left(27 \, a^{3} b + 70 \, a^{2} b^{2} + 55 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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 + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^7 + 28*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*sinh(d*x + c)^7 + 4*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^5 + 4*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4 + 21*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + (27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + 4*(35*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^4 + 27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4 + 10*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^5 + 10*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + 3*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 10*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4 + 30*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 10*a^3*b + 3*a^2*b^2 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 3*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((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 - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*sqrt(-b/a) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c) + 16*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 16*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(7*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^6 + 5*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 9*a^3*b + 14*a^2*b^2 + 5*a*b^3 + 3*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 8*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^8 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 30*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 10*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 15*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 8*((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^7 + 14*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*sinh(d*x + c)^7 + 2*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^5 + 2*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4 + 21*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + (27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + 2*(35*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^4 + 27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4 + 10*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^5 + 10*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + 3*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 10*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4 + 30*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 10*a^3*b + 3*a^2*b^2 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 3*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + a + 4*b)*sinh(d*x + c))*sqrt(b/a)/b) - ((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 10*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4 + 30*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 10*a^3*b + 3*a^2*b^2 + 8*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3 + 3*(45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 10*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (45*a^4 + 150*a^3*b + 209*a^2*b^2 + 104*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 40*a^3*b + 23*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(a*cosh(d*x + c) + a*sinh(d*x + c))*sqrt(b/a)/b) + 2*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c) + 8*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 8*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(9*a^3*b + 14*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^6 + 5*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 9*a^3*b + 14*a^2*b^2 + 5*a*b^3 + 3*(27*a^3*b + 70*a^2*b^2 + 55*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 8*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^8 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 30*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 10*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 15*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 8*((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
46,1,7275,0,0.548741," ","integrate(csch(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 32 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4} + 14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(35 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4} + 15 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, a^{4} - 36 \, a^{3} b - 8 \, a^{2} b^{2} + 32 \, {\left(7 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3} + 6 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left(a^{4} \cosh\left(d x + c\right)^{10} + 10 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{4} \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, a^{4} \cosh\left(d x + c\right)^{2} + 3 \, a^{4} + 8 \, a^{3} b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2} + 14 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{4} \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, a^{4} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} - a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2} + 15 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} + 8 \, {\left(15 \, a^{4} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, a^{4} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{4} - 8 \, a^{3} b - 12 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{4} \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 16 \, {\left(2 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 16 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4} + 14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4} + 15 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} - 18 \, a^{3} b - 4 \, a^{2} b^{2} + 16 \, {\left(7 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3} + 6 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left(a^{4} \cosh\left(d x + c\right)^{10} + 10 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{4} \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, a^{4} \cosh\left(d x + c\right)^{2} + 3 \, a^{4} + 8 \, a^{3} b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2} + 14 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{4} \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, a^{4} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} - a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2} + 15 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} + 8 \, {\left(15 \, a^{4} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, a^{4} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{4} - 8 \, a^{3} b - 12 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{4} \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{4} + 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 8 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 8 \, {\left(2 \, {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^8 + 32*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 4*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*sinh(d*x + c)^8 + 8*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 8*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4 + 14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^3 + 3*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 8*(35*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^4 + 24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4 + 15*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*a^4 - 36*a^3*b - 8*a^2*b^2 + 32*(7*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^5 + 5*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + (24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2 + 8*(14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^6 + 15*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3 + 6*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*(a^4*cosh(d*x + c)^10 + 10*a^4*cosh(d*x + c)*sinh(d*x + c)^9 + a^4*sinh(d*x + c)^10 + (3*a^4 + 8*a^3*b)*cosh(d*x + c)^8 + (45*a^4*cosh(d*x + c)^2 + 3*a^4 + 8*a^3*b)*sinh(d*x + c)^8 + 8*(15*a^4*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 2*(105*a^4*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 8*a^2*b^2 + 14*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*a^4*cosh(d*x + c)^5 + 14*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^3 + 3*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(105*a^4*cosh(d*x + c)^6 + 35*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^4 - a^4 - 4*a^3*b - 8*a^2*b^2 + 15*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 + 8*(15*a^4*cosh(d*x + c)^7 + 7*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^5 + 5*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - (a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^4 + 8*a^3*b)*cosh(d*x + c)^2 + (45*a^4*cosh(d*x + c)^8 + 28*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^6 + 30*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 - 3*a^4 - 8*a^3*b - 12*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*a^4*cosh(d*x + c)^9 + 4*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^7 + 6*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 - 4*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - (3*a^4 + 8*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 16*(2*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^7 + 3*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 2*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^10 + 10*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^10 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^8 + (45*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^8 + 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^6 - 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 35*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 15*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 7*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^5 + 5*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 - (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^6 + 30*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 - 12*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^2 - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 2*(5*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^7 + 6*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^5 - 4*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^8 + 16*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*sinh(d*x + c)^8 + 4*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 4*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4 + 14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^3 + 3*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 4*(35*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^4 + 24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4 + 15*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*a^4 - 18*a^3*b - 4*a^2*b^2 + 16*(7*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^5 + 5*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + (24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2 + 4*(14*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^6 + 15*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3 + 6*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*(a^4*cosh(d*x + c)^10 + 10*a^4*cosh(d*x + c)*sinh(d*x + c)^9 + a^4*sinh(d*x + c)^10 + (3*a^4 + 8*a^3*b)*cosh(d*x + c)^8 + (45*a^4*cosh(d*x + c)^2 + 3*a^4 + 8*a^3*b)*sinh(d*x + c)^8 + 8*(15*a^4*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 2*(105*a^4*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 8*a^2*b^2 + 14*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*a^4*cosh(d*x + c)^5 + 14*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^3 + 3*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(105*a^4*cosh(d*x + c)^6 + 35*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^4 - a^4 - 4*a^3*b - 8*a^2*b^2 + 15*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 + 8*(15*a^4*cosh(d*x + c)^7 + 7*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^5 + 5*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - (a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^4 + 8*a^3*b)*cosh(d*x + c)^2 + (45*a^4*cosh(d*x + c)^8 + 28*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^6 + 30*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 - 3*a^4 - 8*a^3*b - 12*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*a^4*cosh(d*x + c)^9 + 4*(3*a^4 + 8*a^3*b)*cosh(d*x + c)^7 + 6*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 - 4*(a^4 + 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - (3*a^4 + 8*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 8*(2*(8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^7 + 3*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 2*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^10 + 10*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^10 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^8 + (45*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^8 + 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^6 - 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 35*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 15*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 7*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^5 + 5*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 - (a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^6 + 30*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 - 12*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^2 - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 2*(5*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^7 + 6*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^5 - 4*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*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*sech(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*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,1,61,0,0.397071," ","integrate(cosh(d*x+c)^4*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a + 4 \, b\right)} d x + {\left(a \cosh\left(d x + c\right)^{3} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(a*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a + 4*b)*d*x + (a*cosh(d*x + c)^3 + 4*(a + b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
50,1,41,0,0.393716," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{a \sinh\left(d x + c\right)^{3} + 3 \, {\left(a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(a*sinh(d*x + c)^3 + 3*(a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/d","A",0
51,1,28,0,0.405204," ","integrate(cosh(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + 2 \, b\right)} d x + a \cosh\left(d x + c\right) \sinh\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((a + 2*b)*d*x + a*cosh(d*x + c)*sinh(d*x + c))/d","A",0
52,1,93,0,0.450464," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{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} + 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}{2 \, {\left(d \cosh\left(d x + c\right) + d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*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)/(d*cosh(d*x + c) + d*sinh(d*x + c))","B",0
53,1,321,0,0.409133," ","integrate(sech(d*x+c)*(a+b*sech(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
54,1,158,0,0.382948," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(3 \, 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(3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 3 \, a + 3 \, b\right)}}{3 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, d\right)}}"," ",0,"-4/3*((3*a + b)*cosh(d*x + c)^2 - 2*b*cosh(d*x + c)*sinh(d*x + c) + (3*a + b)*sinh(d*x + c)^2 + 3*a + 3*b)/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 + 4*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + 3*d)","B",0
55,1,1112,0,0.421594," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(4 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{7} + {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + 11 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a - 11 \, b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\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)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 12 \, a + 9 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, a + 3 \, b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a + 11 \, b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a - 3 \, 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 + 3*b)*cosh(d*x + c)^7 + 7*(4*a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (4*a + 3*b)*sinh(d*x + c)^7 + (4*a + 11*b)*cosh(d*x + c)^5 + (21*(4*a + 3*b)*cosh(d*x + c)^2 + 4*a + 11*b)*sinh(d*x + c)^5 + 5*(7*(4*a + 3*b)*cosh(d*x + c)^3 + (4*a + 11*b)*cosh(d*x + c))*sinh(d*x + c)^4 - (4*a + 11*b)*cosh(d*x + c)^3 + (35*(4*a + 3*b)*cosh(d*x + c)^4 + 10*(4*a + 11*b)*cosh(d*x + c)^2 - 4*a - 11*b)*sinh(d*x + c)^3 + (21*(4*a + 3*b)*cosh(d*x + c)^5 + 10*(4*a + 11*b)*cosh(d*x + c)^3 - 3*(4*a + 11*b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a + 3*b)*cosh(d*x + c)^8 + 8*(4*a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a + 3*b)*sinh(d*x + c)^8 + 4*(4*a + 3*b)*cosh(d*x + c)^6 + 4*(7*(4*a + 3*b)*cosh(d*x + c)^2 + 4*a + 3*b)*sinh(d*x + c)^6 + 8*(7*(4*a + 3*b)*cosh(d*x + c)^3 + 3*(4*a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(4*a + 3*b)*cosh(d*x + c)^4 + 2*(35*(4*a + 3*b)*cosh(d*x + c)^4 + 30*(4*a + 3*b)*cosh(d*x + c)^2 + 12*a + 9*b)*sinh(d*x + c)^4 + 8*(7*(4*a + 3*b)*cosh(d*x + c)^5 + 10*(4*a + 3*b)*cosh(d*x + c)^3 + 3*(4*a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(4*a + 3*b)*cosh(d*x + c)^2 + 4*(7*(4*a + 3*b)*cosh(d*x + c)^6 + 15*(4*a + 3*b)*cosh(d*x + c)^4 + 9*(4*a + 3*b)*cosh(d*x + c)^2 + 4*a + 3*b)*sinh(d*x + c)^2 + 8*((4*a + 3*b)*cosh(d*x + c)^7 + 3*(4*a + 3*b)*cosh(d*x + c)^5 + 3*(4*a + 3*b)*cosh(d*x + c)^3 + (4*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*a + 3*b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - (4*a + 3*b)*cosh(d*x + c) + (7*(4*a + 3*b)*cosh(d*x + c)^6 + 5*(4*a + 11*b)*cosh(d*x + c)^4 - 3*(4*a + 11*b)*cosh(d*x + c)^2 - 4*a - 3*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
56,1,343,0,0.384442," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(5 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(5 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(5 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{3} + 30 \, {\left(a + b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(5 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 10 \, 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 + b)*cosh(d*x + c)^3 + 6*(5*a + b)*cosh(d*x + c)*sinh(d*x + c)^2 + (5*a - 2*b)*sinh(d*x + c)^3 + 30*(a + b)*cosh(d*x + c) + (3*(5*a - 2*b)*cosh(d*x + c)^2 + 5*a + 10*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
57,1,78,0,0.399040," ","integrate(cosh(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x + {\left(a^{2} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(a^2*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*d*x + (a^2*cosh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
58,1,414,0,0.409166," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{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 \, {\left(3 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 8 \, a b\right)} \sinh\left(d x + c\right)^{2} - a^{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(a^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 8 \, a b\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*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*(3*a^2 + 8*a*b)*cosh(d*x + c)^4 + 3*(5*a^2*cosh(d*x + c)^2 + 3*a^2 + 8*a*b)*sinh(d*x + c)^4 + 4*(5*a^2*cosh(d*x + c)^3 + 3*(3*a^2 + 8*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a^2 + 8*a*b)*cosh(d*x + c)^2 + 3*(5*a^2*cosh(d*x + c)^4 + 6*(3*a^2 + 8*a*b)*cosh(d*x + c)^2 - 3*a^2 - 8*a*b)*sinh(d*x + c)^2 - a^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*cosh(d*x + c)^5 + 2*(3*a^2 + 8*a*b)*cosh(d*x + c)^3 - (3*a^2 + 8*a*b)*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
59,1,80,0,0.391810," ","integrate(cosh(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{a^{2} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{2} + 4 \, a b\right)} d x - 2 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 8 \, b^{2}\right)} \sinh\left(d x + c\right)}{8 \, d \cosh\left(d x + c\right)}"," ",0,"1/8*(a^2*sinh(d*x + c)^3 + 4*((a^2 + 4*a*b)*d*x - 2*b^2)*cosh(d*x + c) + (3*a^2*cosh(d*x + c)^2 + a^2 + 8*b^2)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
60,1,653,0,0.417965," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{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} + {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, {\left({\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 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 \, a^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(5 \, d \cosh\left(d x + c\right)^{4} + 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(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 + (a^2 + 2*b^2)*cosh(d*x + c)^4 + (15*a^2*cosh(d*x + c)^2 + a^2 + 2*b^2)*sinh(d*x + c)^4 + 4*(5*a^2*cosh(d*x + c)^3 + (a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 + 2*b^2)*cosh(d*x + c)^2 + (15*a^2*cosh(d*x + c)^4 + 6*(a^2 + 2*b^2)*cosh(d*x + c)^2 - a^2 - 2*b^2)*sinh(d*x + c)^2 - a^2 + 2*((4*a*b + b^2)*cosh(d*x + c)^5 + 5*(4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a*b + b^2)*sinh(d*x + c)^5 + 2*(4*a*b + b^2)*cosh(d*x + c)^3 + 2*(5*(4*a*b + b^2)*cosh(d*x + c)^2 + 4*a*b + b^2)*sinh(d*x + c)^3 + 2*(5*(4*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a*b + b^2)*cosh(d*x + c) + (5*(4*a*b + b^2)*cosh(d*x + c)^4 + 6*(4*a*b + b^2)*cosh(d*x + c)^2 + 4*a*b + b^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(3*a^2*cosh(d*x + c)^5 + 2*(a^2 + 2*b^2)*cosh(d*x + c)^3 - (a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5 + 2*d*cosh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (5*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
61,1,1372,0,0.429415," ","integrate(sech(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a b + 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a b - 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a b + 11 \, 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 + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a b + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a b - 3 \, 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 + 3*b^2)*cosh(d*x + c)^7 + 7*(8*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (8*a*b + 3*b^2)*sinh(d*x + c)^7 + (8*a*b + 11*b^2)*cosh(d*x + c)^5 + (21*(8*a*b + 3*b^2)*cosh(d*x + c)^2 + 8*a*b + 11*b^2)*sinh(d*x + c)^5 + 5*(7*(8*a*b + 3*b^2)*cosh(d*x + c)^3 + (8*a*b + 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (8*a*b + 11*b^2)*cosh(d*x + c)^3 + (35*(8*a*b + 3*b^2)*cosh(d*x + c)^4 + 10*(8*a*b + 11*b^2)*cosh(d*x + c)^2 - 8*a*b - 11*b^2)*sinh(d*x + c)^3 + (21*(8*a*b + 3*b^2)*cosh(d*x + c)^5 + 10*(8*a*b + 11*b^2)*cosh(d*x + c)^3 - 3*(8*a*b + 11*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 + 3*b^2)*cosh(d*x + c) + (7*(8*a*b + 3*b^2)*cosh(d*x + c)^6 + 5*(8*a*b + 11*b^2)*cosh(d*x + c)^4 - 3*(8*a*b + 11*b^2)*cosh(d*x + c)^2 - 8*a*b - 3*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
62,1,404,0,0.405768," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(15 \, a^{2} + 10 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{2} + 10 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(15 \, a^{2} + 10 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 30 \, a^{2} + 40 \, a b + 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 45 \, a^{2} + 70 \, a b + 40 \, b^{2} - 8 \, {\left({\left(5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a b + 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)^{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 + 10*a*b + 4*b^2)*cosh(d*x + c)^4 - 8*(5*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (15*a^2 + 10*a*b + 4*b^2)*sinh(d*x + c)^4 + 20*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(15*a^2 + 10*a*b + 4*b^2)*cosh(d*x + c)^2 + 30*a^2 + 40*a*b + 10*b^2)*sinh(d*x + c)^2 + 45*a^2 + 70*a*b + 40*b^2 - 8*((5*a*b + 2*b^2)*cosh(d*x + c)^3 + 5*(a*b + b^2)*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
63,1,2946,0,0.432477," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{11} + {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(165 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(55 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(165 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 6 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(231 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 21 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} - 28 \, a b - 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(165 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 72 \, a^{2} - 204 \, a b - 85 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(55 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 40 \, a^{2} + 60 \, a b + 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 12 \, a b + 5 \, b^{2} + 12 \, {\left({\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} + 12 \, a b + 5 \, 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} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(8 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} + 28 \, a b + 33 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(72 \, a^{2} + 204 \, a b + 85 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} - 12 \, a b - 5 \, 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 + 12*a*b + 5*b^2)*cosh(d*x + c)^11 + 33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^11 + (72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^9 + (165*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 72*a^2 + 204*a*b + 85*b^2)*sinh(d*x + c)^9 + 9*(55*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + (72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 6*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^7 + 6*(165*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 6*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^2 + 8*a^2 + 28*a*b + 33*b^2)*sinh(d*x + c)^7 + 42*(33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^5 + 2*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^3 + (8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 6*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^5 + 6*(231*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^6 + 21*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^4 + 21*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^2 - 8*a^2 - 28*a*b - 33*b^2)*sinh(d*x + c)^5 + 6*(165*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^7 + 21*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^5 + 35*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^3 - 5*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^3 + (495*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^8 + 84*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^6 + 210*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^4 - 60*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^2 - 72*a^2 - 204*a*b - 85*b^2)*sinh(d*x + c)^3 + 3*(55*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^9 + 12*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^7 + 42*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^5 - 20*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^3 - (72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^12 + 12*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^12 + 6*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^10 + 6*(11*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^10 + 20*(11*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^8 + 15*(33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 18*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^8 + 24*(33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^5 + 30*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + 5*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^6 + 4*(231*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^6 + 315*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 105*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 40*a^2 + 60*a*b + 25*b^2)*sinh(d*x + c)^6 + 24*(33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^7 + 63*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^5 + 35*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + 5*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 15*(33*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^8 + 84*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^6 + 70*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 20*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^4 + 20*(11*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^9 + 36*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^7 + 42*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^5 + 20*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 6*(11*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^10 + 45*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^8 + 70*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^6 + 50*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^4 + 15*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^2 + 8*a^2 + 12*a*b + 5*b^2)*sinh(d*x + c)^2 + 8*a^2 + 12*a*b + 5*b^2 + 12*((8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^11 + 5*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^9 + 10*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^7 + 10*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^5 + 5*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^3 + (8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c) + 3*(11*(8*a^2 + 12*a*b + 5*b^2)*cosh(d*x + c)^10 + 3*(72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^8 + 14*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^6 - 10*(8*a^2 + 28*a*b + 33*b^2)*cosh(d*x + c)^4 - (72*a^2 + 204*a*b + 85*b^2)*cosh(d*x + c)^2 - 8*a^2 - 12*a*b - 5*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
64,1,677,0,0.389549," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(35 \, a^{2} + 14 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(35 \, a^{2} + 14 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{2} - 28 \, a b - 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 14 \, {\left(25 \, a^{2} + 34 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, {\left(35 \, a^{2} - 28 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 105 \, a^{2} + 84 \, a b - 84 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(10 \, {\left(35 \, a^{2} + 14 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(25 \, a^{2} + 34 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 28 \, {\left(25 \, a^{2} + 46 \, a b + 24 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(35 \, a^{2} - 28 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 63 \, {\left(5 \, a^{2} + 4 \, a b - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 70 \, a^{2} + 112 \, a b + 168 \, 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 + 14*a*b + 6*b^2)*cosh(d*x + c)^5 + 10*(35*a^2 + 14*a*b + 6*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (35*a^2 - 28*a*b - 12*b^2)*sinh(d*x + c)^5 + 14*(25*a^2 + 34*a*b + 6*b^2)*cosh(d*x + c)^3 + (10*(35*a^2 - 28*a*b - 12*b^2)*cosh(d*x + c)^2 + 105*a^2 + 84*a*b - 84*b^2)*sinh(d*x + c)^3 + 2*(10*(35*a^2 + 14*a*b + 6*b^2)*cosh(d*x + c)^3 + 21*(25*a^2 + 34*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 28*(25*a^2 + 46*a*b + 24*b^2)*cosh(d*x + c) + (5*(35*a^2 - 28*a*b - 12*b^2)*cosh(d*x + c)^4 + 63*(5*a^2 + 4*a*b - 4*b^2)*cosh(d*x + c)^2 + 70*a^2 + 112*a*b + 168*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
65,1,153,0,0.395423," ","integrate(cosh(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{a^{3} \sinh\left(d x + c\right)^{5} + {\left(10 \, a^{3} \cosh\left(d x + c\right)^{2} + 9 \, a^{3} + 24 \, a^{2} b\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(8 \, b^{3} - 3 \, {\left(a^{3} + 4 \, a^{2} b + 8 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right) + {\left(5 \, a^{3} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} + 24 \, a^{2} b + 64 \, b^{3} + 9 \, {\left(3 \, a^{3} + 8 \, a^{2} b\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*sinh(d*x + c)^5 + (10*a^3*cosh(d*x + c)^2 + 9*a^3 + 24*a^2*b)*sinh(d*x + c)^3 - 8*(8*b^3 - 3*(a^3 + 4*a^2*b + 8*a*b^2)*d*x)*cosh(d*x + c) + (5*a^3*cosh(d*x + c)^4 + 8*a^3 + 24*a^2*b + 64*b^3 + 9*(3*a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
66,1,1409,0,0.423135," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{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} + {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{2} + 11 \, a^{3} + 36 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{3} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3} + 14 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{3} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, a^{3} \cosh\left(d x + c\right)^{6} + 35 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 18 \, a^{2} b - 12 \, b^{3} + 15 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} - 36 \, a^{2} b - 12 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, 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} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a b^{2} + 2 \, b^{3} + 21 \, {\left(6 \, a b^{2} + 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} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a b^{2} + b^{3} + 20 \, {\left(6 \, a b^{2} + 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} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a b^{2} + 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 \, a^{3} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{3} + 36 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{3} + 18 \, a^{2} b + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{3} + 36 \, a^{2} b\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*cosh(d*x + c)^10 + 10*a^3*cosh(d*x + c)*sinh(d*x + c)^9 + a^3*sinh(d*x + c)^10 + (11*a^3 + 36*a^2*b)*cosh(d*x + c)^8 + (45*a^3*cosh(d*x + c)^2 + 11*a^3 + 36*a^2*b)*sinh(d*x + c)^8 + 8*(15*a^3*cosh(d*x + c)^3 + (11*a^3 + 36*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^6 + 2*(105*a^3*cosh(d*x + c)^4 + 5*a^3 + 18*a^2*b + 12*b^3 + 14*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*a^3*cosh(d*x + c)^5 + 14*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^3 + 3*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^4 + 2*(105*a^3*cosh(d*x + c)^6 + 35*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^4 - 5*a^3 - 18*a^2*b - 12*b^3 + 15*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*a^3*cosh(d*x + c)^7 + 7*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^5 + 5*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^3 - (5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - (11*a^3 + 36*a^2*b)*cosh(d*x + c)^2 + (45*a^3*cosh(d*x + c)^8 + 28*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^6 + 30*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^4 - 11*a^3 - 36*a^2*b - 12*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*((6*a*b^2 + b^3)*cosh(d*x + c)^7 + 7*(6*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a*b^2 + b^3)*sinh(d*x + c)^7 + 2*(6*a*b^2 + b^3)*cosh(d*x + c)^5 + (12*a*b^2 + 2*b^3 + 21*(6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a*b^2 + b^3)*cosh(d*x + c)^3 + 2*(6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a*b^2 + b^3)*cosh(d*x + c)^3 + (35*(6*a*b^2 + b^3)*cosh(d*x + c)^4 + 6*a*b^2 + b^3 + 20*(6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a*b^2 + b^3)*cosh(d*x + c)^5 + 20*(6*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a*b^2 + b^3)*cosh(d*x + c)^6 + 10*(6*a*b^2 + b^3)*cosh(d*x + c)^4 + 3*(6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(5*a^3*cosh(d*x + c)^9 + 4*(11*a^3 + 36*a^2*b)*cosh(d*x + c)^7 + 6*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^5 - 4*(5*a^3 + 18*a^2*b + 12*b^3)*cosh(d*x + c)^3 - (11*a^3 + 36*a^2*b)*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
67,1,270,0,0.426778," ","integrate(cosh(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, a^{3} \sinh\left(d x + c\right)^{5} - 4 \, {\left(18 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(a^{3} + 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(18 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(a^{3} + 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(30 \, a^{3} \cosh\left(d x + c\right)^{2} + 9 \, a^{3} + 72 \, a b^{2} + 16 \, b^{3}\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(18 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(a^{3} + 6 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right) + 3 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 24 \, a b^{2} + 16 \, b^{3} + {\left(9 \, a^{3} + 72 \, a b^{2} + 16 \, 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*sinh(d*x + c)^5 - 4*(18*a*b^2 + 4*b^3 - 3*(a^3 + 6*a^2*b)*d*x)*cosh(d*x + c)^3 - 12*(18*a*b^2 + 4*b^3 - 3*(a^3 + 6*a^2*b)*d*x)*cosh(d*x + c)*sinh(d*x + c)^2 + (30*a^3*cosh(d*x + c)^2 + 9*a^3 + 72*a*b^2 + 16*b^3)*sinh(d*x + c)^3 - 12*(18*a*b^2 + 4*b^3 - 3*(a^3 + 6*a^2*b)*d*x)*cosh(d*x + c) + 3*(5*a^3*cosh(d*x + c)^4 + 2*a^3 + 24*a*b^2 + 16*b^3 + (9*a^3 + 72*a*b^2 + 16*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
68,1,1992,0,0.466347," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} \cosh\left(d x + c\right)^{10} + 20 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 2 \, a^{3} \sinh\left(d x + c\right)^{10} + 3 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(30 \, a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(10 \, a^{3} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(420 \, a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3} + 84 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(84 \, a^{3} \cosh\left(d x + c\right)^{5} + 28 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(420 \, a^{3} \cosh\left(d x + c\right)^{6} + 210 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 12 \, a b^{2} - 11 \, b^{3} + 15 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(60 \, a^{3} \cosh\left(d x + c\right)^{7} + 42 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, a^{3} - 3 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(30 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{3} - 4 \, a b^{2} - b^{3} - 2 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, 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 + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3} + 9 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + 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 + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + 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 + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 4 \, a b^{2} + b^{3} + 15 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(3 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 4 \, a b^{2} + b^{3} + 12 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + 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 \, a^{3} \cosh\left(d x + c\right)^{9} + 12 \, {\left(2 \, a^{3} + 4 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 12 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} + 4 \, a b^{2} + 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*cosh(d*x + c)^10 + 20*a^3*cosh(d*x + c)*sinh(d*x + c)^9 + 2*a^3*sinh(d*x + c)^10 + 3*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^8 + 3*(30*a^3*cosh(d*x + c)^2 + 2*a^3 + 4*a*b^2 + b^3)*sinh(d*x + c)^8 + 24*(10*a^3*cosh(d*x + c)^3 + (2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + (4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^6 + (420*a^3*cosh(d*x + c)^4 + 4*a^3 + 12*a*b^2 + 11*b^3 + 84*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(84*a^3*cosh(d*x + c)^5 + 28*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - (4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + (420*a^3*cosh(d*x + c)^6 + 210*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^4 - 4*a^3 - 12*a*b^2 - 11*b^3 + 15*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(60*a^3*cosh(d*x + c)^7 + 42*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^5 + 5*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - (4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*a^3 - 3*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^2 + 3*(30*a^3*cosh(d*x + c)^8 + 28*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^6 + 5*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^4 - 2*a^3 - 4*a*b^2 - b^3 - 2*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^9 + 9*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^2*b + 4*a*b^2 + b^3)*sinh(d*x + c)^9 + 4*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^7 + 4*(8*a^2*b + 4*a*b^2 + b^3 + 9*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^3 + (8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^5 + 6*(21*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^4 + 8*a^2*b + 4*a*b^2 + b^3 + 14*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^5 + 70*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^3 + 15*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^3 + 4*(21*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^6 + 35*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^4 + 8*a^2*b + 4*a*b^2 + b^3 + 15*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 12*(3*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^7 + 7*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^5 + 5*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^3 + (8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c) + (9*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^6 + 30*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^4 + 8*a^2*b + 4*a*b^2 + b^3 + 12*(8*a^2*b + 4*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(10*a^3*cosh(d*x + c)^9 + 12*(2*a^3 + 4*a*b^2 + b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^5 - 2*(4*a^3 + 12*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - 3*(2*a^3 + 4*a*b^2 + 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
69,1,3465,0,0.473400," ","integrate(sech(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{11} + {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3} + 165 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(55 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 18 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(55 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3} + 2 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, 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 + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 18 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 18 \, {\left(77 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 7 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 8 \, a^{2} b - 14 \, a b^{2} - 11 \, b^{3} + 21 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, 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 + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 630 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 216 \, a^{2} b - 306 \, a b^{2} - 85 \, b^{3} - 180 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, 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 + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 60 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, 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 + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{2} b + 14 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{2} b - 18 \, a b^{2} - 5 \, b^{3} - {\left(216 \, a^{2} b + 306 \, a b^{2} + 85 \, 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 + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 33*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(24*a^2*b + 18*a*b^2 + 5*b^3)*sinh(d*x + c)^11 + (216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^9 + (216*a^2*b + 306*a*b^2 + 85*b^3 + 165*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(55*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 18*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^7 + 18*(55*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 8*a^2*b + 14*a*b^2 + 11*b^3 + 2*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 42*(33*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 2*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^3 + 3*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 18*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^5 + 18*(77*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 7*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^4 - 8*a^2*b - 14*a*b^2 - 11*b^3 + 21*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 18*(55*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 7*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^5 + 35*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - 5*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - (216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^3 + (495*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 84*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^6 + 630*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^4 - 216*a^2*b - 306*a*b^2 - 85*b^3 - 180*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 3*(55*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 12*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^7 + 126*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^5 - 60*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - (216*a^2*b + 306*a*b^2 + 85*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 + 18*a*b^2 + 5*b^3)*cosh(d*x + c) + 3*(11*(24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 3*(216*a^2*b + 306*a*b^2 + 85*b^3)*cosh(d*x + c)^8 + 42*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^6 - 30*(8*a^2*b + 14*a*b^2 + 11*b^3)*cosh(d*x + c)^4 - 24*a^2*b - 18*a*b^2 - 5*b^3 - (216*a^2*b + 306*a*b^2 + 85*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
70,1,816,0,0.436776," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(35 \, a^{3} + 35 \, a^{2} b + 28 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 6 \, {\left(35 \, a^{2} b + 28 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(35 \, a^{3} + 35 \, a^{2} b + 28 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 14 \, {\left(15 \, a^{3} + 25 \, a^{2} b + 14 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(210 \, a^{3} + 350 \, a^{2} b + 196 \, a b^{2} + 56 \, b^{3} + 15 \, {\left(35 \, a^{3} + 35 \, a^{2} b + 28 \, a b^{2} + 8 \, 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 + 28 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(5 \, a^{2} b + 7 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 350 \, a^{3} + 770 \, a^{2} b + 700 \, a b^{2} + 280 \, b^{3} + 7 \, {\left(75 \, a^{3} + 155 \, a^{2} b + 124 \, a b^{2} + 24 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(35 \, a^{3} + 35 \, a^{2} b + 28 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 525 \, a^{3} + 1085 \, a^{2} b + 868 \, a b^{2} + 168 \, b^{3} + 84 \, {\left(15 \, a^{3} + 25 \, a^{2} b + 14 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(3 \, {\left(35 \, a^{2} b + 28 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(5 \, a^{2} b + 7 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(25 \, a^{2} b + 44 \, a b^{2} + 24 \, 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 + 35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)^6 - 6*(35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (35*a^3 + 35*a^2*b + 28*a*b^2 + 8*b^3)*sinh(d*x + c)^6 + 14*(15*a^3 + 25*a^2*b + 14*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + (210*a^3 + 350*a^2*b + 196*a*b^2 + 56*b^3 + 15*(35*a^3 + 35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 4*(5*(35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + 28*(5*a^2*b + 7*a*b^2 + 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 350*a^3 + 770*a^2*b + 700*a*b^2 + 280*b^3 + 7*(75*a^3 + 155*a^2*b + 124*a*b^2 + 24*b^3)*cosh(d*x + c)^2 + (15*(35*a^3 + 35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 525*a^3 + 1085*a^2*b + 868*a*b^2 + 168*b^3 + 84*(15*a^3 + 25*a^2*b + 14*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*(3*(35*a^2*b + 28*a*b^2 + 8*b^3)*cosh(d*x + c)^5 + 56*(5*a^2*b + 7*a*b^2 + 2*b^3)*cosh(d*x + c)^3 + 7*(25*a^2*b + 44*a*b^2 + 24*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
71,1,6114,0,0.504603," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 45 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + 3 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \sinh\left(d x + c\right)^{15} + {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3} + 315 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + {\left(4095 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3} + 78 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(15015 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 715 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3} + 55 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 429 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 55 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + {\left(19305 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1716 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 330 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 960 \, a^{3} - 4464 \, a^{2} b - 6792 \, a b^{2} - 5053 \, b^{3} + 36 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(15015 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 462 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 84 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9009 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1287 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1728 \, a^{3} - 7344 \, a^{2} b - 9192 \, a b^{2} - 2681 \, b^{3} - 21 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(4095 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 715 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 330 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(1365 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 165 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 960 \, a^{3} - 3312 \, a^{2} b - 2760 \, a b^{2} - 805 \, b^{3} - 10 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(315 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 78 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 21 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 16 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \sinh\left(d x + c\right)^{16} + 8 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 8 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 15 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 26 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 143 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 33 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 385 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 12012 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6930 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2240 \, a^{3} + 5040 \, a^{2} b + 4200 \, a b^{2} + 1225 \, b^{3} + 1260 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1386 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 420 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 429 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 143 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 198 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 495 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 175 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 30 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, 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} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 26 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 8 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 91 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 231 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 315 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 245 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3} + 21 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left({\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 7 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 21 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 35 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 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) - 3 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(45 \, {\left(64 \, a^{3} + 144 \, a^{2} b + 120 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 13 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 11 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 9 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 7 \, {\left(960 \, a^{3} + 4464 \, a^{2} b + 6792 \, a b^{2} + 5053 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(1728 \, a^{3} + 7344 \, a^{2} b + 9192 \, a b^{2} + 2681 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 192 \, a^{3} - 432 \, a^{2} b - 360 \, a b^{2} - 105 \, b^{3} - 3 \, {\left(960 \, a^{3} + 3312 \, a^{2} b + 2760 \, a b^{2} + 805 \, 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 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^15 + 45*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)*sinh(d*x + c)^14 + 3*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*sinh(d*x + c)^15 + (960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^13 + (960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3 + 315*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(105*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + (960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + (1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^11 + (4095*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3 + 78*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(819*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 26*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^3 + (1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + (960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^9 + (15015*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 715*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^4 + 960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3 + 55*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(6435*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 429*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^5 + 55*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^3 + 3*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - (960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^7 + (19305*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 1716*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^6 + 330*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^4 - 960*a^3 - 4464*a^2*b - 6792*a*b^2 - 5053*b^3 + 36*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (15015*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 1716*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^7 + 462*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^5 + 84*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^3 - 7*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - (1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^5 + (9009*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 1287*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^8 + 462*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^6 + 126*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^4 - 1728*a^3 - 7344*a^2*b - 9192*a*b^2 - 2681*b^3 - 21*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (4095*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 715*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^9 + 330*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^7 + 126*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^5 - 35*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^3 - 5*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - (960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^3 + (1365*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^12 + 286*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^10 + 165*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^8 + 84*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^6 - 35*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^4 - 960*a^3 - 3312*a^2*b - 2760*a*b^2 - 805*b^3 - 10*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (315*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^13 + 78*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^11 + 55*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^9 + 36*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^7 - 21*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^5 - 10*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^3 - 3*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^16 + 16*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)*sinh(d*x + c)^15 + (64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*sinh(d*x + c)^16 + 8*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^14 + 8*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 15*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 112*(5*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + (64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 28*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^12 + 28*(65*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 26*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 112*(39*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 26*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 3*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 56*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 56*(143*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 143*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 33*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 16*(715*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 1001*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 385*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 70*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 2*(6435*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 12012*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 6930*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 2240*a^3 + 5040*a^2*b + 4200*a*b^2 + 1225*b^3 + 1260*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 1716*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 1386*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 420*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 56*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 56*(143*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 429*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 462*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 210*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 112*(39*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 143*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 198*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 126*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + 3*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 28*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 28*(65*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^12 + 286*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 495*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 420*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 175*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 30*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 112*(5*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^13 + 26*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 55*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 60*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 10*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + (64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 8*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2 + 8*(15*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^14 + 91*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^12 + 231*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^10 + 315*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^8 + 245*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^6 + 105*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^4 + 64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3 + 21*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 16*((64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^15 + 7*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^13 + 21*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^9 + 35*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 21*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^5 + 7*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^3 + (64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c) + (45*(64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*cosh(d*x + c)^14 + 13*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*b^3)*cosh(d*x + c)^12 + 11*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^10 + 9*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^8 - 7*(960*a^3 + 4464*a^2*b + 6792*a*b^2 + 5053*b^3)*cosh(d*x + c)^6 - 5*(1728*a^3 + 7344*a^2*b + 9192*a*b^2 + 2681*b^3)*cosh(d*x + c)^4 - 192*a^3 - 432*a^2*b - 360*a*b^2 - 105*b^3 - 3*(960*a^3 + 3312*a^2*b + 2760*a*b^2 + 805*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
72,1,1190,0,0.416771," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(105 \, a^{3} + 63 \, a^{2} b + 54 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(105 \, a^{3} + 63 \, a^{2} b + 54 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(105 \, a^{3} - 126 \, a^{2} b - 108 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 6 \, {\left(245 \, a^{3} + 399 \, a^{2} b + 162 \, a b^{2} + 48 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(175 \, a^{3} + 42 \, a^{2} b - 324 \, a b^{2} - 96 \, b^{3} + 7 \, {\left(105 \, a^{3} - 126 \, a^{2} b - 108 \, a b^{2} - 32 \, 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} + 63 \, a^{2} b + 54 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(245 \, a^{3} + 399 \, a^{2} b + 162 \, a b^{2} + 48 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 18 \, {\left(245 \, a^{3} + 567 \, a^{2} b + 426 \, a b^{2} + 64 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(105 \, a^{3} - 126 \, a^{2} b - 108 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 945 \, a^{3} + 1134 \, a^{2} b - 108 \, a b^{2} - 1152 \, b^{3} + 30 \, {\left(175 \, a^{3} + 42 \, a^{2} b - 324 \, a b^{2} - 96 \, 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} + 63 \, a^{2} b + 54 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(245 \, a^{3} + 399 \, a^{2} b + 162 \, a b^{2} + 48 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(245 \, a^{3} + 567 \, a^{2} b + 426 \, a b^{2} + 64 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 210 \, {\left(35 \, a^{3} + 93 \, a^{2} b + 90 \, a b^{2} + 32 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(105 \, a^{3} - 126 \, a^{2} b - 108 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(175 \, a^{3} + 42 \, a^{2} b - 324 \, a b^{2} - 96 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 525 \, a^{3} + 882 \, a^{2} b + 756 \, a b^{2} + 1344 \, b^{3} + 27 \, {\left(105 \, a^{3} + 126 \, a^{2} b - 12 \, a b^{2} - 128 \, 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 + 63*a^2*b + 54*a*b^2 + 16*b^3)*cosh(d*x + c)^7 + 14*(105*a^3 + 63*a^2*b + 54*a*b^2 + 16*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (105*a^3 - 126*a^2*b - 108*a*b^2 - 32*b^3)*sinh(d*x + c)^7 + 6*(245*a^3 + 399*a^2*b + 162*a*b^2 + 48*b^3)*cosh(d*x + c)^5 + 3*(175*a^3 + 42*a^2*b - 324*a*b^2 - 96*b^3 + 7*(105*a^3 - 126*a^2*b - 108*a*b^2 - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(105*a^3 + 63*a^2*b + 54*a*b^2 + 16*b^3)*cosh(d*x + c)^3 + 3*(245*a^3 + 399*a^2*b + 162*a*b^2 + 48*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 18*(245*a^3 + 567*a^2*b + 426*a*b^2 + 64*b^3)*cosh(d*x + c)^3 + (35*(105*a^3 - 126*a^2*b - 108*a*b^2 - 32*b^3)*cosh(d*x + c)^4 + 945*a^3 + 1134*a^2*b - 108*a*b^2 - 1152*b^3 + 30*(175*a^3 + 42*a^2*b - 324*a*b^2 - 96*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 6*(7*(105*a^3 + 63*a^2*b + 54*a*b^2 + 16*b^3)*cosh(d*x + c)^5 + 10*(245*a^3 + 399*a^2*b + 162*a*b^2 + 48*b^3)*cosh(d*x + c)^3 + 9*(245*a^3 + 567*a^2*b + 426*a*b^2 + 64*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 210*(35*a^3 + 93*a^2*b + 90*a*b^2 + 32*b^3)*cosh(d*x + c) + (7*(105*a^3 - 126*a^2*b - 108*a*b^2 - 32*b^3)*cosh(d*x + c)^6 + 15*(175*a^3 + 42*a^2*b - 324*a*b^2 - 96*b^3)*cosh(d*x + c)^4 + 525*a^3 + 882*a^2*b + 756*a*b^2 + 1344*b^3 + 27*(105*a^3 + 126*a^2*b - 12*a*b^2 - 128*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
73,1,1713,0,0.458472," ","integrate(cosh(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \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 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(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 + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \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 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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 \, a^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(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 + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 8*(3*a^2 - 4*a*b + 8*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^2 - a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 6*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 + 4*(3*a^2 - 4*a*b + 8*b^2)*d*x + 60*(a^2 - a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 4*(3*a^2 - 4*a*b + 8*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*cosh(d*x + c)^6 + 12*(3*a^2 - 4*a*b + 8*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*(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 + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - a^2 + 8*(a^2*cosh(d*x + c)^7 + 4*(3*a^2 - 4*a*b + 8*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*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4), 1/64*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 8*(3*a^2 - 4*a*b + 8*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^2 - a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 6*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 + 4*(3*a^2 - 4*a*b + 8*b^2)*d*x + 60*(a^2 - a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 4*(3*a^2 - 4*a*b + 8*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*cosh(d*x + c)^6 + 12*(3*a^2 - 4*a*b + 8*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*(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 + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - a^2 + 8*(a^2*cosh(d*x + c)^7 + 4*(3*a^2 - 4*a*b + 8*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*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4)]","B",0
74,1,1616,0,0.465065," ","integrate(cosh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2} + 5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - a^{2} b - 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} + a^{2} b + 4 \, a b^{2} + 6 \, {\left(3 \, a^{3} - a^{2} b - 4 \, 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 6 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2} + 5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - a^{2} b - 3 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} + a^{2} b + 4 \, a b^{2} + 6 \, {\left(3 \, a^{3} - a^{2} b - 4 \, 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, 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 \, {\left(a + b\right)}}\right) + 6 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} - a^{2} b - 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*((a^3 + a^2*b)*cosh(d*x + c)^6 + 6*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + a^2*b)*sinh(d*x + c)^6 + 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 - a^2*b - 4*a*b^2 + 5*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - a^2*b - 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^2 + 3*(5*(a^3 + a^2*b)*cosh(d*x + c)^4 - 3*a^3 + a^2*b + 4*a*b^2 + 6*(3*a^3 - a^2*b - 4*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*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 6*((a^3 + a^2*b)*cosh(d*x + c)^5 + 2*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^3 - (3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^3 + 3*(a^4 + a^3*b)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a^4 + a^3*b)*d*sinh(d*x + c)^3), 1/24*((a^3 + a^2*b)*cosh(d*x + c)^6 + 6*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + a^2*b)*sinh(d*x + c)^6 + 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 - a^2*b - 4*a*b^2 + 5*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - a^2*b - 3*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^2 + 3*(5*(a^3 + a^2*b)*cosh(d*x + c)^4 - 3*a^3 + a^2*b + 4*a*b^2 + 6*(3*a^3 - a^2*b - 4*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*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*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 + b)) + 6*((a^3 + a^2*b)*cosh(d*x + c)^5 + 2*(3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c)^3 - (3*a^3 - a^2*b - 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^3 + 3*(a^4 + a^3*b)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a^4 + a^3*b)*d*sinh(d*x + c)^3)]","B",0
75,1,829,0,0.456929," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a - 2 \, b\right)} d x \cosh\left(d x + c\right)^{2} + 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 \, {\left(2 \, {\left(a - 2 \, b\right)} d x + 3 \, a \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 + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(2 \, {\left(a - 2 \, b\right)} d x \cosh\left(d x + c\right) + a \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) - a}{8 \, {\left(a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2}\right)}}, \frac{4 \, {\left(a - 2 \, b\right)} d x \cosh\left(d x + c\right)^{2} + 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 \, {\left(2 \, {\left(a - 2 \, b\right)} d x + 3 \, a \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 + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(2 \, {\left(a - 2 \, b\right)} d x \cosh\left(d x + c\right) + a \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) - a}{8 \, {\left(a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/8*(4*(a - 2*b)*d*x*cosh(d*x + c)^2 + a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 + 2*(2*(a - 2*b)*d*x + 3*a*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 + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(2*(a - 2*b)*d*x*cosh(d*x + c) + a*cosh(d*x + c)^3)*sinh(d*x + c) - a)/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2), 1/8*(4*(a - 2*b)*d*x*cosh(d*x + c)^2 + a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 + 2*(2*(a - 2*b)*d*x + 3*a*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 + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(2*(a - 2*b)*d*x*cosh(d*x + c) + a*cosh(d*x + c)^3)*sinh(d*x + c) - a)/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2)]","B",0
76,1,718,0,0.459371," ","integrate(cosh(d*x+c)/(a+b*sech(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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - a^{2} - a b}{2 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right) + {\left(a^{3} + a^{2} b\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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, 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 \, {\left(a + b\right)}}\right) - a^{2} - a b}{2 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right) + {\left(a^{3} + a^{2} b\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*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - a^2 - a*b)/((a^3 + a^2*b)*d*cosh(d*x + c) + (a^3 + a^2*b)*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*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*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 + b)) - a^2 - a*b)/((a^3 + a^2*b)*d*cosh(d*x + c) + (a^3 + a^2*b)*d*sinh(d*x + c))]","B",0
77,1,487,0,0.423184," ","integrate(sech(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right)}{2 \, {\left(a^{2} + a b\right)} d}, \frac{\sqrt{a^{2} + a b} \arctan\left(\frac{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, 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 \, {\left(a + b\right)}}\right)}{{\left(a^{2} + a b\right)} d}\right]"," ",0,"[-1/2*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a))/((a^2 + a*b)*d), (sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*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 + b)))/((a^2 + a*b)*d)]","B",0
78,1,411,0,0.429315," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right)}{2 \, \sqrt{a b + b^{2}} d}, \frac{\sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right)}{{\left(a b + b^{2}\right)} d}\right]"," ",0,"[1/2*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a))/(sqrt(a*b + b^2)*d), sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2))/((a*b + b^2)*d)]","B",0
79,1,526,0,0.436811," ","integrate(sech(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{a + b}} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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{a}{a + b}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{2 \, b d}, -\frac{\sqrt{\frac{a}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}}}{2 \, a}\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/(a + b))*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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(-a/(a + b)) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*arctan(cosh(d*x + c) + sinh(d*x + c)))/(b*d), -(sqrt(a/(a + b))*arctan(1/2*sqrt(a/(a + b))*(cosh(d*x + c) + sinh(d*x + c))) + sqrt(a/(a + b))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))*sqrt(a/(a + b))/a) - 2*arctan(cosh(d*x + c) + sinh(d*x + c)))/(b*d)]","B",0
80,1,645,0,0.425839," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\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{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, a b - 4 \, b^{2}}{2 \, {\left({\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a b^{2} + b^{3}\right)} d\right)}}, -\frac{{\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{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 2 \, a b + 2 \, b^{2}}{{\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a b^{2} + b^{3}\right)} d}\right]"," ",0,"[1/2*((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 + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*a*b - 4*b^2)/((a*b^2 + b^3)*d*cosh(d*x + c)^2 + 2*(a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c) + (a*b^2 + b^3)*d*sinh(d*x + c)^2 + (a*b^2 + b^3)*d), -((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 - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 2*a*b + 2*b^2)/((a*b^2 + b^3)*d*cosh(d*x + c)^2 + 2*(a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c) + (a*b^2 + b^3)*d*sinh(d*x + c)^2 + (a*b^2 + b^3)*d)]","B",0
81,1,1518,0,0.488507," ","integrate(sech(d*x+c)^5/(a+b*sech(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(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)} \sqrt{-\frac{a}{a + b}} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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{a}{a + b}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 2 \, {\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) - 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(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)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\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)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}}}{2 \, a}\right) - {\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)}{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*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)*sqrt(-a/(a + b))*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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(-a/(a + b)) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 2*((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)) - 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*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)*sqrt(a/(a + b))*arctan(1/2*sqrt(a/(a + b))*(cosh(d*x + c) + sinh(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)*sqrt(a/(a + b))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))*sqrt(a/(a + b))/a) - ((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))/(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
82,1,1905,0,0.488255," ","integrate(sech(d*x+c)^6/(a+b*sech(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 + 4 \, a b^{2} - 8 \, b^{3} + 24 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(a^{2} b - b^{3} + 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(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)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{6} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d + 6 \, {\left({\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\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 + 2 \, a b^{2} - 4 \, b^{3} + 12 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a^{2} b - b^{3} + 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(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)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 24 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{6} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} + b^{4}\right)} d + 6 \, {\left({\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\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 + 4*a*b^2 - 8*b^3 + 24*(a^2*b - b^3)*cosh(d*x + c)^2 + 24*(a^2*b - b^3 + 3*(a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 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))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 48*((a^2*b + a*b^2)*cosh(d*x + c)^3 + (a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 + b^4)*d*cosh(d*x + c)^6 + 6*(a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a*b^3 + b^4)*d*sinh(d*x + c)^6 + 3*(a*b^3 + b^4)*d*cosh(d*x + c)^4 + 3*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a*b^3 + b^4)*d)*sinh(d*x + c)^4 + 3*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + 4*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^3 + 3*(a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^4 + 6*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a*b^3 + b^4)*d + 6*((a*b^3 + b^4)*d*cosh(d*x + c)^5 + 2*(a*b^3 + b^4)*d*cosh(d*x + c)^3 + (a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 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 + 2*a*b^2 - 4*b^3 + 12*(a^2*b - b^3)*cosh(d*x + c)^2 + 12*(a^2*b - b^3 + 3*(a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 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))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 24*((a^2*b + a*b^2)*cosh(d*x + c)^3 + (a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 + b^4)*d*cosh(d*x + c)^6 + 6*(a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a*b^3 + b^4)*d*sinh(d*x + c)^6 + 3*(a*b^3 + b^4)*d*cosh(d*x + c)^4 + 3*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a*b^3 + b^4)*d)*sinh(d*x + c)^4 + 3*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + 4*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^3 + 3*(a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a*b^3 + b^4)*d*cosh(d*x + c)^4 + 6*(a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a*b^3 + b^4)*d + 6*((a*b^3 + b^4)*d*cosh(d*x + c)^5 + 2*(a*b^3 + b^4)*d*cosh(d*x + c)^3 + (a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
83,1,5842,0,0.539027," ","integrate(cosh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{10} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 16 \, a^{4} b + 31 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 60 \, a b^{4} + 35 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 11 \, a^{5} - 2 \, a^{4} b + 29 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 30 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, 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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} + 34 \, a b^{3} + 20 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 5 \, a b^{3} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, 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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{10} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 16 \, a^{4} b + 31 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 60 \, a b^{4} + 35 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 11 \, a^{5} - 2 \, a^{4} b + 29 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 30 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, 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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} + 34 \, a b^{3} + 20 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 5 \, a b^{3} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, 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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 12 \, {\left({\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} + 34 \, a b^{3} + 20 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 5 \, a b^{3} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, 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} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} + 17 \, a b^{3} + 10 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 5 \, a 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 \, {\left(a + b\right)}}\right) + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{5} + 16 \, a^{4} b - 31 \, a^{3} b^{2} - 102 \, a^{2} b^{3} - 60 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 2 \, a^{4} b - 29 \, a^{3} b^{2} - 20 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*((a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(d*x + c)^10 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^8 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^3 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^6 + 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^4 + 14*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^5 + 14*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^3 + 3*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^6 - 5*a^5 - 16*a^4*b + 31*a^3*b^2 + 102*a^2*b^3 + 60*a*b^4 + 35*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^4 + 15*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^7 + 7*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^5 + 5*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^3 - (5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^8 + 28*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^6 - 11*a^5 - 2*a^4*b + 29*a^3*b^2 + 20*a^2*b^3 + 30*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^4 - 12*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 6*((6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 5*a*b^3)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 + 34*a*b^3 + 20*b^4 + 21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^4 + 6*a^2*b^2 + 5*a*b^3 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^9 + 4*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^7 + 6*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^5 - 4*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^3 - (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 + 7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^7 + 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^7 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (21*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^5 + (a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 5*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 + 20*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b + a^5*b^2)*d)*sinh(d*x + c)^3 + (21*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 + 20*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/24*((a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(d*x + c)^10 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^8 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^3 + (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^6 + 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^4 + 14*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^5 + 14*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^3 + 3*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^6 - 5*a^5 - 16*a^4*b + 31*a^3*b^2 + 102*a^2*b^3 + 60*a*b^4 + 35*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^4 + 15*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^7 + 7*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^5 + 5*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^3 - (5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^8 + 28*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^6 - 11*a^5 - 2*a^4*b + 29*a^3*b^2 + 20*a^2*b^3 + 30*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^4 - 12*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 5*a*b^3)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 + 34*a*b^3 + 20*b^4 + 21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^4 + 6*a^2*b^2 + 5*a*b^3 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 12*((6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 5*a*b^3)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 + 34*a*b^3 + 20*b^4 + 21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^4 + 6*a^2*b^2 + 5*a*b^3 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 + 17*a*b^3 + 10*b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 5*a*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 + b)) + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^9 + 4*(11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c)^7 + 6*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^5 - 4*(5*a^5 + 16*a^4*b - 31*a^3*b^2 - 102*a^2*b^3 - 60*a*b^4)*cosh(d*x + c)^3 - (11*a^5 + 2*a^4*b - 29*a^3*b^2 - 20*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 + 7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^7 + 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^7 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (21*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^5 + (a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 5*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 + 20*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b + a^5*b^2)*d)*sinh(d*x + c)^3 + (21*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 + 20*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
84,1,3739,0,0.492019," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 4 \, a b^{2} - 8 \, b^{3} + 4 \, {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 6 \, a b^{2} - 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b - 6 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x - 24 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\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 + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(10 \, a^{2} b + 28 \, a b^{2} + 16 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b + 4 \, a b^{2} + 12 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, 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 + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 4 \, a 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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 6 \, a b^{2} - 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + a^{4} b\right)} d \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 4 \, a b^{2} - 8 \, b^{3} + 4 \, {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 6 \, a b^{2} - 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b - 6 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x - 24 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\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 + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(10 \, a^{2} b + 28 \, a b^{2} + 16 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b + 4 \, a b^{2} + 12 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, 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 + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{2} b + 14 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 4 \, a 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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(a b^{2} + 2 \, b^{3} - {\left(a^{3} - a^{2} b - 10 \, a b^{2} - 8 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 6 \, a b^{2} - 2 \, {\left(a^{3} - 3 \, a^{2} b - 4 \, 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} + a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + a^{4} b\right)} d \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/8*((a^3 + a^2*b)*cosh(d*x + c)^8 + 8*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + a^2*b)*sinh(d*x + c)^8 + 2*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x + 14*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(14*(a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + a^2*b)*cosh(d*x + c)^4 - 4*a*b^2 - 8*b^3 + 4*(a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x + 15*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + a^2*b)*cosh(d*x + c)^5 + 5*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - a^2*b - 2*(a^3 + 3*a^2*b + 6*a*b^2 - 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + a^2*b)*cosh(d*x + c)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^4 - a^3 - 3*a^2*b - 6*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x - 24*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*((5*a^2*b + 4*a*b^2)*cosh(d*x + c)^6 + 6*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 4*a*b^2)*sinh(d*x + c)^6 + 2*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + (10*a^2*b + 28*a*b^2 + 16*b^3 + 15*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^3 + 2*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^2*b + 4*a*b^2)*cosh(d*x + c)^2 + (15*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^4 + 5*a^2*b + 4*a*b^2 + 12*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^5 + 4*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (5*a^2*b + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(2*(a^3 + a^2*b)*cosh(d*x + c)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^3 - (a^3 + 3*a^2*b + 6*a*b^2 - 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^4*b)*d*cosh(d*x + c)^6 + 6*(a^5 + a^4*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5 + a^4*b)*d*sinh(d*x + c)^6 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^4 + (15*(a^5 + a^4*b)*d*cosh(d*x + c)^2 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d)*sinh(d*x + c)^4 + (a^5 + a^4*b)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + a^4*b)*d*cosh(d*x + c)^3 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + a^4*b)*d*cosh(d*x + c)^4 + 12*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + a^4*b)*d)*sinh(d*x + c)^2 + 2*(3*(a^5 + a^4*b)*d*cosh(d*x + c)^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^3 + a^2*b)*cosh(d*x + c)^8 + 8*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + a^2*b)*sinh(d*x + c)^8 + 2*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x + 14*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(14*(a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + a^2*b)*cosh(d*x + c)^4 - 4*a*b^2 - 8*b^3 + 4*(a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x + 15*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + a^2*b)*cosh(d*x + c)^5 + 5*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - a^2*b - 2*(a^3 + 3*a^2*b + 6*a*b^2 - 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + a^2*b)*cosh(d*x + c)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^4 - a^3 - 3*a^2*b - 6*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x - 24*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((5*a^2*b + 4*a*b^2)*cosh(d*x + c)^6 + 6*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 4*a*b^2)*sinh(d*x + c)^6 + 2*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + (10*a^2*b + 28*a*b^2 + 16*b^3 + 15*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^3 + 2*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^2*b + 4*a*b^2)*cosh(d*x + c)^2 + (15*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^4 + 5*a^2*b + 4*a*b^2 + 12*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 4*a*b^2)*cosh(d*x + c)^5 + 4*(5*a^2*b + 14*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (5*a^2*b + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(2*(a^3 + a^2*b)*cosh(d*x + c)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(a*b^2 + 2*b^3 - (a^3 - a^2*b - 10*a*b^2 - 8*b^3)*d*x)*cosh(d*x + c)^3 - (a^3 + 3*a^2*b + 6*a*b^2 - 2*(a^3 - 3*a^2*b - 4*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^4*b)*d*cosh(d*x + c)^6 + 6*(a^5 + a^4*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5 + a^4*b)*d*sinh(d*x + c)^6 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^4 + (15*(a^5 + a^4*b)*d*cosh(d*x + c)^2 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d)*sinh(d*x + c)^4 + (a^5 + a^4*b)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + a^4*b)*d*cosh(d*x + c)^3 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + a^4*b)*d*cosh(d*x + c)^4 + 12*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + a^4*b)*d)*sinh(d*x + c)^2 + 2*(3*(a^5 + a^4*b)*d*cosh(d*x + c)^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + a^4*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
85,1,3154,0,0.487012," ","integrate(cosh(d*x+c)/(a+b*sech(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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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} - 6 \, a^{3} b - 11 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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 + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 3 \, a b^{2} + 6 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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} - 6 \, a^{3} b - 11 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, 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 + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 3 \, a b^{2} + 6 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) - {\left({\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3} + 5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 3 \, a b^{2} + 6 \, {\left(4 \, a^{2} b + 11 \, a b^{2} + 6 \, 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 \, {\left(a + b\right)}}\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} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 6 \, a^{3} b + 11 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\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 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 2*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*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 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*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 - 6*a^3*b - 11*a^2*b^2 - 6*a*b^3 + 6*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 3*a*b^2)*sinh(d*x + c)^5 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 3*a*b^2)*cosh(d*x + c) + (5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 4*a^2*b + 3*a*b^2 + 6*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*(3*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 2*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 - (a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^5 + 5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^6 + 2*a^5*b + a^4*b^2)*d*sinh(d*x + c)^5 + 2*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c)^3 + 2*(5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^2 + (a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d)*sinh(d*x + c)^3 + (a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c) + 2*(5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^3 + 3*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^4 + 6*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + 2*a^5*b + a^4*b^2)*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 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + (a^4 + 6*a^3*b + 11*a^2*b^2 + 6*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 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^4 + 6*a^3*b + 11*a^2*b^2 + 6*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 - 6*a^3*b - 11*a^2*b^2 - 6*a*b^3 + 6*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 3*a*b^2)*sinh(d*x + c)^5 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 3*a*b^2)*cosh(d*x + c) + (5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 4*a^2*b + 3*a*b^2 + 6*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) - ((4*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 3*a*b^2)*sinh(d*x + c)^5 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b + 11*a*b^2 + 6*b^3 + 5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^2*b + 11*a*b^2 + 6*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 3*a*b^2)*cosh(d*x + c) + (5*(4*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 4*a^2*b + 3*a*b^2 + 6*(4*a^2*b + 11*a*b^2 + 6*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 + b)) + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 2*(a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 - (a^4 + 6*a^3*b + 11*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^5 + 5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^6 + 2*a^5*b + a^4*b^2)*d*sinh(d*x + c)^5 + 2*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c)^3 + 2*(5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^2 + (a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d)*sinh(d*x + c)^3 + (a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c) + 2*(5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^3 + 3*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^6 + 2*a^5*b + a^4*b^2)*d*cosh(d*x + c)^4 + 6*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + 2*a^5*b + a^4*b^2)*d)*sinh(d*x + c))]","B",0
86,1,1856,0,0.452896," ","integrate(sech(d*x+c)/(a+b*sech(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} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + a b + 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} - a b} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 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} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + a b + 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) - {\left({\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + a b + 4 \, {\left({\left(2 \, a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{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 \, {\left(a + b\right)}}\right) - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a^{2} b + a b^{2} - 3 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 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 + a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + a*b)*cosh(d*x + c)^2 + 2*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b + 4*((2*a^2 + a*b)*cosh(d*x + c)^3 + (2*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 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 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 2*a^4*b + a^3*b^2)*d*sinh(d*x + c)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 2*a^4*b + a^3*b^2)*d + 4*((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 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 + a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + a*b)*cosh(d*x + c)^2 + 2*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b + 4*((2*a^2 + a*b)*cosh(d*x + c)^3 + (2*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) - ((2*a^2 + a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + a*b)*cosh(d*x + c)^2 + 2*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b + 4*((2*a^2 + a*b)*cosh(d*x + c)^3 + (2*a^2 + 5*a*b + 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 + b)) - 2*(a^2*b + a*b^2)*cosh(d*x + c) - 2*(a^2*b + a*b^2 - 3*(a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 2*a^4*b + a^3*b^2)*d*sinh(d*x + c)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 2*a^4*b + a^3*b^2)*d + 4*((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
87,1,1489,0,0.444231," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \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)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^2*b + 4*a*b^2 + 4*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 8*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c) + 4*(a^2*b + 3*a*b^2 + 2*b^3)*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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/((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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a^2*b + 2*a*b^2 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 4*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c) + 2*(a^2*b + 3*a*b^2 + 2*b^3)*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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)))/((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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
88,1,1570,0,0.475174," ","integrate(sech(d*x+c)^3/(a+b*sech(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(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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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\right)} \sqrt{-a^{2} - a b} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 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)} \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(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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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\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 \, {\left(a + b\right)}}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 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)*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*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 + 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 + 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + (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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/(a + b)) - 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
89,1,1569,0,0.451491," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + {\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right)}{4 \, {\left({\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d + 4 \, {\left({\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\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 + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + {\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right)}{2 \, {\left({\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d + 4 \, {\left({\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 4 \, a^{2} b^{3} + 5 \, a b^{4} + 2 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^2*b + 4*a*b^2 + 4*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 8*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c) + 4*(a^2*b + 3*a*b^2 + 2*b^3)*sinh(d*x + c)^2 + ((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 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + 4*((a^2 + 2*a*b)*cosh(d*x + c)^3 + (a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/((a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d)*sinh(d*x + c)^2 + (a^3*b^2 + 2*a^2*b^3 + a*b^4)*d + 4*((a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*a^2*b + 2*a*b^2 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 4*(a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c) + 2*(a^2*b + 3*a*b^2 + 2*b^3)*sinh(d*x + c)^2 + ((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 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + 4*((a^2 + 2*a*b)*cosh(d*x + c)^3 + (a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)))/((a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d)*sinh(d*x + c)^2 + (a^3*b^2 + 2*a^2*b^3 + a*b^4)*d + 4*((a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^3*b^2 + 4*a^2*b^3 + 5*a*b^4 + 2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
90,1,2069,0,0.498074," ","integrate(sech(d*x+c)^5/(a+b*sech(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(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{a + b}} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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{a}{a + b}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 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(3 \, a b \cosh\left(d x + c\right)^{2} - a b\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} + 3 \, a b^{3} + 2 \, b^{4}\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} + 3 \, a b^{3} + 2 \, b^{4}\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} + 3 \, a b^{3} + 2 \, b^{4}\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(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 7 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\left(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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}}}{2 \, a}\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} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 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(3 \, a b \cosh\left(d x + c\right)^{2} - a b\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} + 3 \, a b^{3} + 2 \, b^{4}\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} + 3 \, a b^{3} + 2 \, b^{4}\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} + 3 \, a b^{3} + 2 \, 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*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) - ((2*a^2 + 3*a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 3*a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(d*x + c)^2 + 2*a^2 + 7*a*b + 6*b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(d*x + c)^3 + (2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/(a + b))*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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(-a/(a + b)) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 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 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + a*b)*cosh(d*x + c)^2 + a^2 + 3*a*b + 2*b^2)*sinh(d*x + c)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(d*x + c)^3 + (a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 4*(3*a*b*cosh(d*x + c)^2 - a*b)*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 + 3*a*b^3 + 2*b^4)*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 + 3*a*b^3 + 2*b^4)*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 + 3*a*b^3 + 2*b^4)*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) + ((2*a^2 + 3*a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 3*a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(d*x + c)^2 + 2*a^2 + 7*a*b + 6*b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(d*x + c)^3 + (2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*sqrt(a/(a + b))*(cosh(d*x + c) + sinh(d*x + c))) + ((2*a^2 + 3*a*b)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 3*a*b)*sinh(d*x + c)^4 + 2*(2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(d*x + c)^2 + 2*a^2 + 7*a*b + 6*b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(d*x + c)^3 + (2*a^2 + 7*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))*sqrt(a/(a + b))/a) - 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 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + a*b)*cosh(d*x + c)^2 + a^2 + 3*a*b + 2*b^2)*sinh(d*x + c)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(d*x + c)^3 + (a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(3*a*b*cosh(d*x + c)^2 - a*b)*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 + 3*a*b^3 + 2*b^4)*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 + 3*a*b^3 + 2*b^4)*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 + 3*a*b^3 + 2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
91,1,2958,0,0.480298," ","integrate(sech(d*x+c)^6/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 12 \, a^{3} b + 20 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \sinh\left(d x + c\right)^{6} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2} + 15 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a^{3} + 4 \, a^{2} b + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2} + 6 \, {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 16 \, {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d + 2 \, {\left(3 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a^{3} b + 10 \, a^{2} b^{2} + 4 \, a b^{3} + 4 \, {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \sinh\left(d x + c\right)^{6} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2} + 15 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a^{3} + 4 \, a^{2} b + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2} + 6 \, {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 24 \, a^{2} b + 16 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 8 \, {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b + 10 \, a^{2} b^{2} + 11 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d + 2 \, {\left(3 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 11 \, a b^{5} + 4 \, b^{6}\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 + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 16*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*sinh(d*x + c)^4 + 12*a^3*b + 20*a^2*b^2 + 8*a*b^3 + 8*(3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4)*cosh(d*x + c)^2 + 8*(3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4 + 3*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^3 + 4*a^2*b)*cosh(d*x + c)^6 + 6*(3*a^3 + 4*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3 + 4*a^2*b)*sinh(d*x + c)^6 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^4 + (9*a^3 + 24*a^2*b + 16*a*b^2 + 15*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^3 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a^3 + 4*a^2*b + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^2 + (15*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^4 + 9*a^3 + 24*a^2*b + 16*a*b^2 + 6*(9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^5 + 2*(9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^3 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 16*((3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + (3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^6 + 6*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*sinh(d*x + c)^6 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^4 + (15*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^2 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d)*sinh(d*x + c)^4 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^2 + 4*(5*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^3 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^4 + 6*(3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^2 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d)*sinh(d*x + c)^2 + (a^3*b^3 + 2*a^2*b^4 + a*b^5)*d + 2*(3*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^5 + 2*(3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^3 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 8*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*sinh(d*x + c)^4 + 6*a^3*b + 10*a^2*b^2 + 4*a*b^3 + 4*(3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4)*cosh(d*x + c)^2 + 4*(3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4 + 3*(3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^3 + 4*a^2*b)*cosh(d*x + c)^6 + 6*(3*a^3 + 4*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3 + 4*a^2*b)*sinh(d*x + c)^6 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^4 + (9*a^3 + 24*a^2*b + 16*a*b^2 + 15*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^3 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a^3 + 4*a^2*b + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^2 + (15*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^4 + 9*a^3 + 24*a^2*b + 16*a*b^2 + 6*(9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^3 + 4*a^2*b)*cosh(d*x + c)^5 + 2*(9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c)^3 + (9*a^3 + 24*a^2*b + 16*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 8*((3*a^3*b + 7*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + (3*a^3*b + 10*a^2*b^2 + 11*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^6 + 6*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*sinh(d*x + c)^6 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^4 + (15*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^2 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d)*sinh(d*x + c)^4 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^2 + 4*(5*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^3 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^4 + 6*(3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^2 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d)*sinh(d*x + c)^2 + (a^3*b^3 + 2*a^2*b^4 + a*b^5)*d + 2*(3*(a^3*b^3 + 2*a^2*b^4 + a*b^5)*d*cosh(d*x + c)^5 + 2*(3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c)^3 + (3*a^3*b^3 + 10*a^2*b^4 + 11*a*b^5 + 4*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
92,1,6499,0,0.580880," ","integrate(sech(d*x+c)^7/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3} + 21 \, {\left(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(7 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - 5 \, a b^{2} - 4 \, b^{3} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, 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 + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2} + 30 \, {\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)^{4} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 5 \, a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{a + b}} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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{a}{a + b}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, {\left({\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 7 \, {\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)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3} + 30 \, {\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)^{4} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 3 \, {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - 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) - 4 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - a b^{2} - 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\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 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b^{3} + 2 \, 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^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + a b^{4}\right)} d + 8 \, {\left({\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3} + 21 \, {\left(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(7 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - 5 \, a b^{2} - 4 \, b^{3} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, 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 + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2} + 30 \, {\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)^{4} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 5 \, a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2} + 30 \, {\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)^{4} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 5 \, a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\left(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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}}}{2 \, a}\right) - 2 \, {\left({\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 7 \, {\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)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3} + 30 \, {\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)^{4} + 8 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 4 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 3 \, {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 25 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - 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) - 2 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - a b^{2} - 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\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 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b^{3} + 2 \, 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^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + a b^{4}\right)} d + 8 \, {\left({\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} b^{3} + 7 \, a b^{4} + 4 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 28*(2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(2*a^2*b + a*b^2)*sinh(d*x + c)^7 + 4*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + 4*(2*a^2*b + 5*a*b^2 + 4*b^3 + 21*(2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(2*a^2*b + a*b^2)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + 4*(35*(2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 2*a^2*b - 5*a*b^2 - 4*b^3 + 10*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 10*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - 3*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a^3 + 5*a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + 5*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 5*a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2 + 7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 31*a^2*b + 20*a*b^2 + 30*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 5*a^2*b + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 5*a*b^2 + 3*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 5*a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/(a + b))*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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(-a/(a + b)) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*((4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^8 + 8*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 3*a^2*b - a*b^2)*sinh(d*x + c)^8 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^6 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^4 + 12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3 + 30*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^3 + (12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 3*a^2*b - a*b^2 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^6 + 15*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 3*(12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^7 + 3*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^5 + (12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + (4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(2*a^2*b + a*b^2)*cosh(d*x + c) + 4*(7*(2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 5*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^4 - 2*a^2*b - a*b^2 - 3*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((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 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^2*b^3 + 2*a*b^4 + b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + 3*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 30*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d)*sinh(d*x + c)^4 + 4*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 10*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 15*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 3*(3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^2 + (a^2*b^3 + 2*a*b^4 + b^5)*d)*sinh(d*x + c)^2 + (a^2*b^3 + a*b^4)*d + 8*((a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 3*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^5 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^3 + (a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 14*(2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(2*a^2*b + a*b^2)*sinh(d*x + c)^7 + 2*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + 2*(2*a^2*b + 5*a*b^2 + 4*b^3 + 21*(2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(2*a^2*b + a*b^2)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + 2*(35*(2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 2*a^2*b - 5*a*b^2 - 4*b^3 + 10*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 10*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - 3*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a^3 + 5*a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + 5*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 5*a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2 + 7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 31*a^2*b + 20*a*b^2 + 30*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 5*a^2*b + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 5*a*b^2 + 3*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 5*a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*sqrt(a/(a + b))*(cosh(d*x + c) + sinh(d*x + c))) + ((4*a^3 + 5*a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + 5*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 5*a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 5*a*b^2 + 7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 31*a^2*b + 20*a*b^2 + 30*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 5*a^2*b + 4*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 5*a*b^2 + 3*(12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 5*a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))*sqrt(a/(a + b))/a) - 2*((4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^8 + 8*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 3*a^2*b - a*b^2)*sinh(d*x + c)^8 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^6 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^4 + 12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3 + 30*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^3 + (12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 3*a^2*b - a*b^2 + 4*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^6 + 15*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 3*(12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^7 + 3*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^5 + (12*a^3 + 25*a^2*b + 9*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + (4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(2*a^2*b + a*b^2)*cosh(d*x + c) + 2*(7*(2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 5*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^4 - 2*a^2*b - a*b^2 - 3*(2*a^2*b + 5*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((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 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^2*b^3 + 2*a*b^4 + b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + 3*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 30*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d)*sinh(d*x + c)^4 + 4*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 10*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 15*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 3*(3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^2 + (a^2*b^3 + 2*a*b^4 + b^5)*d)*sinh(d*x + c)^2 + (a^2*b^3 + a*b^4)*d + 8*((a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 3*(a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c)^5 + (3*a^2*b^3 + 7*a*b^4 + 4*b^5)*d*cosh(d*x + c)^3 + (a^2*b^3 + 2*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
93,1,11740,0,0.655079," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2 \, a^{5} + 8 \, a^{4} b + 10 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x + 33 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 495 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x + 180 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(462 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 39 \, a^{3} b^{2} - 134 \, a^{2} b^{3} - 184 \, a b^{4} - 80 \, b^{5} + 420 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, a^{5} - 4 \, a^{4} b - 2 \, a^{3} b^{2} - 2 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 26 \, a^{4} b - 131 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4} + 70 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x - 30 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{5} + 8 \, a^{4} b + 23 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2 \, a^{5} - 8 \, a^{4} b - 23 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 15 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x - 3 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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 + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(140 \, a^{4} b + 504 \, a^{3} b^{2} + 544 \, a^{2} b^{3} + 192 \, a b^{4} + 45 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 56 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, a^{4} b + 252 \, a^{3} b^{2} + 272 \, a^{2} b^{3} + 96 \, a b^{4} + 140 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, 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 + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 30 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{5} + 8 \, a^{4} b + 23 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(2 \, a^{5} + 8 \, a^{4} b + 10 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x + 33 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 495 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x + 180 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(462 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 39 \, a^{3} b^{2} - 134 \, a^{2} b^{3} - 184 \, a b^{4} - 80 \, b^{5} + 420 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 26 \, a^{4} b - 131 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4} + 70 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x - 30 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{5} + 8 \, a^{4} b + 23 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2 \, a^{5} - 8 \, a^{4} b - 23 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 15 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x - 3 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\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 + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(140 \, a^{4} b + 504 \, a^{3} b^{2} + 544 \, a^{2} b^{3} + 192 \, a b^{4} + 45 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 56 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, a^{4} b + 252 \, a^{3} b^{2} + 272 \, a^{2} b^{3} + 96 \, a b^{4} + 140 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, 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 + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 30 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(105 \, a^{4} b + 448 \, a^{3} b^{2} + 800 \, a^{2} b^{3} + 640 \, a b^{4} + 192 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(35 \, a^{4} b + 126 \, a^{3} b^{2} + 136 \, a^{2} b^{3} + 48 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 56 \, a^{3} b^{2} + 24 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{5} + 26 \, a^{4} b + 27 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 32 \, a b^{4} + 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(39 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 184 \, a b^{4} + 80 \, b^{5} - 4 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 57 \, a^{3} b^{2} - 138 \, a^{2} b^{3} - 136 \, a b^{4} - 48 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{5} + 26 \, a^{4} b + 131 \, a^{3} b^{2} + 256 \, a^{2} b^{3} + 128 \, a b^{4} - 16 \, {\left(a^{5} - 2 \, a^{4} b - 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 12 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{5} + 8 \, a^{4} b + 23 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 11 \, a^{3} b^{2} - 6 \, 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} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(2*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^12 + 24*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^5 + 2*a^4*b + a^3*b^2)*sinh(d*x + c)^12 + 8*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^10 + 4*(2*a^5 + 8*a^4*b + 10*a^3*b^2 + 4*a^2*b^3 + 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x + 33*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(11*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^3 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^8 + 2*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 495*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x + 180*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^5 + 60*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^6 + 4*(462*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^6 - 39*a^3*b^2 - 134*a^2*b^3 - 184*a*b^4 - 80*b^5 + 420*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(198*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^7 + 252*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^3 - 3*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*a^5 - 4*a^4*b - 2*a^3*b^2 - 2*(5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^8 + 840*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 5*a^5 - 26*a^4*b - 131*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4 + 70*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x - 30*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(55*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^9 + 120*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^5 - 10*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^3 - (5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^5 + 8*a^4*b + 23*a^3*b^2 + 14*a^2*b^3 - 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^10 + 90*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^6 - 2*a^5 - 8*a^4*b - 23*a^3*b^2 - 14*a^2*b^3 - 15*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^4 + 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x - 3*(5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^10 + 10*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*sinh(d*x + c)^10 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^8 + (140*a^4*b + 504*a^3*b^2 + 544*a^2*b^3 + 192*a*b^4 + 45*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^3 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^6 + 2*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5 + 105*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^4 + 56*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^5 + 56*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^3 + 3*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^6 + 70*a^4*b + 252*a^3*b^2 + 272*a^2*b^3 + 96*a*b^4 + 140*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^4 + 15*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^7 + 28*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^5 + 5*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^3 + 2*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^2 + (45*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^8 + 112*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^6 + 35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3 + 30*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^4 + 24*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^9 + 16*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^7 + 6*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^5 + 8*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^3 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^11 + 10*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^7 - 3*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^5 - (5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^3 - (2*a^5 + 8*a^4*b + 23*a^3*b^2 + 14*a^2*b^3 - 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^10 + 10*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 2*a^7*b + a^6*b^2)*d*sinh(d*x + c)^10 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^8 + (45*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d)*sinh(d*x + c)^8 + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^3 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^4 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^2 + (3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^5 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^3 + 3*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^6 + 140*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^4 + 15*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d)*sinh(d*x + c)^4 + (a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^7 + 28*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^5 + 5*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^3 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^8 + 112*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^6 + 30*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^4 + 24*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^2 + (a^8 + 2*a^7*b + a^6*b^2)*d)*sinh(d*x + c)^2 + 2*(5*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^9 + 16*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^7 + 6*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^5 + 8*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^3 + (a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^12 + 12*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(d*x + c)^12 + 4*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^10 + 2*(2*a^5 + 8*a^4*b + 10*a^3*b^2 + 4*a^2*b^3 + 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x + 33*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^3 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + (5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^8 + (5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 495*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x + 180*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^5 + 60*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^6 + 2*(462*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^6 - 39*a^3*b^2 - 134*a^2*b^3 - 184*a*b^4 - 80*b^5 + 420*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(198*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^7 + 252*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^3 - 3*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 2*a^4*b - a^3*b^2 - (5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^4 + (495*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^8 + 840*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 5*a^5 - 26*a^4*b - 131*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4 + 70*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x - 30*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^9 + 120*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^5 - 10*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^3 - (5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^5 + 8*a^4*b + 23*a^3*b^2 + 14*a^2*b^3 - 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^2 + 2*(33*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^10 + 90*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^6 - 2*a^5 - 8*a^4*b - 23*a^3*b^2 - 14*a^2*b^3 - 15*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^4 + 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x - 3*(5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^10 + 10*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*sinh(d*x + c)^10 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^8 + (140*a^4*b + 504*a^3*b^2 + 544*a^2*b^3 + 192*a*b^4 + 45*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^3 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^6 + 2*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5 + 105*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^4 + 56*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^5 + 56*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^3 + 3*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^6 + 70*a^4*b + 252*a^3*b^2 + 272*a^2*b^3 + 96*a*b^4 + 140*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^4 + 15*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^7 + 28*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^5 + 5*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^3 + 2*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^2 + (45*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^8 + 112*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^6 + 35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3 + 30*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^4 + 24*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c)^9 + 16*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^7 + 6*(105*a^4*b + 448*a^3*b^2 + 800*a^2*b^3 + 640*a*b^4 + 192*b^5)*cosh(d*x + c)^5 + 8*(35*a^4*b + 126*a^3*b^2 + 136*a^2*b^3 + 48*a*b^4)*cosh(d*x + c)^3 + (35*a^4*b + 56*a^3*b^2 + 24*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(d*x + c)^11 + 10*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + (a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^5 + 26*a^4*b + 27*a^3*b^2 - 32*a^2*b^3 - 32*a*b^4 + 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^7 - 3*(39*a^3*b^2 + 134*a^2*b^3 + 184*a*b^4 + 80*b^5 - 4*(3*a^5 - 4*a^4*b - 57*a^3*b^2 - 138*a^2*b^3 - 136*a*b^4 - 48*b^5)*d*x)*cosh(d*x + c)^5 - (5*a^5 + 26*a^4*b + 131*a^3*b^2 + 256*a^2*b^3 + 128*a*b^4 - 16*(a^5 - 2*a^4*b - 19*a^3*b^2 - 28*a^2*b^3 - 12*a*b^4)*d*x)*cosh(d*x + c)^3 - (2*a^5 + 8*a^4*b + 23*a^3*b^2 + 14*a^2*b^3 - 2*(a^5 - 4*a^4*b - 11*a^3*b^2 - 6*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^10 + 10*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 2*a^7*b + a^6*b^2)*d*sinh(d*x + c)^10 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^8 + (45*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d)*sinh(d*x + c)^8 + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^3 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^4 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^2 + (3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^5 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^3 + 3*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^6 + 140*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^4 + 15*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d)*sinh(d*x + c)^4 + (a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^7 + 28*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^5 + 5*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^3 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^8 + 112*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^6 + 30*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^4 + 24*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^2 + (a^8 + 2*a^7*b + a^6*b^2)*d)*sinh(d*x + c)^2 + 2*(5*(a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c)^9 + 16*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^7 + 6*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^5 + 8*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*d*cosh(d*x + c)^3 + (a^8 + 2*a^7*b + a^6*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
94,1,9856,0,0.638791," ","integrate(cosh(d*x+c)/(a+b*sech(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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{8} + 4 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} - 28 \, a^{5} b - 104 \, a^{4} b^{2} - 209 \, a^{3} b^{3} - 189 \, a^{2} b^{4} - 60 \, a b^{5} + 70 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{6} - 34 \, a^{5} b - 78 \, a^{4} b^{2} - 75 \, a^{3} b^{3} - 25 \, a^{2} b^{4} + 15 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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 + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 35 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, 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 + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 10 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} - 28 \, a^{5} b - 104 \, a^{4} b^{2} - 209 \, a^{3} b^{3} - 189 \, a^{2} b^{4} - 60 \, a b^{5} + 70 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{6} - 34 \, a^{5} b - 78 \, a^{4} b^{2} - 75 \, a^{3} b^{3} - 25 \, a^{2} b^{4} + 15 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, 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 + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 35 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, 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 + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 10 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) - 3 \, {\left({\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4} + 35 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, 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 + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 12 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 10 \, {\left(24 \, a^{4} b + 100 \, a^{3} b^{2} + 175 \, a^{2} b^{3} + 136 \, a b^{4} + 40 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 28 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 10 \, a 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 \, {\left(a + b\right)}}\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} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} + 28 \, a^{5} b + 104 \, a^{4} b^{2} + 209 \, a^{3} b^{3} + 189 \, a^{2} b^{4} + 60 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{6} + 34 \, a^{5} b + 78 \, a^{4} b^{2} + 75 \, a^{3} b^{3} + 25 \, a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{9} + 17 \, a^{8} b + 41 \, a^{7} b^{2} + 51 \, a^{6} b^{3} + 32 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 2 \, a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3}\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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^8 + 4*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4 + 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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^6 + 4*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^3 + 3*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 - 28*a^5*b - 104*a^4*b^2 - 209*a^3*b^3 - 189*a^2*b^4 - 60*a*b^5 + 70*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^4 + 15*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^5 + 5*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^3 - (4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^6 - 6*a^6 - 34*a^5*b - 78*a^4*b^2 - 75*a^3*b^3 - 25*a^2*b^4 + 15*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^4 - 6*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^9 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*sinh(d*x + c)^9 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^7 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^3 + (8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5 + 63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^4 + 42*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^5 + 70*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^6 + 8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 35*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^4 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^7 + 21*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^5 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c) + (9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^8 + 28*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^6 + 8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3 + 10*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^7 + 3*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^5 - 2*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^3 - (6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^9 + 9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*sinh(d*x + c)^9 + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^7 + 4*(9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^2 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d)*sinh(d*x + c)^7 + 2*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^5 + 28*(3*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^3 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^4 + 42*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^2 + (3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d)*sinh(d*x + c)^5 + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^3 + 2*(63*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^5 + 70*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^3 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^6 + 35*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^4 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^2 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d)*sinh(d*x + c)^3 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c) + 4*(9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^7 + 21*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^5 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^3 + 3*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^8 + 28*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^6 + 10*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^4 + 12*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^2 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^8 + 2*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4 + 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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^6 + 2*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^3 + 3*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 - 28*a^5*b - 104*a^4*b^2 - 209*a^3*b^3 - 189*a^2*b^4 - 60*a*b^5 + 70*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^4 + 15*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^5 + 5*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^3 - (4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^6 - 6*a^6 - 34*a^5*b - 78*a^4*b^2 - 75*a^3*b^3 - 25*a^2*b^4 + 15*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^4 - 6*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^9 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*sinh(d*x + c)^9 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^7 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^3 + (8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5 + 63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^4 + 42*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^5 + 70*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^6 + 8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 35*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^4 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^7 + 21*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^5 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c) + (9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^8 + 28*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^6 + 8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3 + 10*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) - 3*((8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^9 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*sinh(d*x + c)^9 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^7 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^3 + (8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5 + 63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^4 + 42*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^5 + 70*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^6 + 8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4 + 35*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^4 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^7 + 21*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^5 + 5*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c) + (9*(8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^8 + 28*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*b^4)*cosh(d*x + c)^6 + 8*a^4*b + 12*a^3*b^2 + 5*a^2*b^3 + 10*(24*a^4*b + 100*a^3*b^2 + 175*a^2*b^3 + 136*a*b^4 + 40*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 28*a^3*b^2 + 29*a^2*b^3 + 10*a*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 + b)) + 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 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c)^7 + 3*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^5 - 2*(4*a^6 + 28*a^5*b + 104*a^4*b^2 + 209*a^3*b^3 + 189*a^2*b^4 + 60*a*b^5)*cosh(d*x + c)^3 - (6*a^6 + 34*a^5*b + 78*a^4*b^2 + 75*a^3*b^3 + 25*a^2*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^9 + 9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*sinh(d*x + c)^9 + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^7 + 4*(9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^2 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d)*sinh(d*x + c)^7 + 2*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^5 + 28*(3*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^3 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^4 + 42*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^2 + (3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d)*sinh(d*x + c)^5 + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^3 + 2*(63*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^5 + 70*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^3 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^6 + 35*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^4 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^2 + (a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d)*sinh(d*x + c)^3 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c) + 4*(9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^7 + 21*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^5 + 5*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^3 + 3*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d*cosh(d*x + c)^8 + 28*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^6 + 10*(3*a^9 + 17*a^8*b + 41*a^7*b^2 + 51*a^6*b^3 + 32*a^5*b^4 + 8*a^4*b^5)*d*cosh(d*x + c)^4 + 12*(a^9 + 5*a^8*b + 9*a^7*b^2 + 7*a^6*b^3 + 2*a^5*b^4)*d*cosh(d*x + c)^2 + (a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3)*d)*sinh(d*x + c))]","B",0
95,1,6806,0,0.541434," ","integrate(sech(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4} + 21 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4} - 35 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, 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 + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, 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(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{4} b - 13 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, 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} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4} + 21 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4} - 35 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, 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 + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, 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(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) - {\left({\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, 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(8 \, a^{4} + 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 88 \, a^{3} b + 137 \, a^{2} b^{2} + 88 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 24 \, a^{3} b + 19 \, a^{2} b^{2} + 6 \, a 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 \, {\left(a + b\right)}}\right) - 2 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(8 \, a^{4} b + 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{4} b - 13 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} b + 37 \, a^{3} b^{2} + 41 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, 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} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} 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*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^7 + 28*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*sinh(d*x + c)^7 + 4*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^5 + 4*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4 + 21*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^3 + (8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - 4*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4 - 35*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^4 - 10*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^5 + 10*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - 3*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 8*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4 + 30*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 8*a^3*b + 3*a^2*b^2 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 3*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c) + 4*(7*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^6 - 8*a^4*b - 13*a^3*b^2 - 5*a^2*b^3 + 5*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 - 3*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d + 8*((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^7 + 14*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*sinh(d*x + c)^7 + 2*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^5 + 2*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4 + 21*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^3 + (8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - 2*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4 - 35*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^4 - 10*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^5 + 10*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - 3*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 8*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4 + 30*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 8*a^3*b + 3*a^2*b^2 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 3*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) - ((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 8*a^3*b + 3*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4 + 30*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 8*a^3*b + 3*a^2*b^2 + 8*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3 + 3*(24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 88*a^3*b + 137*a^2*b^2 + 88*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (8*a^4 + 24*a^3*b + 19*a^2*b^2 + 6*a*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 + b)) - 2*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c) + 2*(7*(8*a^4*b + 13*a^3*b^2 + 5*a^2*b^3)*cosh(d*x + c)^6 - 8*a^4*b - 13*a^3*b^2 - 5*a^2*b^3 + 5*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 - 3*(8*a^4*b + 37*a^3*b^2 + 41*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d + 8*((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
96,1,5109,0,0.507532," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 20 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3} + 4 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5} + 15 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, 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 + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4} + 15 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, 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 + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, 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 + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d + 8 \, {\left({\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, 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 + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 10 \, a^{4} b + 14 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5} + 15 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, 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 + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4} + 15 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{4} \cosh\left(d x + c\right)^{8} + 8 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, a^{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{4} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 30 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + 3 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(3 \, {\left(5 \, a^{4} b + 21 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b + 61 \, a^{3} b^{2} + 102 \, a^{2} b^{3} + 72 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 47 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, 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 + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, 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 + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d + 8 \, {\left({\left(a^{7} b + 3 \, a^{6} b^{2} + 3 \, a^{5} b^{3} + a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 17 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 51 \, a^{4} b^{4} + 32 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 2 \, 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 + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^6 + 24*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*sinh(d*x + c)^6 + 20*a^4*b + 28*a^3*b^2 + 8*a^2*b^3 + 4*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^4 + 4*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5 + 15*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2 + 4*(15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4 + 15*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^4 + 6*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^5 + 2*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^3 + (15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^8 + 8*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*sinh(d*x + c)^8 + 4*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^3 + 3*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^4 + 30*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^5 + 10*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^6 + 15*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d)*sinh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d + 8*((a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^7 + 3*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^3 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^6 + 12*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*sinh(d*x + c)^6 + 10*a^4*b + 14*a^3*b^2 + 4*a^2*b^3 + 2*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^4 + 2*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5 + 15*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2 + 2*(15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4 + 15*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^4 + 6*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(a^4*cosh(d*x + c)^8 + 8*a^4*cosh(d*x + c)*sinh(d*x + c)^7 + a^4*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^6 + 4*(7*a^4*cosh(d*x + c)^2 + a^4 + 2*a^3*b)*sinh(d*x + c)^6 + 8*(7*a^4*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^4*cosh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 30*(a^4 + 2*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*(7*a^4*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b)*cosh(d*x + c)^3 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b)*cosh(d*x + c)^2 + 4*(7*a^4*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b)*cosh(d*x + c)^4 + a^4 + 2*a^3*b + 3*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^4*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b)*cosh(d*x + c)^5 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(3*(5*a^4*b + 21*a^3*b^2 + 24*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^5 + 2*(15*a^4*b + 61*a^3*b^2 + 102*a^2*b^3 + 72*a*b^4 + 16*b^5)*cosh(d*x + c)^3 + (15*a^4*b + 47*a^3*b^2 + 40*a^2*b^3 + 8*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^8 + 8*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*sinh(d*x + c)^8 + 4*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^3 + 3*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^4 + 30*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^5 + 10*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^6 + 15*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d)*sinh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d + 8*((a^7*b + 3*a^6*b^2 + 3*a^5*b^3 + a^4*b^4)*d*cosh(d*x + c)^7 + 3*(a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^7*b + 17*a^6*b^2 + 41*a^5*b^3 + 51*a^4*b^4 + 32*a^3*b^5 + 8*a^2*b^6)*d*cosh(d*x + c)^3 + (a^7*b + 5*a^6*b^2 + 9*a^5*b^3 + 7*a^4*b^4 + 2*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
97,1,6037,0,0.525930," ","integrate(sech(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 21 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 13 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} + 10 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a 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{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 5 \, a^{3} b - a^{2} b^{2} - 3 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 21 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 13 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} + 10 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a 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{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\left({\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + a^{2} b + 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 35 \, a^{2} b + 40 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 2 \, a 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 \, {\left(a + b\right)}}\right) - 2 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(4 \, a^{4} + 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 5 \, a^{3} b - a^{2} b^{2} - 3 \, {\left(4 \, a^{4} + 13 \, a^{3} b + 5 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, 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} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 8 \, {\left({\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 17 \, a^{6} b + 41 \, a^{5} b^{2} + 51 \, a^{4} b^{3} + 32 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 2 \, 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 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^7 + 28*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(4*a^4 + 5*a^3*b + a^2*b^2)*sinh(d*x + c)^7 + 4*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 4*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 21*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + (4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 4*(35*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^4 - 4*a^4 - 13*a^3*b - 5*a^2*b^2 + 4*a*b^3 + 10*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 10*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((4*a^3 + a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2 + 7*(4*a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3 + 30*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + a^2*b + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 2*a*b^2 + 3*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c) + 4*(7*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 5*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 5*a^3*b - a^2*b^2 - 3*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 8*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^8 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 30*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 10*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 15*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 8*((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^7 + 14*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(4*a^4 + 5*a^3*b + a^2*b^2)*sinh(d*x + c)^7 + 2*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 2*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 21*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + (4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 2*(35*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^4 - 4*a^4 - 13*a^3*b - 5*a^2*b^2 + 4*a*b^3 + 10*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 10*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a^3 + a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2 + 7*(4*a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3 + 30*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + a^2*b + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 2*a*b^2 + 3*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((4*a^3 + a^2*b)*cosh(d*x + c)^8 + 8*(4*a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + a^2*b)*sinh(d*x + c)^8 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 9*a^2*b + 2*a*b^2 + 7*(4*a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^3 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + a^2*b)*cosh(d*x + c)^4 + 12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3 + 30*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^5 + 10*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + a^2*b + 4*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + a^2*b)*cosh(d*x + c)^6 + 15*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 9*a^2*b + 2*a*b^2 + 3*(12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + a^2*b)*cosh(d*x + c)^7 + 3*(4*a^3 + 9*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 35*a^2*b + 40*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 2*a*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 + b)) - 2*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c) + 2*(7*(4*a^4 + 5*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 5*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 5*a^3*b - a^2*b^2 - 3*(4*a^4 + 13*a^3*b + 5*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 8*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^8 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 30*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 10*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 15*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d + 8*((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 17*a^6*b + 41*a^5*b^2 + 51*a^4*b^3 + 32*a^3*b^4 + 8*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 5*a^6*b + 9*a^5*b^2 + 7*a^4*b^3 + 2*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
98,1,5447,0,0.518872," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, a^{4} b - 4 \, a^{3} b^{2} - 8 \, a^{2} b^{3} + 4 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5} + 15 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, a b^{4} + 15 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2} + 7 \, {\left(a^{4} + 4 \, a^{3} b\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\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3} + 30 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2} + 3 \, {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\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\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, 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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, 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^{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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, 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} + 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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, a^{4} b - 2 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 2 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5} + 15 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, a b^{4} + 15 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2} + 7 \, {\left(a^{4} + 4 \, a^{3} b\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\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3} + 30 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2} + 3 \, {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\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\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 20 \, a^{3} b + 40 \, a^{2} b^{2} + 32 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(3 \, {\left(a^{4} b + 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 5 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 24 \, a b^{4} - 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b - a^{3} b^{2} - 20 \, a^{2} b^{3} - 16 \, 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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, 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^{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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, 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} + 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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\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} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 17 \, a^{5} b^{3} + 41 \, a^{4} b^{4} + 51 \, a^{3} b^{5} + 32 \, a^{2} b^{6} + 8 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 9 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 2 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(4*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^6 + 24*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*sinh(d*x + c)^6 + 4*a^4*b - 4*a^3*b^2 - 8*a^2*b^3 + 4*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^4 + 4*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5 + 15*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^3 + (3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*a*b^4)*cosh(d*x + c)^2 + 4*(3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*a*b^4 + 15*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^4 + 6*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((a^4 + 4*a^3*b)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b)*sinh(d*x + c)^8 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2 + 7*(a^4 + 4*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^3 + 3*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b)*cosh(d*x + c)^4 + 3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3 + 30*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 8*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^5 + 10*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^6 + 15*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + a^4 + 6*a^3*b + 8*a^2*b^2 + 3*(3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b)*cosh(d*x + c)^7 + 3*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + (3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + (a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^5 + 2*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^3 + (3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d*cosh(d*x + c)^3 + (a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^6 + 12*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*sinh(d*x + c)^6 + 2*a^4*b - 2*a^3*b^2 - 4*a^2*b^3 + 2*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^4 + 2*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5 + 15*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^3 + (3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*a*b^4)*cosh(d*x + c)^2 + 2*(3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*a*b^4 + 15*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^4 + 6*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((a^4 + 4*a^3*b)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b)*sinh(d*x + c)^8 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2 + 7*(a^4 + 4*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^3 + 3*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b)*cosh(d*x + c)^4 + 3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3 + 30*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 8*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^5 + 10*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + (3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b)*cosh(d*x + c)^6 + 15*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + a^4 + 6*a^3*b + 8*a^2*b^2 + 3*(3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b)*cosh(d*x + c)^7 + 3*(a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + (3*a^4 + 20*a^3*b + 40*a^2*b^2 + 32*a*b^3)*cosh(d*x + c)^3 + (a^4 + 6*a^3*b + 8*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(3*(a^4*b + 5*a^3*b^2 + 4*a^2*b^3)*cosh(d*x + c)^5 + 2*(3*a^4*b + 5*a^3*b^2 - 6*a^2*b^3 - 24*a*b^4 - 16*b^5)*cosh(d*x + c)^3 + (3*a^4*b - a^3*b^2 - 20*a^2*b^3 - 16*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*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 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 17*a^5*b^3 + 41*a^4*b^4 + 51*a^3*b^5 + 32*a^2*b^6 + 8*a*b^7)*d*cosh(d*x + c)^3 + (a^6*b^2 + 5*a^5*b^3 + 9*a^4*b^4 + 7*a^3*b^5 + 2*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
99,1,5006,0,0.512382," ","integrate(sech(d*x+c)^5/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 84 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 12 \, {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2} + 63 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(21 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(105 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} - 31 \, a^{2} b - 20 \, a b^{2} + 10 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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)} \sqrt{-a^{2} - a b} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 12 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) + 4 \, {\left(21 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 3 \, a^{2} b - 3 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2} + 63 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(105 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} - 31 \, a^{2} b - 20 \, a b^{2} + 10 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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)} \sqrt{a^{2} + a b} \arctan\left(\frac{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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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)} \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 \, {\left(a + b\right)}}\right) - 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right) + 2 \, {\left(21 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 3 \, a^{2} b - 3 \, {\left(11 \, a^{3} + 31 \, a^{2} b + 20 \, 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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\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} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 17 \, a^{5} b + 41 \, a^{4} b^{2} + 51 \, a^{3} b^{3} + 32 \, a^{2} b^{4} + 8 \, a b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 5 \, a^{5} b + 9 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(12*(a^3 + a^2*b)*cosh(d*x + c)^7 + 84*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 12*(a^3 + a^2*b)*sinh(d*x + c)^7 + 4*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^5 + 4*(11*a^3 + 31*a^2*b + 20*a*b^2 + 63*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(21*(a^3 + a^2*b)*cosh(d*x + c)^3 + (11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 + 4*(105*(a^3 + a^2*b)*cosh(d*x + c)^4 - 11*a^3 - 31*a^2*b - 20*a*b^2 + 10*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(63*(a^3 + a^2*b)*cosh(d*x + c)^5 + 10*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 - 3*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 12*(a^3 + a^2*b)*cosh(d*x + c) + 4*(21*(a^3 + a^2*b)*cosh(d*x + c)^6 + 5*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 3*a^2*b - 3*(11*a^3 + 31*a^2*b + 20*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d*cosh(d*x + c)^2 + (a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^5 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d*cosh(d*x + c)^3 + (a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(6*(a^3 + a^2*b)*cosh(d*x + c)^7 + 42*(a^3 + a^2*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 6*(a^3 + a^2*b)*sinh(d*x + c)^7 + 2*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^5 + 2*(11*a^3 + 31*a^2*b + 20*a*b^2 + 63*(a^3 + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(21*(a^3 + a^2*b)*cosh(d*x + c)^3 + (11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 + 2*(105*(a^3 + a^2*b)*cosh(d*x + c)^4 - 11*a^3 - 31*a^2*b - 20*a*b^2 + 10*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(63*(a^3 + a^2*b)*cosh(d*x + c)^5 + 10*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^3 - 3*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 3*(a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + b)) - 6*(a^3 + a^2*b)*cosh(d*x + c) + 2*(21*(a^3 + a^2*b)*cosh(d*x + c)^6 + 5*(11*a^3 + 31*a^2*b + 20*a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 3*a^2*b - 3*(11*a^3 + 31*a^2*b + 20*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d*cosh(d*x + c)^2 + (a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*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 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c)^5 + (3*a^6 + 17*a^5*b + 41*a^4*b^2 + 51*a^3*b^3 + 32*a^2*b^4 + 8*a*b^5)*d*cosh(d*x + c)^3 + (a^6 + 5*a^5*b + 9*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
100,1,5887,0,0.527554," ","integrate(sech(d*x+c)^6/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 12 \, a^{4} b + 36 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 12 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5} + 5 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, 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 + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4} + 15 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a 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^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{4} b + 18 \, a^{3} b^{2} + 12 \, a^{2} b^{3} + 6 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5} + 5 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, 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 + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4} + 15 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 8 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 48 \, a^{3} b + 112 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(3 \, {\left(3 \, a^{4} b + 11 \, a^{3} b^{2} + 16 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{4} b + 17 \, a^{3} b^{2} + 38 \, a^{2} b^{3} + 40 \, a b^{4} + 16 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b + 49 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 40 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a 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^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 41 \, a^{3} b^{5} + 51 \, a^{2} b^{6} + 32 \, a b^{7} + 8 \, b^{8}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 5 \, a^{4} b^{4} + 9 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 2 \, a b^{7}\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 + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^6 + 24*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*sinh(d*x + c)^6 + 12*a^4*b + 36*a^3*b^2 + 24*a^2*b^3 + 12*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^4 + 12*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5 + 5*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^3 + 3*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4)*cosh(d*x + c)^2 + 4*(9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4 + 15*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^4 + 18*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3 + 7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4 + 30*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3 + 3*(9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^5 + 6*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^3 + (9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^8 + 4*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 3*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 30*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^2 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d)*sinh(d*x + c)^4 + 4*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 10*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^3 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 15*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^2 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d)*sinh(d*x + c)^2 + (a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d + 8*((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 3*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^5 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^3 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^6 + 12*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*sinh(d*x + c)^6 + 6*a^4*b + 18*a^3*b^2 + 12*a^2*b^3 + 6*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^4 + 6*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5 + 5*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^3 + 3*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4)*cosh(d*x + c)^2 + 2*(9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4 + 15*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^4 + 18*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 8*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3 + 7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4 + 30*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 8*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3 + 3*(9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 8*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 48*a^3*b + 112*a^2*b^2 + 128*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 14*a^3*b + 24*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(3*(3*a^4*b + 11*a^3*b^2 + 16*a^2*b^3 + 8*a*b^4)*cosh(d*x + c)^5 + 6*(3*a^4*b + 17*a^3*b^2 + 38*a^2*b^3 + 40*a*b^4 + 16*b^5)*cosh(d*x + c)^3 + (9*a^4*b + 49*a^3*b^2 + 80*a^2*b^3 + 40*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^8 + 4*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 3*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 30*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^2 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d)*sinh(d*x + c)^4 + 4*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 10*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^3 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 15*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^2 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d)*sinh(d*x + c)^2 + (a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d + 8*((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 3*(a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c)^5 + (3*a^5*b^3 + 17*a^4*b^4 + 41*a^3*b^5 + 51*a^2*b^6 + 32*a*b^7 + 8*b^8)*d*cosh(d*x + c)^3 + (a^5*b^3 + 5*a^4*b^4 + 9*a^3*b^5 + 7*a^2*b^6 + 2*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
101,1,7993,0,0.624159," ","integrate(sech(d*x+c)^7/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3} + 21 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 31 \, a^{2} b^{2} - 36 \, a b^{3} + 10 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, 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^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4} + 30 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{a + b}} \log\left(\frac{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 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 2 \, 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{a}{a + b}} + a}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a 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) - 4 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} - 3 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3} + 21 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 31 \, a^{2} b^{2} - 36 \, a b^{3} + 10 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, 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^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4} + 30 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4} + 30 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{4} + 20 \, a^{3} b + 15 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} + 124 \, a^{3} b + 269 \, a^{2} b^{2} + 280 \, a b^{3} + 120 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} + 36 \, a^{3} b + 55 \, a^{2} b^{2} + 30 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}} \arctan\left(\frac{{\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} + {\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a + b}}}{2 \, a}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a 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) - 2 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(4 \, a^{3} b + 7 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} - 3 \, {\left(4 \, a^{3} b + 31 \, a^{2} b^{2} + 36 \, a b^{3}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\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} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} b^{3} + 14 \, a^{3} b^{4} + 27 \, a^{2} b^{5} + 24 \, a b^{6} + 8 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} b^{3} + 4 \, a^{3} b^{4} + 5 \, a^{2} b^{5} + 2 \, a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^7 + 28*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(4*a^3*b + 7*a^2*b^2)*sinh(d*x + c)^7 + 4*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^5 + 4*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3 + 21*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^3 + (4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^3 + 4*(35*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^4 - 4*a^3*b - 31*a^2*b^2 - 36*a*b^3 + 10*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^5 + 10*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 20*a^3*b + 15*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4 + 30*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 20*a^3*b + 15*a^2*b^2 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 3*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^3 + (8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/(a + b))*log((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(3*a + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - 3*a - 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (3*a + 2*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(-a/(a + b)) + a)/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c) + 4*(7*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^6 + 5*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^4 - 4*a^3*b - 7*a^2*b^2 - 3*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^2 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d)*sinh(d*x + c)^4 + 4*(a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^3 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d*cosh(d*x + c)^2 + (a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^5 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d*cosh(d*x + c)^3 + (a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^7 + 14*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(4*a^3*b + 7*a^2*b^2)*sinh(d*x + c)^7 + 2*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^5 + 2*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3 + 21*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^3 + (4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^3 + 2*(35*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^4 - 4*a^3*b - 31*a^2*b^2 - 36*a*b^3 + 10*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^5 + 10*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 20*a^3*b + 15*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4 + 30*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 20*a^3*b + 15*a^2*b^2 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 3*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^3 + (8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*sqrt(a/(a + b))*(cosh(d*x + c) + sinh(d*x + c))) + ((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^8 + 8*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 20*a^3*b + 15*a^2*b^2)*sinh(d*x + c)^8 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^6 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^3 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^4 + 24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4 + 30*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 20*a^3*b + 15*a^2*b^2 + 8*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^5 + 10*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^3 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^6 + 15*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^4 + 8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3 + 3*(24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 20*a^3*b + 15*a^2*b^2)*cosh(d*x + c)^7 + 3*(8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c)^5 + (24*a^4 + 124*a^3*b + 269*a^2*b^2 + 280*a*b^3 + 120*b^4)*cosh(d*x + c)^3 + (8*a^4 + 36*a^3*b + 55*a^2*b^2 + 30*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a + b))*arctan(1/2*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 + (3*a + 4*b)*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 + 3*a + 4*b)*sinh(d*x + c))*sqrt(a/(a + b))/a) - 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c) + 2*(7*(4*a^3*b + 7*a^2*b^2)*cosh(d*x + c)^6 + 5*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*cosh(d*x + c)^4 - 4*a^3*b - 7*a^2*b^2 - 3*(4*a^3*b + 31*a^2*b^2 + 36*a*b^3)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^2 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d)*sinh(d*x + c)^4 + 4*(a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^3 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d*cosh(d*x + c)^2 + (a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*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 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c)^5 + (3*a^4*b^3 + 14*a^3*b^4 + 27*a^2*b^5 + 24*a*b^6 + 8*b^7)*d*cosh(d*x + c)^3 + (a^4*b^3 + 4*a^3*b^4 + 5*a^2*b^5 + 2*a*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
102,1,327,0,0.420626," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(20 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(2 \, {\left(20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 8 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, a d x + 20 \, a - 3 \, b\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(20 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a - 6 \, 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*d*x + 20*a - 3*b)*cosh(d*x + c)^5 + 5*(15*a*d*x + 20*a - 3*b)*cosh(d*x + c)*sinh(d*x + c)^4 - (20*a - 3*b)*sinh(d*x + c)^5 + 5*(15*a*d*x + 20*a - 3*b)*cosh(d*x + c)^3 - 5*(2*(20*a - 3*b)*cosh(d*x + c)^2 + 8*a + 3*b)*sinh(d*x + c)^3 + 5*(2*(15*a*d*x + 20*a - 3*b)*cosh(d*x + c)^3 + 3*(15*a*d*x + 20*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*a*d*x + 20*a - 3*b)*cosh(d*x + c) - 5*((20*a - 3*b)*cosh(d*x + c)^4 + 3*(8*a + 3*b)*cosh(d*x + c)^2 + 4*a - 6*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
103,1,1072,0,0.429904," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a d x \cosh\left(d x + c\right)^{8} + 8 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{2} + 2 \, a d x - a + b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a d x \cosh\left(d x + c\right)^{4} + 3 \, a d x + 15 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a d x + 2 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{4} + 2 \, a d x + 6 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} - {\left(a \cosh\left(d x + c\right)^{8} + 8 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a \sinh\left(d x + c\right)^{8} + 4 \, a \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, a \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a \cosh\left(d x + c\right)^{4} + 30 \, a \cosh\left(d x + c\right)^{2} + 3 \, a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{5} + 10 \, a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{6} + 15 \, a \cosh\left(d x + c\right)^{4} + 9 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{7} + 3 \, a \cosh\left(d x + c\right)^{5} + 3 \, 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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, a d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a d x - a + b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a d x - 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*d*x*cosh(d*x + c)^8 + 8*a*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a*d*x*sinh(d*x + c)^8 + 2*(2*a*d*x - a + b)*cosh(d*x + c)^6 + 2*(14*a*d*x*cosh(d*x + c)^2 + 2*a*d*x - a + b)*sinh(d*x + c)^6 + 4*(14*a*d*x*cosh(d*x + c)^3 + 3*(2*a*d*x - a + b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a*d*x - 2*a)*cosh(d*x + c)^4 + 2*(35*a*d*x*cosh(d*x + c)^4 + 3*a*d*x + 15*(2*a*d*x - a + b)*cosh(d*x + c)^2 - 2*a)*sinh(d*x + c)^4 + 8*(7*a*d*x*cosh(d*x + c)^5 + 5*(2*a*d*x - a + b)*cosh(d*x + c)^3 + (3*a*d*x - 2*a)*cosh(d*x + c))*sinh(d*x + c)^3 + a*d*x + 2*(2*a*d*x - a + b)*cosh(d*x + c)^2 + 2*(14*a*d*x*cosh(d*x + c)^6 + 15*(2*a*d*x - a + b)*cosh(d*x + c)^4 + 2*a*d*x + 6*(3*a*d*x - 2*a)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 - (a*cosh(d*x + c)^8 + 8*a*cosh(d*x + c)*sinh(d*x + c)^7 + a*sinh(d*x + c)^8 + 4*a*cosh(d*x + c)^6 + 4*(7*a*cosh(d*x + c)^2 + a)*sinh(d*x + c)^6 + 8*(7*a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c))*sinh(d*x + c)^5 + 6*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 + 30*a*cosh(d*x + c)^2 + 3*a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*x + c)^5 + 10*a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a*cosh(d*x + c)^2 + 4*(7*a*cosh(d*x + c)^6 + 15*a*cosh(d*x + c)^4 + 9*a*cosh(d*x + c)^2 + a)*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^7 + 3*a*cosh(d*x + c)^5 + 3*a*cosh(d*x + c)^3 + a*cosh(d*x + c))*sinh(d*x + c) + a)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*a*d*x*cosh(d*x + c)^7 + 3*(2*a*d*x - a + b)*cosh(d*x + c)^5 + 2*(3*a*d*x - 2*a)*cosh(d*x + c)^3 + (2*a*d*x - 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
104,1,155,0,0.398390," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a d x + 3 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a d x + 3 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, a - b\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a d x + 3 \, a - b\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(3 \, a - b\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*d*x + 3*a - b)*cosh(d*x + c)^3 + 3*(3*a*d*x + 3*a - b)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*a - b)*sinh(d*x + c)^3 + 3*(3*a*d*x + 3*a - b)*cosh(d*x + c) - 3*((3*a - b)*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
105,1,359,0,0.418695," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c),x, algorithm=""fricas"")","-\frac{a d x \cosh\left(d x + c\right)^{4} + 4 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d x \sinh\left(d x + c\right)^{4} + a d x + 2 \, {\left(a d x + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d x \cosh\left(d x + c\right)^{2} + a d x + b\right)} \sinh\left(d x + c\right)^{2} - {\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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(a d x \cosh\left(d x + c\right)^{3} + {\left(a 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*d*x*cosh(d*x + c)^4 + 4*a*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*x*sinh(d*x + c)^4 + a*d*x + 2*(a*d*x + b)*cosh(d*x + c)^2 + 2*(3*a*d*x*cosh(d*x + c)^2 + a*d*x + b)*sinh(d*x + c)^2 - (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(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(a*d*x*cosh(d*x + c)^3 + (a*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
106,1,36,0,0.403260," ","integrate(a+b*sech(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(a 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*d*x - b)*cosh(d*x + c) + b*sinh(d*x + c))/(d*cosh(d*x + c))","B",0
107,1,69,0,0.420446," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{a 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) - {\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)}{d}"," ",0,"-(a*d*x + b*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a + b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/d","B",0
108,1,39,0,0.414438," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} \cosh\left(d x + c\right) - {\left(a d x + a + b\right)} \sinh\left(d x + c\right)}{d \sinh\left(d x + c\right)}"," ",0,"-((a + b)*cosh(d*x + c) - (a*d*x + a + b)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
109,1,378,0,0.418540," ","integrate(coth(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{a d x \cosh\left(d x + c\right)^{4} + 4 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d x \sinh\left(d x + c\right)^{4} + a d x - 2 \, {\left(a d x - a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d x \cosh\left(d x + c\right)^{2} - a d x + a + b\right)} \sinh\left(d x + c\right)^{2} - {\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(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(a d x \cosh\left(d x + c\right)^{3} - {\left(a d x - a - 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*d*x*cosh(d*x + c)^4 + 4*a*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*x*sinh(d*x + c)^4 + a*d*x - 2*(a*d*x - a - b)*cosh(d*x + c)^2 + 2*(3*a*d*x*cosh(d*x + c)^2 - a*d*x + a + b)*sinh(d*x + c)^2 - (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(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(a*d*x*cosh(d*x + c)^3 - (a*d*x - a - 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
110,1,140,0,0.414488," ","integrate(coth(d*x+c)^4*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, a d x + 4 \, a + b\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) + 3 \, {\left(3 \, a d x - {\left(3 \, a d x + 4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, 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*((4*a + b)*cosh(d*x + c)^3 + 3*(4*a + b)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*a*d*x + 4*a + b)*sinh(d*x + c)^3 + 3*b*cosh(d*x + c) + 3*(3*a*d*x - (3*a*d*x + 4*a + b)*cosh(d*x + c)^2 + 4*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
111,1,1099,0,0.425518," ","integrate(coth(d*x+c)^5*(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{a d x \cosh\left(d x + c\right)^{8} + 8 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{2} - 2 \, a d x + 2 \, a + b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a d x \cosh\left(d x + c\right)^{4} + 3 \, a d x - 15 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a d x - 2 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{4} - 2 \, a d x + 6 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{2} + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} - {\left(a \cosh\left(d x + c\right)^{8} + 8 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a \sinh\left(d x + c\right)^{8} - 4 \, a \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{3} - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, a \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a \cosh\left(d x + c\right)^{4} - 30 \, a \cosh\left(d x + c\right)^{2} + 3 \, a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{5} - 10 \, a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, a \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{6} - 15 \, a \cosh\left(d x + c\right)^{4} + 9 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{7} - 3 \, a \cosh\left(d x + c\right)^{5} + 3 \, 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(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, a d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, a d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a d x - 2 \, a\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a 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*d*x*cosh(d*x + c)^8 + 8*a*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a*d*x*sinh(d*x + c)^8 - 2*(2*a*d*x - 2*a - b)*cosh(d*x + c)^6 + 2*(14*a*d*x*cosh(d*x + c)^2 - 2*a*d*x + 2*a + b)*sinh(d*x + c)^6 + 4*(14*a*d*x*cosh(d*x + c)^3 - 3*(2*a*d*x - 2*a - b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a*d*x - 2*a)*cosh(d*x + c)^4 + 2*(35*a*d*x*cosh(d*x + c)^4 + 3*a*d*x - 15*(2*a*d*x - 2*a - b)*cosh(d*x + c)^2 - 2*a)*sinh(d*x + c)^4 + 8*(7*a*d*x*cosh(d*x + c)^5 - 5*(2*a*d*x - 2*a - b)*cosh(d*x + c)^3 + (3*a*d*x - 2*a)*cosh(d*x + c))*sinh(d*x + c)^3 + a*d*x - 2*(2*a*d*x - 2*a - b)*cosh(d*x + c)^2 + 2*(14*a*d*x*cosh(d*x + c)^6 - 15*(2*a*d*x - 2*a - b)*cosh(d*x + c)^4 - 2*a*d*x + 6*(3*a*d*x - 2*a)*cosh(d*x + c)^2 + 2*a + b)*sinh(d*x + c)^2 - (a*cosh(d*x + c)^8 + 8*a*cosh(d*x + c)*sinh(d*x + c)^7 + a*sinh(d*x + c)^8 - 4*a*cosh(d*x + c)^6 + 4*(7*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^6 + 8*(7*a*cosh(d*x + c)^3 - 3*a*cosh(d*x + c))*sinh(d*x + c)^5 + 6*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 - 30*a*cosh(d*x + c)^2 + 3*a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*x + c)^5 - 10*a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c))*sinh(d*x + c)^3 - 4*a*cosh(d*x + c)^2 + 4*(7*a*cosh(d*x + c)^6 - 15*a*cosh(d*x + c)^4 + 9*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^7 - 3*a*cosh(d*x + c)^5 + 3*a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*a*d*x*cosh(d*x + c)^7 - 3*(2*a*d*x - 2*a - b)*cosh(d*x + c)^5 + 2*(3*a*d*x - 2*a)*cosh(d*x + c)^3 - (2*a*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
112,1,721,0,0.417369," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 2 \, {\left(70 \, a^{2} - 21 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, {\left(70 \, a^{2} - 21 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 40 \, a^{2} + 9 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 14 \, {\left(5 \, {\left(70 \, a^{2} - 21 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(40 \, a^{2} + 9 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 60 \, a^{2} - 3 \, a b + 21 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(3 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(105 \, a^{2} d x + 140 \, a^{2} - 42 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right) - 14 \, {\left({\left(70 \, a^{2} - 21 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(40 \, a^{2} + 9 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(20 \, a^{2} - a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 30 \, a^{2} - 15 \, a b - 45 \, b^{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^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^7 + 7*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 - 2*(70*a^2 - 21*a*b - 3*b^2)*sinh(d*x + c)^7 + 7*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^5 - 14*(3*(70*a^2 - 21*a*b - 3*b^2)*cosh(d*x + c)^2 + 40*a^2 + 9*a*b - 3*b^2)*sinh(d*x + c)^5 + 35*((105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^3 + (105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^3 - 14*(5*(70*a^2 - 21*a*b - 3*b^2)*cosh(d*x + c)^4 + 10*(40*a^2 + 9*a*b - 3*b^2)*cosh(d*x + c)^2 + 60*a^2 - 3*a*b + 21*b^2)*sinh(d*x + c)^3 + 7*(3*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^5 + 10*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c)^3 + 9*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(105*a^2*d*x + 140*a^2 - 42*a*b - 6*b^2)*cosh(d*x + c) - 14*((70*a^2 - 21*a*b - 3*b^2)*cosh(d*x + c)^6 + 5*(40*a^2 + 9*a*b - 3*b^2)*cosh(d*x + c)^4 + 9*(20*a^2 - a*b + 7*b^2)*cosh(d*x + c)^2 + 30*a^2 - 15*a*b - 45*b^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
113,1,2591,0,0.449551," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^3,x, algorithm=""fricas"")","-\frac{3 \, a^{2} d x \cosh\left(d x + c\right)^{12} + 36 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, a^{2} d x \sinh\left(d x + c\right)^{12} + 6 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(33 \, a^{2} d x \cosh\left(d x + c\right)^{2} + 3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, a^{2} d x \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(495 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 15 \, a^{2} d x + 90 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(99 \, a^{2} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 315 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{2} d x + 21 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, a^{2} d x \cosh\left(d x + c\right)^{7} + 63 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, a^{2} d x \cosh\left(d x + c\right)^{8} + 420 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{2} d x + 20 \, {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} d x + 4 \, {\left(165 \, a^{2} d x \cosh\left(d x + c\right)^{9} + 180 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, a^{2} d x \cosh\left(d x + c\right)^{10} + 45 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d x + 3 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{12} + 12 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{2} \sinh\left(d x + c\right)^{12} + 6 \, a^{2} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{10} + 15 \, a^{2} \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, 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)^{9} + 15 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{4} + 18 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{8} + 20 \, a^{2} \cosh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{5} + 30 \, 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} + 4 \, {\left(231 \, a^{2} \cosh\left(d x + c\right)^{6} + 315 \, a^{2} \cosh\left(d x + c\right)^{4} + 105 \, a^{2} \cosh\left(d x + c\right)^{2} + 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{6} + 15 \, a^{2} \cosh\left(d x + c\right)^{4} + 24 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{7} + 63 \, a^{2} \cosh\left(d x + c\right)^{5} + 35 \, 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)^{5} + 15 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{8} + 84 \, a^{2} \cosh\left(d x + c\right)^{6} + 70 \, a^{2} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a^{2} \cosh\left(d x + c\right)^{2} + 20 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{9} + 36 \, a^{2} \cosh\left(d x + c\right)^{7} + 42 \, a^{2} \cosh\left(d x + c\right)^{5} + 20 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{10} + 45 \, a^{2} \cosh\left(d x + c\right)^{8} + 70 \, a^{2} \cosh\left(d x + c\right)^{6} + 50 \, 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)^{2} + a^{2} + 12 \, {\left(a^{2} \cosh\left(d x + c\right)^{11} + 5 \, a^{2} \cosh\left(d x + c\right)^{9} + 10 \, a^{2} \cosh\left(d x + c\right)^{7} + 10 \, 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)\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 \, a^{2} d x \cosh\left(d x + c\right)^{11} + 5 \, {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(15 \, a^{2} d x - 9 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{2} d x - 8 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x - a^{2} + 2 \, a b\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*d*x*cosh(d*x + c)^12 + 36*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*a^2*d*x*sinh(d*x + c)^12 + 6*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^10 + 6*(33*a^2*d*x*cosh(d*x + c)^2 + 3*a^2*d*x - a^2 + 2*a*b)*sinh(d*x + c)^10 + 60*(11*a^2*d*x*cosh(d*x + c)^3 + (3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^8 + 3*(495*a^2*d*x*cosh(d*x + c)^4 + 15*a^2*d*x + 90*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^2 - 8*a^2 + 8*a*b + 4*b^2)*sinh(d*x + c)^8 + 24*(99*a^2*d*x*cosh(d*x + c)^5 + 30*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^3 + (15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^6 + 4*(693*a^2*d*x*cosh(d*x + c)^6 + 315*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^4 + 15*a^2*d*x + 21*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^2 - 9*a^2 + 6*a*b - 2*b^2)*sinh(d*x + c)^6 + 24*(99*a^2*d*x*cosh(d*x + c)^7 + 63*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^5 + 7*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^3 + (15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^4 + 3*(495*a^2*d*x*cosh(d*x + c)^8 + 420*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^6 + 70*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^4 + 15*a^2*d*x + 20*(15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^2 - 8*a^2 + 8*a*b + 4*b^2)*sinh(d*x + c)^4 + 3*a^2*d*x + 4*(165*a^2*d*x*cosh(d*x + c)^9 + 180*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^7 + 42*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^5 + 20*(15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^2 + 6*(33*a^2*d*x*cosh(d*x + c)^10 + 45*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^8 + 14*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^6 + 10*(15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^4 + 3*a^2*d*x + 3*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^2 - a^2 + 2*a*b)*sinh(d*x + c)^2 - 3*(a^2*cosh(d*x + c)^12 + 12*a^2*cosh(d*x + c)*sinh(d*x + c)^11 + a^2*sinh(d*x + c)^12 + 6*a^2*cosh(d*x + c)^10 + 6*(11*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^10 + 15*a^2*cosh(d*x + c)^8 + 20*(11*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(33*a^2*cosh(d*x + c)^4 + 18*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^8 + 20*a^2*cosh(d*x + c)^6 + 24*(33*a^2*cosh(d*x + c)^5 + 30*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*a^2*cosh(d*x + c)^6 + 315*a^2*cosh(d*x + c)^4 + 105*a^2*cosh(d*x + c)^2 + 5*a^2)*sinh(d*x + c)^6 + 15*a^2*cosh(d*x + c)^4 + 24*(33*a^2*cosh(d*x + c)^7 + 63*a^2*cosh(d*x + c)^5 + 35*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(33*a^2*cosh(d*x + c)^8 + 84*a^2*cosh(d*x + c)^6 + 70*a^2*cosh(d*x + c)^4 + 20*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 + 6*a^2*cosh(d*x + c)^2 + 20*(11*a^2*cosh(d*x + c)^9 + 36*a^2*cosh(d*x + c)^7 + 42*a^2*cosh(d*x + c)^5 + 20*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(11*a^2*cosh(d*x + c)^10 + 45*a^2*cosh(d*x + c)^8 + 70*a^2*cosh(d*x + c)^6 + 50*a^2*cosh(d*x + c)^4 + 15*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 12*(a^2*cosh(d*x + c)^11 + 5*a^2*cosh(d*x + c)^9 + 10*a^2*cosh(d*x + c)^7 + 10*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))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*a^2*d*x*cosh(d*x + c)^11 + 5*(3*a^2*d*x - a^2 + 2*a*b)*cosh(d*x + c)^9 + 2*(15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^7 + 2*(15*a^2*d*x - 9*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^5 + (15*a^2*d*x - 8*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^3 + (3*a^2*d*x - a^2 + 2*a*b)*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
114,1,435,0,0.423319," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(2 \, {\left(15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, a^{2} d x + 15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(15 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(9 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 4 \, a b + 8 \, 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*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^5 + 5*(15*a^2*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^2 - 10*a*b - 2*b^2)*sinh(d*x + c)^5 + 5*(15*a^2*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^3 - 5*(2*(15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^2 + 9*a^2 + 2*a*b - 2*b^2)*sinh(d*x + c)^3 + 5*(2*(15*a^2*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(15*a^2*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*a^2*d*x + 15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c) - 5*((15*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^4 + 3*(9*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 + 4*a*b + 8*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
115,1,1180,0,0.417647," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c),x, algorithm=""fricas"")","-\frac{a^{2} d x \cosh\left(d x + c\right)^{8} + 8 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{2} + a^{2} d x + a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} d x + 4 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d x + 30 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} d x + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x + 4 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{4} + a^{2} d x + 3 \, {\left(3 \, a^{2} d x + 4 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, a^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, 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)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, 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} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, a^{2} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, a^{2} \cosh\left(d x + c\right)^{5} + 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)\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(a^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} d x + a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} d x + 4 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} d x + 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*d*x*cosh(d*x + c)^8 + 8*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*d*x*sinh(d*x + c)^8 + 4*(a^2*d*x + a*b)*cosh(d*x + c)^6 + 4*(7*a^2*d*x*cosh(d*x + c)^2 + a^2*d*x + a*b)*sinh(d*x + c)^6 + 8*(7*a^2*d*x*cosh(d*x + c)^3 + 3*(a^2*d*x + a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2*d*x + 4*a*b + 2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*d*x*cosh(d*x + c)^4 + 3*a^2*d*x + 30*(a^2*d*x + a*b)*cosh(d*x + c)^2 + 4*a*b + 2*b^2)*sinh(d*x + c)^4 + a^2*d*x + 8*(7*a^2*d*x*cosh(d*x + c)^5 + 10*(a^2*d*x + a*b)*cosh(d*x + c)^3 + (3*a^2*d*x + 4*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2*d*x + a*b)*cosh(d*x + c)^2 + 4*(7*a^2*d*x*cosh(d*x + c)^6 + 15*(a^2*d*x + a*b)*cosh(d*x + c)^4 + a^2*d*x + 3*(3*a^2*d*x + 4*a*b + 2*b^2)*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*a^2*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^6 + 6*a^2*cosh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 + 30*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^4 + 4*a^2*cosh(d*x + c)^2 + 8*(7*a^2*cosh(d*x + c)^5 + 10*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^2*cosh(d*x + c)^6 + 15*a^2*cosh(d*x + c)^4 + 9*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*a^2*cosh(d*x + c)^5 + 3*a^2*cosh(d*x + c)^3 + a^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*d*x*cosh(d*x + c)^7 + 3*(a^2*d*x + a*b)*cosh(d*x + c)^5 + (3*a^2*d*x + 4*a*b + 2*b^2)*cosh(d*x + c)^3 + (a^2*d*x + 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
116,1,176,0,0.395926," ","integrate((a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d x - 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} d x - 6 \, a b - 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} + 3 \, {\left(3 \, a^{2} d x - 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) + 6 \, {\left({\left(3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a b + b^{2}\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*d*x - 6*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(3*a^2*d*x - 6*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(3*a*b + b^2)*sinh(d*x + c)^3 + 3*(3*a^2*d*x - 6*a*b - 2*b^2)*cosh(d*x + c) + 6*((3*a*b + b^2)*cosh(d*x + c)^2 + a*b + 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
117,1,665,0,0.458064," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{a^{2} d x \cosh\left(d x + c\right)^{4} + 4 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} d x \sinh\left(d x + c\right)^{4} + a^{2} d x + 2 \, {\left(a^{2} d x - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} d x \cosh\left(d x + c\right)^{2} + a^{2} 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({\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} + 2 \, a b + 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} + 2 \, a b + 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} + 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) + 4 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{3} + {\left(a^{2} 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*d*x*cosh(d*x + c)^4 + 4*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*d*x*sinh(d*x + c)^4 + a^2*d*x + 2*(a^2*d*x - b^2)*cosh(d*x + c)^2 + 2*(3*a^2*d*x*cosh(d*x + c)^2 + a^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 + 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 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(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 + 4*((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))) + 4*(a^2*d*x*cosh(d*x + c)^3 + (a^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
118,1,106,0,0.437993," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 2 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} d x + a^{2} + 2 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b}{2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)}"," ",0,"-1/2*((a^2 + 2*a*b + 2*b^2)*cosh(d*x + c)^2 - 2*(a^2*d*x + a^2 + 2*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + 2*b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b)/(d*cosh(d*x + c)*sinh(d*x + c))","B",0
119,1,637,0,0.448957," ","integrate(coth(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{a^{2} d x \cosh\left(d x + c\right)^{4} + 4 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} d x \sinh\left(d x + c\right)^{4} + a^{2} d x - 2 \, {\left(a^{2} d x - a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} d x \cosh\left(d x + c\right)^{2} - a^{2} d x + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} - 2 \, 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} - 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) + 4 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{3} - {\left(a^{2} d x - a^{2} - 2 \, 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)^{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*d*x*cosh(d*x + c)^4 + 4*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*d*x*sinh(d*x + c)^4 + a^2*d*x - 2*(a^2*d*x - a^2 - 2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*a^2*d*x*cosh(d*x + c)^2 - a^2*d*x + a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 - (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 - 2*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 - 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))) + 4*(a^2*d*x*cosh(d*x + c)^3 - (a^2*d*x - a^2 - 2*a*b - 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
120,1,201,0,0.427320," ","integrate(coth(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(3 \, a^{2} d x - {\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} + 2 \, a b - 2 \, b^{2}\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 + a*b - b^2)*cosh(d*x + c)^3 + 6*(2*a^2 + a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*sinh(d*x + c)^3 + 6*(a*b + b^2)*cosh(d*x + c) + 3*(3*a^2*d*x - (3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^2 + 4*a^2 + 2*a*b - 2*b^2)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
121,1,1252,0,0.443879," ","integrate(coth(d*x+c)^5*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{a^{2} d x \cosh\left(d x + c\right)^{8} + 8 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, 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)^{6} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} d x - 2 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d x - 30 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} d x + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x - 2 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} - a^{2} d x + 3 \, {\left(3 \, a^{2} d x - 2 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} - 4 \, a^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, 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)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} - 30 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, a^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} - 10 \, 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} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} - 15 \, a^{2} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} - 3 \, a^{2} \cosh\left(d x + c\right)^{5} + 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)\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)^{7} - 3 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} d x - 2 \, a^{2} + 2 \, b^{2}\right)} \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)}{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*d*x*cosh(d*x + c)^8 + 8*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*d*x*sinh(d*x + c)^8 - 4*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^6 + 4*(7*a^2*d*x*cosh(d*x + c)^2 - a^2*d*x + a^2 + a*b)*sinh(d*x + c)^6 + 8*(7*a^2*d*x*cosh(d*x + c)^3 - 3*(a^2*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2*d*x - 2*a^2 + 2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*d*x*cosh(d*x + c)^4 + 3*a^2*d*x - 30*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^2 - 2*a^2 + 2*b^2)*sinh(d*x + c)^4 + a^2*d*x + 8*(7*a^2*d*x*cosh(d*x + c)^5 - 10*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^3 + (3*a^2*d*x - 2*a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^2 + 4*(7*a^2*d*x*cosh(d*x + c)^6 - 15*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^4 - a^2*d*x + 3*(3*a^2*d*x - 2*a^2 + 2*b^2)*cosh(d*x + c)^2 + a^2 + a*b)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 - 4*a^2*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^6 + 6*a^2*cosh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^3 - 3*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*cosh(d*x + c)^4 - 30*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^4 - 4*a^2*cosh(d*x + c)^2 + 8*(7*a^2*cosh(d*x + c)^5 - 10*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^2*cosh(d*x + c)^6 - 15*a^2*cosh(d*x + c)^4 + 9*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 - 3*a^2*cosh(d*x + c)^5 + 3*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))) + 8*(a^2*d*x*cosh(d*x + c)^7 - 3*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^5 + (3*a^2*d*x - 2*a^2 + 2*b^2)*cosh(d*x + c)^3 - (a^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
122,1,425,0,0.421717," ","integrate(coth(d*x+c)^6*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{2} d x + 23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(5 \, a^{2} - 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(15 \, a^{2} d x - 2 \, {\left(15 \, a^{2} d x + 23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} - 6 \, 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} + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(15 \, a^{2} d x + 23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{2} d x - 3 \, {\left(15 \, a^{2} d x + 23 \, a^{2} + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 46 \, a^{2} + 12 \, a b - 4 \, 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 + 6*a*b - 2*b^2)*cosh(d*x + c)^5 + 5*(23*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^2*d*x + 23*a^2 + 6*a*b - 2*b^2)*sinh(d*x + c)^5 - 5*(5*a^2 - 6*a*b - 2*b^2)*cosh(d*x + c)^3 + 5*(15*a^2*d*x - 2*(15*a^2*d*x + 23*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^2 + 23*a^2 + 6*a*b - 2*b^2)*sinh(d*x + c)^3 + 5*(2*(23*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^3 - 3*(5*a^2 - 6*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^2 + 6*a*b + 4*b^2)*cosh(d*x + c) - 5*((15*a^2*d*x + 23*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^4 + 30*a^2*d*x - 3*(15*a^2*d*x + 23*a^2 + 6*a*b - 2*b^2)*cosh(d*x + c)^2 + 46*a^2 + 12*a*b - 4*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
123,1,2548,0,0.477738," ","integrate(coth(d*x+c)^7*(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} d x \cosh\left(d x + c\right)^{12} + 36 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, a^{2} d x \sinh\left(d x + c\right)^{12} - 6 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(33 \, a^{2} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{2} d x + 3 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, a^{2} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(495 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 15 \, a^{2} d x - 90 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(99 \, a^{2} d x \cosh\left(d x + c\right)^{5} - 30 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, a^{2} d x \cosh\left(d x + c\right)^{6} - 315 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{2} d x + 21 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 17 \, a^{2} + 10 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, a^{2} d x \cosh\left(d x + c\right)^{7} - 63 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, a^{2} d x \cosh\left(d x + c\right)^{8} - 420 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{2} d x - 20 \, {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} d x + 4 \, {\left(165 \, a^{2} d x \cosh\left(d x + c\right)^{9} - 180 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, a^{2} d x \cosh\left(d x + c\right)^{10} - 45 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{2} d x + 3 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{12} + 12 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{2} \sinh\left(d x + c\right)^{12} - 6 \, a^{2} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{10} + 15 \, a^{2} \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, 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)^{9} + 15 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{4} - 18 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{8} - 20 \, a^{2} \cosh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{5} - 30 \, 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} + 4 \, {\left(231 \, a^{2} \cosh\left(d x + c\right)^{6} - 315 \, a^{2} \cosh\left(d x + c\right)^{4} + 105 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{6} + 15 \, a^{2} \cosh\left(d x + c\right)^{4} + 24 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{7} - 63 \, a^{2} \cosh\left(d x + c\right)^{5} + 35 \, 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)^{5} + 15 \, {\left(33 \, a^{2} \cosh\left(d x + c\right)^{8} - 84 \, a^{2} \cosh\left(d x + c\right)^{6} + 70 \, a^{2} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a^{2} \cosh\left(d x + c\right)^{2} + 20 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{9} - 36 \, a^{2} \cosh\left(d x + c\right)^{7} + 42 \, a^{2} \cosh\left(d x + c\right)^{5} - 20 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(11 \, a^{2} \cosh\left(d x + c\right)^{10} - 45 \, a^{2} \cosh\left(d x + c\right)^{8} + 70 \, a^{2} \cosh\left(d x + c\right)^{6} - 50 \, 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)^{2} + a^{2} + 12 \, {\left(a^{2} \cosh\left(d x + c\right)^{11} - 5 \, a^{2} \cosh\left(d x + c\right)^{9} + 10 \, a^{2} \cosh\left(d x + c\right)^{7} - 10 \, 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)\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 \, a^{2} d x \cosh\left(d x + c\right)^{11} - 5 \, {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 2 \, {\left(15 \, a^{2} d x - 17 \, a^{2} - 10 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{2} d x - 12 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} d x - 3 \, a^{2} - 2 \, a b\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*d*x*cosh(d*x + c)^12 + 36*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*a^2*d*x*sinh(d*x + c)^12 - 6*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^10 + 6*(33*a^2*d*x*cosh(d*x + c)^2 - 3*a^2*d*x + 3*a^2 + 2*a*b)*sinh(d*x + c)^10 + 60*(11*a^2*d*x*cosh(d*x + c)^3 - (3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^8 + 3*(495*a^2*d*x*cosh(d*x + c)^4 + 15*a^2*d*x - 90*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^2 - 12*a^2 + 4*b^2)*sinh(d*x + c)^8 + 24*(99*a^2*d*x*cosh(d*x + c)^5 - 30*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^3 + (15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^6 + 4*(693*a^2*d*x*cosh(d*x + c)^6 - 315*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^4 - 15*a^2*d*x + 21*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^2 + 17*a^2 + 10*a*b + 2*b^2)*sinh(d*x + c)^6 + 24*(99*a^2*d*x*cosh(d*x + c)^7 - 63*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^5 + 7*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^3 - (15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^4 + 3*(495*a^2*d*x*cosh(d*x + c)^8 - 420*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^6 + 70*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^4 + 15*a^2*d*x - 20*(15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^2 - 12*a^2 + 4*b^2)*sinh(d*x + c)^4 + 3*a^2*d*x + 4*(165*a^2*d*x*cosh(d*x + c)^9 - 180*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^7 + 42*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^5 - 20*(15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^3 + 3*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^2 + 6*(33*a^2*d*x*cosh(d*x + c)^10 - 45*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^8 + 14*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^6 - 10*(15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^4 - 3*a^2*d*x + 3*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*a*b)*sinh(d*x + c)^2 - 3*(a^2*cosh(d*x + c)^12 + 12*a^2*cosh(d*x + c)*sinh(d*x + c)^11 + a^2*sinh(d*x + c)^12 - 6*a^2*cosh(d*x + c)^10 + 6*(11*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^10 + 15*a^2*cosh(d*x + c)^8 + 20*(11*a^2*cosh(d*x + c)^3 - 3*a^2*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(33*a^2*cosh(d*x + c)^4 - 18*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^8 - 20*a^2*cosh(d*x + c)^6 + 24*(33*a^2*cosh(d*x + c)^5 - 30*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*a^2*cosh(d*x + c)^6 - 315*a^2*cosh(d*x + c)^4 + 105*a^2*cosh(d*x + c)^2 - 5*a^2)*sinh(d*x + c)^6 + 15*a^2*cosh(d*x + c)^4 + 24*(33*a^2*cosh(d*x + c)^7 - 63*a^2*cosh(d*x + c)^5 + 35*a^2*cosh(d*x + c)^3 - 5*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(33*a^2*cosh(d*x + c)^8 - 84*a^2*cosh(d*x + c)^6 + 70*a^2*cosh(d*x + c)^4 - 20*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 - 6*a^2*cosh(d*x + c)^2 + 20*(11*a^2*cosh(d*x + c)^9 - 36*a^2*cosh(d*x + c)^7 + 42*a^2*cosh(d*x + c)^5 - 20*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(11*a^2*cosh(d*x + c)^10 - 45*a^2*cosh(d*x + c)^8 + 70*a^2*cosh(d*x + c)^6 - 50*a^2*cosh(d*x + c)^4 + 15*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^2 + a^2 + 12*(a^2*cosh(d*x + c)^11 - 5*a^2*cosh(d*x + c)^9 + 10*a^2*cosh(d*x + c)^7 - 10*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))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*a^2*d*x*cosh(d*x + c)^11 - 5*(3*a^2*d*x - 3*a^2 - 2*a*b)*cosh(d*x + c)^9 + 2*(15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^7 - 2*(15*a^2*d*x - 17*a^2 - 10*a*b - 2*b^2)*cosh(d*x + c)^5 + (15*a^2*d*x - 12*a^2 + 4*b^2)*cosh(d*x + c)^3 - (3*a^2*d*x - 3*a^2 - 2*a*b)*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
124,1,1323,0,0.434760," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - {\left(420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(280 \, a^{3} + 21 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3} + 4 \, {\left(420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(4 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 9 \, {\left(14 \, {\left(420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 700 \, a^{3} + 84 \, a^{2} b + 204 \, a b^{2} - 32 \, b^{3} + 21 \, {\left(280 \, a^{3} + 21 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(14 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(28 \, {\left(420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(280 \, a^{3} + 21 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2660 \, a^{3} - 252 \, a^{2} b - 252 \, a b^{2} + 896 \, b^{3} + 120 \, {\left(175 \, a^{3} + 21 \, a^{2} b + 51 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(4 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, {\left(315 \, a^{3} d x + 420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) - 9 \, {\left({\left(420 \, a^{3} - 189 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(280 \, a^{3} + 21 \, a^{2} b - 54 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(175 \, a^{3} + 21 \, a^{2} b + 51 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 420 \, a^{3} - 126 \, a^{2} b - 336 \, a b^{2} - 672 \, b^{3} + 28 \, {\left(95 \, a^{3} - 9 \, a^{2} b - 9 \, a b^{2} + 32 \, 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*((315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^9 + 9*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 - (420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*sinh(d*x + c)^9 + 9*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^7 - 9*(280*a^3 + 21*a^2*b - 54*a*b^2 - 8*b^3 + 4*(420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(4*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 3*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^5 - 9*(14*(420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 700*a^3 + 84*a^2*b + 204*a*b^2 - 32*b^3 + 21*(280*a^3 + 21*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(14*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^5 + 35*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 20*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^3 - 3*(28*(420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^6 + 105*(280*a^3 + 21*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 2660*a^3 - 252*a^2*b - 252*a*b^2 + 896*b^3 + 120*(175*a^3 + 21*a^2*b + 51*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(4*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^7 + 21*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^5 + 40*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 28*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 126*(315*a^3*d*x + 420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c) - 9*((420*a^3 - 189*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^8 + 7*(280*a^3 + 21*a^2*b - 54*a*b^2 - 8*b^3)*cosh(d*x + c)^6 + 20*(175*a^3 + 21*a^2*b + 51*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 420*a^3 - 126*a^2*b - 336*a*b^2 - 672*b^3 + 28*(95*a^3 - 9*a^2*b - 9*a*b^2 + 32*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
125,1,4658,0,0.513206," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} d x \cosh\left(d x + c\right)^{16} + 48 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 3 \, a^{3} d x \sinh\left(d x + c\right)^{16} + 6 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} + 6 \, {\left(60 \, a^{3} d x \cosh\left(d x + c\right)^{2} + 4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \sinh\left(d x + c\right)^{14} + 84 \, {\left(20 \, a^{3} d x \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 12 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} + 6 \, {\left(910 \, a^{3} d x \cosh\left(d x + c\right)^{4} + 14 \, a^{3} d x - 6 \, a^{3} + 12 \, a^{2} b + 6 \, a b^{2} + 91 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 24 \, {\left(546 \, a^{3} d x \cosh\left(d x + c\right)^{5} + 91 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 2 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(12012 \, a^{3} d x \cosh\left(d x + c\right)^{6} + 84 \, a^{3} d x + 3003 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3} + 396 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(8580 \, a^{3} d x \cosh\left(d x + c\right)^{7} + 3003 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 660 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(19305 \, a^{3} d x \cosh\left(d x + c\right)^{8} + 9009 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 105 \, a^{3} d x + 2970 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3} + 45 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(2145 \, a^{3} d x \cosh\left(d x + c\right)^{9} + 1287 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 594 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(12012 \, a^{3} d x \cosh\left(d x + c\right)^{10} + 9009 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 5544 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 84 \, a^{3} d x + 210 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3} + 28 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(3276 \, a^{3} d x \cosh\left(d x + c\right)^{11} + 3003 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 2376 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, a^{3} d x + 12 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(2730 \, a^{3} d x \cosh\left(d x + c\right)^{12} + 3003 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 2970 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 42 \, a^{3} d x + 70 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 18 \, a^{3} + 36 \, a^{2} b + 18 \, a b^{2} + 15 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(210 \, a^{3} d x \cosh\left(d x + c\right)^{13} + 273 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 330 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(180 \, a^{3} d x \cosh\left(d x + c\right)^{14} + 273 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 396 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, a^{3} d x + 15 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} + 9 \, a^{2} b + 36 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(12 \, a^{3} d x \cosh\left(d x + c\right)^{15} + 21 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 36 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(105 \, a^{3} d x - 60 \, a^{3} + 72 \, a^{2} b + 12 \, a b^{2} - 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(84 \, a^{3} d x - 45 \, a^{3} + 63 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 12 \, {\left(7 \, a^{3} d x - 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} d x - a^{3} + 3 \, a^{2} b\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*d*x*cosh(d*x + c)^16 + 48*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^15 + 3*a^3*d*x*sinh(d*x + c)^16 + 6*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^14 + 6*(60*a^3*d*x*cosh(d*x + c)^2 + 4*a^3*d*x - a^3 + 3*a^2*b)*sinh(d*x + c)^14 + 84*(20*a^3*d*x*cosh(d*x + c)^3 + (4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^13 + 12*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^12 + 6*(910*a^3*d*x*cosh(d*x + c)^4 + 14*a^3*d*x - 6*a^3 + 12*a^2*b + 6*a*b^2 + 91*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 24*(546*a^3*d*x*cosh(d*x + c)^5 + 91*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^3 + 6*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 + 2*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^10 + 2*(12012*a^3*d*x*cosh(d*x + c)^6 + 84*a^3*d*x + 3003*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^4 - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3 + 396*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(8580*a^3*d*x*cosh(d*x + c)^7 + 3003*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^5 + 660*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 5*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^8 + 2*(19305*a^3*d*x*cosh(d*x + c)^8 + 9009*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^6 + 105*a^3*d*x + 2970*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3 + 45*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(2145*a^3*d*x*cosh(d*x + c)^9 + 1287*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^7 + 594*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 + 15*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^3 + (105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^6 + 2*(12012*a^3*d*x*cosh(d*x + c)^10 + 9009*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^8 + 5544*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^6 + 84*a^3*d*x + 210*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^4 - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3 + 28*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(3276*a^3*d*x*cosh(d*x + c)^11 + 3003*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^9 + 2376*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^7 + 126*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^5 + 28*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^3 + 3*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*a^3*d*x + 12*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 2*(2730*a^3*d*x*cosh(d*x + c)^12 + 3003*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^10 + 2970*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^8 + 210*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^6 + 42*a^3*d*x + 70*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^4 - 18*a^3 + 36*a^2*b + 18*a*b^2 + 15*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(210*a^3*d*x*cosh(d*x + c)^13 + 273*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^11 + 330*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^9 + 30*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^7 + 14*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^5 + 5*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^3 + 6*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^2 + 2*(180*a^3*d*x*cosh(d*x + c)^14 + 273*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^12 + 396*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^10 + 45*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^8 + 28*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^6 + 12*a^3*d*x + 15*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^4 - 3*a^3 + 9*a^2*b + 36*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(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(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(12*a^3*d*x*cosh(d*x + c)^15 + 21*(4*a^3*d*x - a^3 + 3*a^2*b)*cosh(d*x + c)^13 + 36*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^11 + 5*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^9 + 4*(105*a^3*d*x - 60*a^3 + 72*a^2*b + 12*a*b^2 - 16*b^3)*cosh(d*x + c)^7 + 3*(84*a^3*d*x - 45*a^3 + 63*a^2*b + 24*a*b^2 + 16*b^3)*cosh(d*x + c)^5 + 12*(7*a^3*d*x - 3*a^3 + 6*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3*d*x - a^3 + 3*a^2*b)*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
126,1,881,0,0.416639," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - {\left(105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(75 \, a^{3} - 15 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3} + 3 \, {\left(105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(5 \, {\left(105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 135 \, a^{3} + 45 \, a^{2} b + 54 \, a b^{2} - 24 \, b^{3} + 10 \, {\left(75 \, a^{3} - 15 \, a^{2} b - 42 \, a b^{2} - 8 \, 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} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(105 \, a^{3} d x + 105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) - 7 \, {\left({\left(105 \, a^{3} - 105 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(75 \, a^{3} - 15 \, a^{2} b - 42 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 45 \, a^{2} b + 90 \, a b^{2} + 120 \, b^{3} + 9 \, {\left(45 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} - 8 \, 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*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^7 + 7*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 - (105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*sinh(d*x + c)^7 + 7*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^5 - 7*(75*a^3 - 15*a^2*b - 42*a*b^2 - 8*b^3 + 3*(105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 35*((105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + (105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^3 - 7*(5*(105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 135*a^3 + 45*a^2*b + 54*a*b^2 - 24*b^3 + 10*(75*a^3 - 15*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 7*(3*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^5 + 10*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 9*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(105*a^3*d*x + 105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c) - 7*((105*a^3 - 105*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^6 + 5*(75*a^3 - 15*a^2*b - 42*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 75*a^3 + 45*a^2*b + 90*a*b^2 + 120*b^3 + 9*(45*a^3 + 15*a^2*b + 18*a*b^2 - 8*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
127,1,2519,0,0.441201," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c),x, algorithm=""fricas"")","-\frac{3 \, a^{3} d x \cosh\left(d x + c\right)^{12} + 36 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, a^{3} d x \sinh\left(d x + c\right)^{12} + 18 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 18 \, {\left(11 \, a^{3} d x \cosh\left(d x + c\right)^{2} + a^{3} d x + a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, a^{3} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(165 \, a^{3} d x \cosh\left(d x + c\right)^{4} + 5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2} + 90 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 72 \, {\left(33 \, a^{3} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, a^{3} d x \cosh\left(d x + c\right)^{6} + 15 \, a^{3} d x + 945 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3} + 63 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, a^{3} d x \cosh\left(d x + c\right)^{7} + 189 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 21 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, a^{3} d x + 9 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, a^{3} d x \cosh\left(d x + c\right)^{8} + 1260 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, a^{3} d x + 210 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{2} b + 12 \, a b^{2} + 20 \, {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, a^{3} d x \cosh\left(d x + c\right)^{9} + 540 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 18 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, a^{3} d x \cosh\left(d x + c\right)^{10} + 135 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 3 \, a^{3} d x + 10 \, {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} b + 9 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} + 6 \, a^{3} \cosh\left(d x + c\right)^{10} + 15 \, a^{3} \cosh\left(d x + c\right)^{8} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, 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)^{9} + 20 \, a^{3} \cosh\left(d x + c\right)^{6} + 15 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{4} + 18 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{5} + 30 \, a^{3} \cosh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 15 \, a^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} + 315 \, a^{3} \cosh\left(d x + c\right)^{4} + 105 \, a^{3} \cosh\left(d x + c\right)^{2} + 5 \, a^{3}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{7} + 63 \, a^{3} \cosh\left(d x + c\right)^{5} + 35 \, a^{3} \cosh\left(d x + c\right)^{3} + 5 \, 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} + 15 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{8} + 84 \, a^{3} \cosh\left(d x + c\right)^{6} + 70 \, a^{3} \cosh\left(d x + c\right)^{4} + 20 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{9} + 36 \, a^{3} \cosh\left(d x + c\right)^{7} + 42 \, a^{3} \cosh\left(d x + c\right)^{5} + 20 \, 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} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{10} + 45 \, a^{3} \cosh\left(d x + c\right)^{8} + 70 \, a^{3} \cosh\left(d x + c\right)^{6} + 50 \, 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)^{2} + 12 \, {\left(a^{3} \cosh\left(d x + c\right)^{11} + 5 \, a^{3} \cosh\left(d x + c\right)^{9} + 10 \, a^{3} \cosh\left(d x + c\right)^{7} + 10 \, 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)\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 \, a^{3} d x \cosh\left(d x + c\right)^{11} + 15 \, {\left(a^{3} d x + a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 6 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(15 \, a^{3} d x + 27 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(5 \, a^{3} d x + 8 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d x + a^{2} b\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*d*x*cosh(d*x + c)^12 + 36*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*a^3*d*x*sinh(d*x + c)^12 + 18*(a^3*d*x + a^2*b)*cosh(d*x + c)^10 + 18*(11*a^3*d*x*cosh(d*x + c)^2 + a^3*d*x + a^2*b)*sinh(d*x + c)^10 + 60*(11*a^3*d*x*cosh(d*x + c)^3 + 3*(a^3*d*x + a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 9*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^8 + 9*(165*a^3*d*x*cosh(d*x + c)^4 + 5*a^3*d*x + 8*a^2*b + 4*a*b^2 + 90*(a^3*d*x + a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 72*(33*a^3*d*x*cosh(d*x + c)^5 + 30*(a^3*d*x + a^2*b)*cosh(d*x + c)^3 + (5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^6 + 4*(693*a^3*d*x*cosh(d*x + c)^6 + 15*a^3*d*x + 945*(a^3*d*x + a^2*b)*cosh(d*x + c)^4 + 27*a^2*b + 18*a*b^2 + 8*b^3 + 63*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(99*a^3*d*x*cosh(d*x + c)^7 + 189*(a^3*d*x + a^2*b)*cosh(d*x + c)^5 + 21*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^3 + (15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*a^3*d*x + 9*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^4 + 3*(495*a^3*d*x*cosh(d*x + c)^8 + 1260*(a^3*d*x + a^2*b)*cosh(d*x + c)^6 + 15*a^3*d*x + 210*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^4 + 24*a^2*b + 12*a*b^2 + 20*(15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(165*a^3*d*x*cosh(d*x + c)^9 + 540*(a^3*d*x + a^2*b)*cosh(d*x + c)^7 + 126*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^5 + 20*(15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + 9*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 18*(a^3*d*x + a^2*b)*cosh(d*x + c)^2 + 6*(33*a^3*d*x*cosh(d*x + c)^10 + 135*(a^3*d*x + a^2*b)*cosh(d*x + c)^8 + 42*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^6 + 3*a^3*d*x + 10*(15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 3*a^2*b + 9*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 + 6*a^3*cosh(d*x + c)^10 + 15*a^3*cosh(d*x + c)^8 + 6*(11*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^9 + 20*a^3*cosh(d*x + c)^6 + 15*(33*a^3*cosh(d*x + c)^4 + 18*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^8 + 24*(33*a^3*cosh(d*x + c)^5 + 30*a^3*cosh(d*x + c)^3 + 5*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 15*a^3*cosh(d*x + c)^4 + 4*(231*a^3*cosh(d*x + c)^6 + 315*a^3*cosh(d*x + c)^4 + 105*a^3*cosh(d*x + c)^2 + 5*a^3)*sinh(d*x + c)^6 + 24*(33*a^3*cosh(d*x + c)^7 + 63*a^3*cosh(d*x + c)^5 + 35*a^3*cosh(d*x + c)^3 + 5*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 6*a^3*cosh(d*x + c)^2 + 15*(33*a^3*cosh(d*x + c)^8 + 84*a^3*cosh(d*x + c)^6 + 70*a^3*cosh(d*x + c)^4 + 20*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 20*(11*a^3*cosh(d*x + c)^9 + 36*a^3*cosh(d*x + c)^7 + 42*a^3*cosh(d*x + c)^5 + 20*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 6*(11*a^3*cosh(d*x + c)^10 + 45*a^3*cosh(d*x + c)^8 + 70*a^3*cosh(d*x + c)^6 + 50*a^3*cosh(d*x + c)^4 + 15*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 12*(a^3*cosh(d*x + c)^11 + 5*a^3*cosh(d*x + c)^9 + 10*a^3*cosh(d*x + c)^7 + 10*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))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*a^3*d*x*cosh(d*x + c)^11 + 15*(a^3*d*x + a^2*b)*cosh(d*x + c)^9 + 6*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^7 + 2*(15*a^3*d*x + 27*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^5 + 3*(5*a^3*d*x + 8*a^2*b + 4*a*b^2)*cosh(d*x + c)^3 + 3*(a^3*d*x + a^2*b)*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
128,1,470,0,0.424980," ","integrate((a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(45 \, a^{2} b + 30 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(27 \, a^{2} b + 30 \, a b^{2} + 8 \, b^{3} + 2 \, {\left(45 \, a^{2} b + 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, a^{3} d x - 45 \, a^{2} b - 30 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) + 5 \, {\left({\left(45 \, a^{2} b + 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 18 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3} + 3 \, {\left(27 \, a^{2} b + 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{15 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 5 \, d \cosh\left(d x + c\right)^{3} + 5 \, {\left(2 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/15*((15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c)^5 + 5*(15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (45*a^2*b + 30*a*b^2 + 8*b^3)*sinh(d*x + c)^5 + 5*(15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 5*(27*a^2*b + 30*a*b^2 + 8*b^3 + 2*(45*a^2*b + 30*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 3*(15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*a^3*d*x - 45*a^2*b - 30*a*b^2 - 8*b^3)*cosh(d*x + c) + 5*((45*a^2*b + 30*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 18*a^2*b + 24*a*b^2 + 16*b^3 + 3*(27*a^2*b + 30*a*b^2 + 8*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
129,1,2376,0,0.457258," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{a^{3} d x \cosh\left(d x + c\right)^{8} + 8 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{2} + 2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + a^{3} d x + 2 \, {\left(3 \, a^{3} d x - 6 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{3} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{3} d x - 6 \, a b^{2} - 4 \, b^{3} + 15 \, {\left(2 \, a^{3} d x - 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 \, a^{3} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} d x - 6 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{6} + 2 \, a^{3} d x + 15 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - b^{3} + 6 \, {\left(3 \, a^{3} d x - 6 \, a b^{2} - 4 \, b^{3}\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({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\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)^{7} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 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} + 8 \, {\left(7 \, {\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} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\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)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, 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} + 8 \, {\left(7 \, {\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} + 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} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\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} + 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} + 9 \, {\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} + 8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\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) + 4 \, {\left(2 \, a^{3} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} d x - 6 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d x - 3 \, a b^{2} - b^{3}\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*d*x*cosh(d*x + c)^8 + 8*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*d*x*sinh(d*x + c)^8 + 2*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^6 + 2*(14*a^3*d*x*cosh(d*x + c)^2 + 2*a^3*d*x - 3*a*b^2 - b^3)*sinh(d*x + c)^6 + 4*(14*a^3*d*x*cosh(d*x + c)^3 + 3*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + a^3*d*x + 2*(3*a^3*d*x - 6*a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 2*(35*a^3*d*x*cosh(d*x + c)^4 + 3*a^3*d*x - 6*a*b^2 - 4*b^3 + 15*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^3*d*x*cosh(d*x + c)^5 + 5*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + (3*a^3*d*x - 6*a*b^2 - 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(14*a^3*d*x*cosh(d*x + c)^6 + 2*a^3*d*x + 15*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^4 - 3*a*b^2 - b^3 + 6*(3*a^3*d*x - 6*a*b^2 - 4*b^3)*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 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^8 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + 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 + 8*(7*(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 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 3*a^3 + 9*a^2*b + 9*a*b^2 + 3*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 + 8*(7*(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 + 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 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 4*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 15*(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 + 9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 3*(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))) + 4*(2*a^3*d*x*cosh(d*x + c)^7 + 3*(2*a^3*d*x - 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(3*a^3*d*x - 6*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + (2*a^3*d*x - 3*a*b^2 - 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 + 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
130,1,359,0,0.412809," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} d x + 3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 9 \, a^{3} + 27 \, a^{2} b + 18 \, a b^{2} + 4 \, {\left(3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{3} + 18 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(3 \, a^{3} d x + 3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} d x + 3 \, a^{3} + 9 \, a^{2} b + 18 \, a b^{2} + 8 \, b^{3}\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^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^4 - 4*(3*a^3*d*x + 3*a^3 + 9*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^3 + 9*a^2*b + 18*a*b^2 + 8*b^3)*sinh(d*x + c)^4 + 9*a^3 + 27*a^2*b + 18*a*b^2 + 4*(3*a^3 + 9*a^2*b + 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 2*(6*a^3 + 18*a^2*b + 18*a*b^2 + 8*b^3 + 3*(3*a^3 + 9*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*((3*a^3*d*x + 3*a^3 + 9*a^2*b + 18*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + (3*a^3*d*x + 3*a^3 + 9*a^2*b + 18*a*b^2 + 8*b^3)*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
131,1,1701,0,0.443239," ","integrate(coth(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{a^{3} d x \cosh\left(d x + c\right)^{8} + 8 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{2} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + a^{3} d x - 2 \, {\left(a^{3} d x - 2 \, a^{3} - 6 \, a^{2} b - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{3} d x \cosh\left(d x + c\right)^{4} - a^{3} d x + 2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} d x - 2 \, a^{3} - 6 \, a^{2} b - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3} - 6 \, {\left(a^{3} d x - 2 \, a^{3} - 6 \, a^{2} b - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a b^{2} + 2 \, b^{3} + 4 \, {\left(7 \, {\left(3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a b^{2} + 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} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - {\left(3 \, a b^{2} + 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 b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\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 \, a^{3} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} d x - 2 \, a^{3} - 6 \, a^{2} b - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, 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*d*x*cosh(d*x + c)^8 + 8*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*d*x*sinh(d*x + c)^8 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^6 + 2*(14*a^3*d*x*cosh(d*x + c)^2 + a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*sinh(d*x + c)^6 + 4*(14*a^3*d*x*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + a^3*d*x - 2*(a^3*d*x - 2*a^3 - 6*a^2*b - 6*a*b^2)*cosh(d*x + c)^4 + 2*(35*a^3*d*x*cosh(d*x + c)^4 - a^3*d*x + 2*a^3 + 6*a^2*b + 6*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^3*d*x*cosh(d*x + c)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^3 - (a^3*d*x - 2*a^3 - 6*a^2*b - 6*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 2*(14*a^3*d*x*cosh(d*x + c)^6 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3 - 6*(a^3*d*x - 2*a^3 - 6*a^2*b - 6*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a*b^2 + 2*b^3)*cosh(d*x + c)^8 + 56*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(3*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a*b^2 + 2*b^3)*sinh(d*x + c)^8 - 2*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^4 + 2*(35*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^4 - 3*a*b^2 - 2*b^3)*sinh(d*x + c)^4 + 8*(7*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^5 - (3*a*b^2 + 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a*b^2 + 2*b^3 + 4*(7*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^6 - 3*(3*a*b^2 + 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a*b^2 + 2*b^3)*cosh(d*x + c)^7 - (3*a*b^2 + 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*b^2 - 2*b^3)*cosh(d*x + c)^8 + 56*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 - 3*a*b^2 - 2*b^3)*sinh(d*x + c)^8 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^4 + 2*(35*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^4 - a^3 + 3*a*b^2 + 2*b^3)*sinh(d*x + c)^4 + 8*(7*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^5 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 3*a*b^2 - 2*b^3 + 4*(7*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^6 - 3*(a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^3 - 3*a*b^2 - 2*b^3)*cosh(d*x + c)^7 - (a^3 - 3*a*b^2 - 2*b^3)*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*d*x*cosh(d*x + c)^7 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*cosh(d*x + c)^5 - 2*(a^3*d*x - 2*a^3 - 6*a^2*b - 6*a*b^2)*cosh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + 2*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
132,1,354,0,0.400636," ","integrate(coth(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} d x + 4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 9 \, a^{2} b + 18 \, a b^{2} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 8 \, b^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(3 \, a^{3} d x + 4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} d x + 4 \, a^{3} + 3 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\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 + 3*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^4 - 4*(3*a^3*d*x + 4*a^3 + 3*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^3 + 3*a^2*b - 6*a*b^2 - 8*b^3)*sinh(d*x + c)^4 + 9*a^2*b + 18*a*b^2 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 2*(2*a^3 + 6*a^2*b + 6*a*b^2 + 8*b^3 + 3*(4*a^3 + 3*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*((3*a^3*d*x + 4*a^3 + 3*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^3 - (3*a^3*d*x + 4*a^3 + 3*a^2*b - 6*a*b^2 - 8*b^3)*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
133,1,1830,0,0.448969," ","integrate(coth(d*x+c)^5*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{a^{3} d x \cosh\left(d x + c\right)^{8} + 8 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{3} d x + 2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + a^{3} d x + 2 \, {\left(3 \, a^{3} d x - 2 \, a^{3} + 6 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{3} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{3} d x - 2 \, a^{3} + 6 \, a b^{2} + 4 \, b^{3} - 15 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} d x - 2 \, a^{3} + 6 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a^{3} d x \cosh\left(d x + c\right)^{6} - 2 \, a^{3} d x - 15 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 6 \, {\left(3 \, a^{3} d x - 2 \, a^{3} + 6 \, a b^{2} + 4 \, b^{3}\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} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + b^{3}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{3} + b^{3} - 7 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + b^{3}\right)} \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} + 6 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 3 \, b^{3} - 30 \, {\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} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} + b^{3}\right)} \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)^{3} + a^{3} + b^{3} - 4 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + b^{3}\right)} \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} + 9 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{3} + b^{3}\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)\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 \, a^{3} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} d x - 2 \, a^{3} + 6 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} d x - 2 \, a^{3} - 3 \, a^{2} b + b^{3}\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*d*x*cosh(d*x + c)^8 + 8*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*d*x*sinh(d*x + c)^8 - 2*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^6 + 2*(14*a^3*d*x*cosh(d*x + c)^2 - 2*a^3*d*x + 2*a^3 + 3*a^2*b - b^3)*sinh(d*x + c)^6 + 4*(14*a^3*d*x*cosh(d*x + c)^3 - 3*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + a^3*d*x + 2*(3*a^3*d*x - 2*a^3 + 6*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 2*(35*a^3*d*x*cosh(d*x + c)^4 + 3*a^3*d*x - 2*a^3 + 6*a*b^2 + 4*b^3 - 15*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^3*d*x*cosh(d*x + c)^5 - 5*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^3 + (3*a^3*d*x - 2*a^3 + 6*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^2 + 2*(14*a^3*d*x*cosh(d*x + c)^6 - 2*a^3*d*x - 15*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^4 + 2*a^3 + 3*a^2*b - b^3 + 6*(3*a^3*d*x - 2*a^3 + 6*a*b^2 + 4*b^3)*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 + b^3)*cosh(d*x + c)^8 + 8*(a^3 + b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + b^3)*sinh(d*x + c)^8 - 4*(a^3 + b^3)*cosh(d*x + c)^6 - 4*(a^3 + b^3 - 7*(a^3 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^3 + b^3)*cosh(d*x + c)^3 - 3*(a^3 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a^3 + b^3)*cosh(d*x + c)^4 + 2*(35*(a^3 + b^3)*cosh(d*x + c)^4 + 3*a^3 + 3*b^3 - 30*(a^3 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + b^3)*cosh(d*x + c)^5 - 10*(a^3 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + b^3 - 4*(a^3 + b^3)*cosh(d*x + c)^2 + 4*(7*(a^3 + b^3)*cosh(d*x + c)^6 - 15*(a^3 + b^3)*cosh(d*x + c)^4 - a^3 - b^3 + 9*(a^3 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^3 + b^3)*cosh(d*x + c)^7 - 3*(a^3 + b^3)*cosh(d*x + c)^5 + 3*(a^3 + b^3)*cosh(d*x + c)^3 - (a^3 + b^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*d*x*cosh(d*x + c)^7 - 3*(2*a^3*d*x - 2*a^3 - 3*a^2*b + b^3)*cosh(d*x + c)^5 + 2*(3*a^3*d*x - 2*a^3 + 6*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (2*a^3*d*x - 2*a^3 - 3*a^2*b + 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 - 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
134,1,521,0,0.408393," ","integrate(coth(d*x+c)^6*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{3} d x + 23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(15 \, a^{3} d x + 23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3} - 2 \, {\left(15 \, a^{3} d x + 23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{3} - 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{3} + 9 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) - 5 \, {\left(30 \, a^{3} d x + {\left(15 \, a^{3} d x + 23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 46 \, a^{3} + 18 \, a^{2} b - 12 \, a b^{2} + 16 \, b^{3} - 3 \, {\left(15 \, a^{3} d x + 23 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} + 8 \, b^{3}\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 + 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)^5 + 5*(23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^3*d*x + 23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*sinh(d*x + c)^5 - 5*(5*a^3 - 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + 5*(15*a^3*d*x + 23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3 - 2*(15*a^3*d*x + 23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)^3 - 3*(5*a^3 - 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^3 + 9*a^2*b + 12*a*b^2 + 8*b^3)*cosh(d*x + c) - 5*(30*a^3*d*x + (15*a^3*d*x + 23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 46*a^3 + 18*a^2*b - 12*a*b^2 + 16*b^3 - 3*(15*a^3*d*x + 23*a^3 + 9*a^2*b - 6*a*b^2 + 8*b^3)*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
135,1,2632,0,0.464014," ","integrate(coth(d*x+c)^7*(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} d x \cosh\left(d x + c\right)^{12} + 36 \, a^{3} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, a^{3} d x \sinh\left(d x + c\right)^{12} - 18 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 18 \, {\left(11 \, a^{3} d x \cosh\left(d x + c\right)^{2} - a^{3} d x + a^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, a^{3} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(165 \, a^{3} d x \cosh\left(d x + c\right)^{4} + 5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2} - 90 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 72 \, {\left(33 \, a^{3} d x \cosh\left(d x + c\right)^{5} - 30 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, a^{3} d x \cosh\left(d x + c\right)^{6} - 15 \, a^{3} d x - 945 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 17 \, a^{3} + 15 \, a^{2} b + 6 \, a b^{2} + 8 \, b^{3} + 63 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, a^{3} d x \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 21 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, a^{3} d x + 9 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, a^{3} d x \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, a^{3} d x + 210 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} + 12 \, a b^{2} - 20 \, {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, a^{3} d x \cosh\left(d x + c\right)^{9} - 540 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 18 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, a^{3} d x \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 3 \, a^{3} d x - 10 \, {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 3 \, a^{2} b + 9 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} - 6 \, a^{3} \cosh\left(d x + c\right)^{10} + 15 \, a^{3} \cosh\left(d x + c\right)^{8} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, 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)^{9} - 20 \, a^{3} \cosh\left(d x + c\right)^{6} + 15 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{4} - 18 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{5} - 30 \, a^{3} \cosh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 15 \, a^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} - 315 \, a^{3} \cosh\left(d x + c\right)^{4} + 105 \, a^{3} \cosh\left(d x + c\right)^{2} - 5 \, a^{3}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{7} - 63 \, a^{3} \cosh\left(d x + c\right)^{5} + 35 \, a^{3} \cosh\left(d x + c\right)^{3} - 5 \, 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} + 15 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{8} - 84 \, a^{3} \cosh\left(d x + c\right)^{6} + 70 \, a^{3} \cosh\left(d x + c\right)^{4} - 20 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{9} - 36 \, a^{3} \cosh\left(d x + c\right)^{7} + 42 \, a^{3} \cosh\left(d x + c\right)^{5} - 20 \, 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} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{10} - 45 \, a^{3} \cosh\left(d x + c\right)^{8} + 70 \, a^{3} \cosh\left(d x + c\right)^{6} - 50 \, 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)^{2} + 12 \, {\left(a^{3} \cosh\left(d x + c\right)^{11} - 5 \, a^{3} \cosh\left(d x + c\right)^{9} + 10 \, a^{3} \cosh\left(d x + c\right)^{7} - 10 \, 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)\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 \, a^{3} d x \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{3} d x - a^{3} - a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 6 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 2 \, {\left(15 \, a^{3} d x - 17 \, a^{3} - 15 \, a^{2} b - 6 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(5 \, a^{3} d x - 4 \, a^{3} + 4 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} d x - a^{3} - a^{2} b\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*d*x*cosh(d*x + c)^12 + 36*a^3*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*a^3*d*x*sinh(d*x + c)^12 - 18*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^10 + 18*(11*a^3*d*x*cosh(d*x + c)^2 - a^3*d*x + a^3 + a^2*b)*sinh(d*x + c)^10 + 60*(11*a^3*d*x*cosh(d*x + c)^3 - 3*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 9*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^8 + 9*(165*a^3*d*x*cosh(d*x + c)^4 + 5*a^3*d*x - 4*a^3 + 4*a*b^2 - 90*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 72*(33*a^3*d*x*cosh(d*x + c)^5 - 30*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^3 + (5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^6 + 4*(693*a^3*d*x*cosh(d*x + c)^6 - 15*a^3*d*x - 945*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^4 + 17*a^3 + 15*a^2*b + 6*a*b^2 + 8*b^3 + 63*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(99*a^3*d*x*cosh(d*x + c)^7 - 189*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^5 + 21*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^3 - (15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*a^3*d*x + 9*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^4 + 3*(495*a^3*d*x*cosh(d*x + c)^8 - 1260*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^6 + 15*a^3*d*x + 210*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^4 - 12*a^3 + 12*a*b^2 - 20*(15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(165*a^3*d*x*cosh(d*x + c)^9 - 540*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^7 + 126*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^5 - 20*(15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^3 + 9*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 18*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^2 + 6*(33*a^3*d*x*cosh(d*x + c)^10 - 135*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^8 + 42*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^6 - 3*a^3*d*x - 10*(15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^4 + 3*a^3 + 3*a^2*b + 9*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 - 6*a^3*cosh(d*x + c)^10 + 15*a^3*cosh(d*x + c)^8 + 6*(11*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 - 3*a^3*cosh(d*x + c))*sinh(d*x + c)^9 - 20*a^3*cosh(d*x + c)^6 + 15*(33*a^3*cosh(d*x + c)^4 - 18*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^8 + 24*(33*a^3*cosh(d*x + c)^5 - 30*a^3*cosh(d*x + c)^3 + 5*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 15*a^3*cosh(d*x + c)^4 + 4*(231*a^3*cosh(d*x + c)^6 - 315*a^3*cosh(d*x + c)^4 + 105*a^3*cosh(d*x + c)^2 - 5*a^3)*sinh(d*x + c)^6 + 24*(33*a^3*cosh(d*x + c)^7 - 63*a^3*cosh(d*x + c)^5 + 35*a^3*cosh(d*x + c)^3 - 5*a^3*cosh(d*x + c))*sinh(d*x + c)^5 - 6*a^3*cosh(d*x + c)^2 + 15*(33*a^3*cosh(d*x + c)^8 - 84*a^3*cosh(d*x + c)^6 + 70*a^3*cosh(d*x + c)^4 - 20*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 20*(11*a^3*cosh(d*x + c)^9 - 36*a^3*cosh(d*x + c)^7 + 42*a^3*cosh(d*x + c)^5 - 20*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 6*(11*a^3*cosh(d*x + c)^10 - 45*a^3*cosh(d*x + c)^8 + 70*a^3*cosh(d*x + c)^6 - 50*a^3*cosh(d*x + c)^4 + 15*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^2 + 12*(a^3*cosh(d*x + c)^11 - 5*a^3*cosh(d*x + c)^9 + 10*a^3*cosh(d*x + c)^7 - 10*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))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*a^3*d*x*cosh(d*x + c)^11 - 15*(a^3*d*x - a^3 - a^2*b)*cosh(d*x + c)^9 + 6*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^7 - 2*(15*a^3*d*x - 17*a^3 - 15*a^2*b - 6*a*b^2 - 8*b^3)*cosh(d*x + c)^5 + 3*(5*a^3*d*x - 4*a^3 + 4*a*b^2)*cosh(d*x + c)^3 - 3*(a^3*d*x - a^3 - a^2*b)*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
136,1,941,0,0.424348," ","integrate((a+b*sech(d*x+c)^2)^4,x, algorithm=""fricas"")","\frac{{\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(105 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(75 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4} + 3 \, {\left(105 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(5 \, {\left(105 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 135 \, a^{3} b + 225 \, a^{2} b^{2} + 168 \, a b^{3} + 36 \, b^{4} + 10 \, {\left(75 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(3 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(105 \, a^{4} d x - 420 \, a^{3} b - 420 \, a^{2} b^{2} - 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right) + 28 \, {\left({\left(105 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(75 \, a^{3} b + 105 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} b + 135 \, a^{2} b^{2} + 120 \, a b^{3} + 60 \, b^{4} + 9 \, {\left(45 \, a^{3} b + 75 \, a^{2} b^{2} + 56 \, a b^{3} + 12 \, 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*((105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^7 + 7*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(105*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*sinh(d*x + c)^7 + 7*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^5 + 28*(75*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4 + 3*(105*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 35*((105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^3 + (105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^3 + 28*(5*(105*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 135*a^3*b + 225*a^2*b^2 + 168*a*b^3 + 36*b^4 + 10*(75*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 7*(3*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^5 + 10*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c)^3 + 9*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(105*a^4*d*x - 420*a^3*b - 420*a^2*b^2 - 224*a*b^3 - 48*b^4)*cosh(d*x + c) + 28*((105*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*cosh(d*x + c)^6 + 5*(75*a^3*b + 105*a^2*b^2 + 56*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 75*a^3*b + 135*a^2*b^2 + 120*a*b^3 + 60*b^4 + 9*(45*a^3*b + 75*a^2*b^2 + 56*a*b^3 + 12*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
137,1,1652,0,0.427105," ","integrate((a+b*sech(d*x+c)^2)^5,x, algorithm=""fricas"")","\frac{{\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(1575 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(1225 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5} + 4 \, {\left(1575 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(4 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 9 \, {\left(3500 \, a^{4} b + 7000 \, a^{3} b^{2} + 6720 \, a^{2} b^{3} + 2880 \, a b^{4} + 512 \, b^{5} + 14 \, {\left(1575 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(1225 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(14 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(28 \, {\left(1575 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 14700 \, a^{4} b + 32200 \, a^{3} b^{2} + 35840 \, a^{2} b^{3} + 20160 \, a b^{4} + 3584 \, b^{5} + 105 \, {\left(1225 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, 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} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(4 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, {\left(315 \, a^{5} d x - 1575 \, a^{4} b - 2100 \, a^{3} b^{2} - 1680 \, a^{2} b^{3} - 720 \, a b^{4} - 128 \, b^{5}\right)} \cosh\left(d x + c\right) + 9 \, {\left({\left(1575 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(1225 \, a^{4} b + 2100 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2450 \, a^{4} b + 5600 \, a^{3} b^{2} + 6720 \, a^{2} b^{3} + 4480 \, a b^{4} + 1792 \, b^{5} + 20 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(525 \, a^{4} b + 1150 \, a^{3} b^{2} + 1280 \, a^{2} b^{3} + 720 \, a b^{4} + 128 \, 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*((315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^9 + 9*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)*sinh(d*x + c)^8 + (1575*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*sinh(d*x + c)^9 + 9*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^7 + 9*(1225*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5 + 4*(1575*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(4*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^3 + 3*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^5 + 9*(3500*a^4*b + 7000*a^3*b^2 + 6720*a^2*b^3 + 2880*a*b^4 + 512*b^5 + 14*(1575*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^4 + 21*(1225*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(14*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^5 + 35*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^3 + 20*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^3 + 3*(28*(1575*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^6 + 14700*a^4*b + 32200*a^3*b^2 + 35840*a^2*b^3 + 20160*a*b^4 + 3584*b^5 + 105*(1225*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^4 + 120*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(4*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^7 + 21*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^5 + 40*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c)^3 + 28*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + 126*(315*a^5*d*x - 1575*a^4*b - 2100*a^3*b^2 - 1680*a^2*b^3 - 720*a*b^4 - 128*b^5)*cosh(d*x + c) + 9*((1575*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^8 + 7*(1225*a^4*b + 2100*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^6 + 2450*a^4*b + 5600*a^3*b^2 + 6720*a^2*b^3 + 4480*a*b^4 + 1792*b^5 + 20*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 720*a*b^4 + 128*b^5)*cosh(d*x + c)^4 + 28*(525*a^4*b + 1150*a^3*b^2 + 1280*a^2*b^3 + 720*a*b^4 + 128*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
138,1,736,0,0.484650," ","integrate(tanh(d*x+c)^5/(a+b*sech(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\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\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} + 2 \, a b + 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} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 2 \, {\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 \, \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\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} d \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} d \cosh\left(d x + c\right)^{2} + a b^{2} d + 2 \, {\left(3 \, a b^{2} d \cosh\left(d x + c\right)^{2} + a b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} d \cosh\left(d x + c\right)^{3} + a b^{2} 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)*cosh(d*x + c)^2 + 4*(3*b^2*d*x*cosh(d*x + c)^2 + b^2*d*x + a*b)*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 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(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 + 4*((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*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 2*((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*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)*cosh(d*x + c))*sinh(d*x + c))/(a*b^2*d*cosh(d*x + c)^4 + 4*a*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*d*sinh(d*x + c)^4 + 2*a*b^2*d*cosh(d*x + c)^2 + a*b^2*d + 2*(3*a*b^2*d*cosh(d*x + c)^2 + a*b^2*d)*sinh(d*x + c)^2 + 4*(a*b^2*d*cosh(d*x + c)^3 + a*b^2*d*cosh(d*x + c))*sinh(d*x + c))","B",0
139,1,683,0,0.449242," ","integrate(tanh(d*x+c)^4/(a+b*sech(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({\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}{b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b + 2 \, b^{2}\right)} \sqrt{\frac{a + b}{b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, a}{2 \, {\left(a b d \cosh\left(d x + c\right)^{2} + 2 \, a b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b d \sinh\left(d x + c\right)^{2} + a b 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({\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}{b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{a + b}{b}}}{2 \, {\left(a + b\right)}}\right) - 2 \, a}{a b d \cosh\left(d x + c\right)^{2} + 2 \, a b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b d \sinh\left(d x + c\right)^{2} + a b 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 + 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)/b)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 2*b^2)*sqrt((a + b)/b))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*a)/(a*b*d*cosh(d*x + c)^2 + 2*a*b*d*cosh(d*x + c)*sinh(d*x + c) + a*b*d*sinh(d*x + c)^2 + a*b*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 + 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)/b)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-(a + b)/b)/(a + b)) - 2*a)/(a*b*d*cosh(d*x + c)^2 + 2*a*b*d*cosh(d*x + c)*sinh(d*x + c) + a*b*d*sinh(d*x + c)^2 + a*b*d)]","B",0
140,1,112,0,0.459754," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, b d x - {\left(a + b\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 2 \, a \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{2 \, a b d}"," ",0,"-1/2*(2*b*d*x - (a + b)*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 2*a*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/(a*b*d)","B",0
141,1,419,0,0.454543," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{\frac{a + b}{b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b + 2 \, b^{2}\right)} \sqrt{\frac{a + b}{b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right)}{2 \, a d}, \frac{d x - \sqrt{-\frac{a + b}{b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{a + b}{b}}}{2 \, {\left(a + b\right)}}\right)}{a d}\right]"," ",0,"[1/2*(2*d*x + sqrt((a + b)/b)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 2*b^2)*sqrt((a + b)/b))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/(a*d), (d*x - sqrt(-(a + b)/b)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-(a + b)/b)/(a + b)))/(a*d)]","B",0
142,1,76,0,0.420677," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, d x - \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right)}{2 \, a d}"," ",0,"-1/2*(2*d*x - log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(a*d)","B",0
143,1,436,0,0.441488," ","integrate(1/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right)}{2 \, a d}, \frac{d x - \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right)}{a d}\right]"," ",0,"[1/2*(2*d*x + sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/(a*d), (d*x - sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b))/(a*d)]","B",0
144,1,115,0,0.460959," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a + b\right)} d x - b \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, a \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 + b)*d*x - b*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*a*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^2 + a*b)*d)","B",0
145,1,749,0,0.456767," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + 4 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a + b\right)} d x \sinh\left(d x + c\right)^{2} - 2 \, {\left(a + b\right)} 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 + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 4 \, a}{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{{\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} d x \sinh\left(d x + c\right)^{2} - {\left(a + b\right)} 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 + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 2 \, a}{{\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 + b)*d*x*cosh(d*x + c)^2 + 4*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c) + 2*(a + b)*d*x*sinh(d*x + c)^2 - 2*(a + b)*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 + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*a)/((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 + b)*d*x*cosh(d*x + c)^2 + 2*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c) + (a + b)*d*x*sinh(d*x + c)^2 - (a + b)*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 + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - 2*a)/((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
146,1,862,0,0.523895," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\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(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} + 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(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\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) + 8 \, {\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} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\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)^4 + 8*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^4 + 2*(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*(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 + 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*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((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))) + 8*((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 - a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 2*a^2*b + a*b^2)*d*sinh(d*x + c)^4 - 2*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 - (a^3 + 2*a^2*b + a*b^2)*d)*sinh(d*x + c)^2 + (a^3 + 2*a^2*b + a*b^2)*d + 4*((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^3 - (a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
147,1,2705,0,0.464519," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 36 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{6} - 6 \, {\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)^{4} + 6 \, {\left(15 \, {\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 - 4 \, a^{2} - 6 \, a b\right)} \sinh\left(d x + c\right)^{4} + 24 \, {\left(5 \, {\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 + 4 \, a^{2} + 6 \, a b\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)} d x + 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(15 \, {\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 - 6 \, {\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} + 8 \, a b\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 + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) - 16 \, a^{2} - 28 \, a b + 12 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\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)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d + 6 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{6} - 3 \, {\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)^{4} + 3 \, {\left(15 \, {\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 - 4 \, a^{2} - 6 \, a b\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(5 \, {\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 + 4 \, a^{2} + 6 \, a b\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 + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, {\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 - 6 \, {\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} + 8 \, a b\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 + b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 8 \, a^{2} - 14 \, a b + 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\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)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 8 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d + 6 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(6*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 36*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 6*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^6 - 6*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^4 + 6*(15*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 - 3*(a^2 + 2*a*b + b^2)*d*x - 4*a^2 - 6*a*b)*sinh(d*x + c)^4 + 24*(5*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 - (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(a^2 + 2*a*b + b^2)*d*x + 6*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 8*a*b)*cosh(d*x + c)^2 + 6*(15*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*x - 6*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^2 + 4*a^2 + 8*a*b)*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 + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 16*a^2 - 28*a*b + 12*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 - 2*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 8*a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + 2*a^2*b + a*b^2)*d*sinh(d*x + c)^6 - 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^4 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 - (a^3 + 2*a^2*b + a*b^2)*d)*sinh(d*x + c)^4 + 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^3 - 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^4 - 6*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b + a*b^2)*d)*sinh(d*x + c)^2 - (a^3 + 2*a^2*b + a*b^2)*d + 6*((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^5 - 2*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^3 + (a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/3*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 18*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 3*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^6 - 3*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^4 + 3*(15*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 - 3*(a^2 + 2*a*b + b^2)*d*x - 4*a^2 - 6*a*b)*sinh(d*x + c)^4 + 12*(5*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 - (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^2 + 2*a*b + b^2)*d*x + 3*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 8*a*b)*cosh(d*x + c)^2 + 3*(15*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*x - 6*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^2 + 4*a^2 + 8*a*b)*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 + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) - 8*a^2 - 14*a*b + 6*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 - 2*(3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 8*a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + 2*a^2*b + a*b^2)*d*sinh(d*x + c)^6 - 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^4 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 - (a^3 + 2*a^2*b + a*b^2)*d)*sinh(d*x + c)^4 + 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^3 - 3*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^4 - 6*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b + a*b^2)*d)*sinh(d*x + c)^2 - (a^3 + 2*a^2*b + a*b^2)*d + 6*((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^5 - 2*(a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c)^3 + (a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
148,1,853,0,0.495362," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a b^{2} d x \cosh\left(d x + c\right)^{4} + 8 \, a b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a b^{2} d x \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} d x - 4 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a b^{2} d x \cosh\left(d x + c\right)^{2} - a^{2} b - 2 \, a b^{2} - b^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} - a b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{3} - a b^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\left(a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} \sinh\left(d x + c\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\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(a b^{2} d x \cosh\left(d x + c\right)^{3} - {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b^{2} d \sinh\left(d x + c\right)^{4} + a^{3} b^{2} d + 2 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b^{2} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 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*b^2*d*x*cosh(d*x + c)^4 + 8*a*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a*b^2*d*x*sinh(d*x + c)^4 + 2*a*b^2*d*x - 4*(a^2*b + 2*a*b^2 + b^3 - (a*b^2 + 2*b^3)*d*x)*cosh(d*x + c)^2 + 4*(3*a*b^2*d*x*cosh(d*x + c)^2 - a^2*b - 2*a*b^2 - b^3 + (a*b^2 + 2*b^3)*d*x)*sinh(d*x + c)^2 + ((a^3 - a*b^2)*cosh(d*x + c)^4 + 4*(a^3 - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 - a*b^2)*sinh(d*x + c)^4 + a^3 - a*b^2 + 2*(a^3 + 2*a^2*b - a*b^2 - 2*b^3)*cosh(d*x + c)^2 + 2*(a^3 + 2*a^2*b - a*b^2 - 2*b^3 + 3*(a^3 - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 - a*b^2)*cosh(d*x + c)^3 + (a^3 + 2*a^2*b - a*b^2 - 2*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(a^3*cosh(d*x + c)^4 + 4*a^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*sinh(d*x + c)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(d*x + c)^2 + 2*(3*a^3*cosh(d*x + c)^2 + a^3 + 2*a^2*b)*sinh(d*x + c)^2 + 4*(a^3*cosh(d*x + c)^3 + (a^3 + 2*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))) + 8*(a*b^2*d*x*cosh(d*x + c)^3 - (a^2*b + 2*a*b^2 + b^3 - (a*b^2 + 2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a^3*b^2*d*cosh(d*x + c)^4 + 4*a^3*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b^2*d*sinh(d*x + c)^4 + a^3*b^2*d + 2*(a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*a^3*b^2*d*cosh(d*x + c)^2 + (a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + 4*(a^3*b^2*d*cosh(d*x + c)^3 + (a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
149,1,1479,0,0.450176," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a b d x \cosh\left(d x + c\right)^{4} + 16 \, a b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, a b d x \sinh\left(d x + c\right)^{4} + 4 \, a b d x + 4 \, {\left(2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, a b d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\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} - 4 \, b^{2}\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} - 4 \, b^{2}\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} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b + 2 \, b^{2}\right)} \sqrt{\frac{a + b}{b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, a^{2} + 4 \, a b + 8 \, {\left(2 \, a b d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(a^{3} b d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b d \sinh\left(d x + c\right)^{4} + a^{3} b d + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, a b d x \cosh\left(d x + c\right)^{4} + 8 \, a b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a b d x \sinh\left(d x + c\right)^{4} + 2 \, a b d x + 2 \, {\left(2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a b d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\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} - 4 \, b^{2}\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} - 4 \, b^{2}\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} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a + b}{b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{a + b}{b}}}{2 \, {\left(a + b\right)}}\right) + 2 \, a^{2} + 2 \, a b + 4 \, {\left(2 \, a b d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a b + 2 \, b^{2}\right)} d x + a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} b d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b d \sinh\left(d x + c\right)^{4} + a^{3} b d + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 2 \, 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*d*x*cosh(d*x + c)^4 + 16*a*b*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*a*b*d*x*sinh(d*x + c)^4 + 4*a*b*d*x + 4*(2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 4*(6*a*b*d*x*cosh(d*x + c)^2 + 2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*sinh(d*x + c)^2 - ((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 - 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - 2*a*b)*cosh(d*x + c)^2 + a^2 - 4*b^2)*sinh(d*x + c)^2 + a^2 - 2*a*b + 4*((a^2 - 2*a*b)*cosh(d*x + c)^3 + (a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/b)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 2*b^2)*sqrt((a + b)/b))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*a^2 + 4*a*b + 8*(2*a*b*d*x*cosh(d*x + c)^3 + (2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a^3*b*d*cosh(d*x + c)^4 + 4*a^3*b*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*d*sinh(d*x + c)^4 + a^3*b*d + 2*(a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*a^3*b*d*cosh(d*x + c)^2 + (a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + 4*(a^3*b*d*cosh(d*x + c)^3 + (a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*a*b*d*x*cosh(d*x + c)^4 + 8*a*b*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a*b*d*x*sinh(d*x + c)^4 + 2*a*b*d*x + 2*(2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(6*a*b*d*x*cosh(d*x + c)^2 + 2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*sinh(d*x + c)^2 + ((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 - 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - 2*a*b)*cosh(d*x + c)^2 + a^2 - 4*b^2)*sinh(d*x + c)^2 + a^2 - 2*a*b + 4*((a^2 - 2*a*b)*cosh(d*x + c)^3 + (a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a + b)/b)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-(a + b)/b)/(a + b)) + 2*a^2 + 2*a*b + 4*(2*a*b*d*x*cosh(d*x + c)^3 + (2*(a*b + 2*b^2)*d*x + a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a^3*b*d*cosh(d*x + c)^4 + 4*a^3*b*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*d*sinh(d*x + c)^4 + a^3*b*d + 2*(a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*a^3*b*d*cosh(d*x + c)^2 + (a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + 4*(a^3*b*d*cosh(d*x + c)^3 + (a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
150,1,485,0,0.415988," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a d x \cosh\left(d x + c\right)^{4} + 8 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a d x \sinh\left(d x + c\right)^{4} + 2 \, a d x + 4 \, {\left({\left(a + 2 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a d x \cosh\left(d x + c\right)^{2} + {\left(a + 2 \, b\right)} d x - a - b\right)} \sinh\left(d x + c\right)^{2} - {\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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 8 \, {\left(a d x \cosh\left(d x + c\right)^{3} + {\left({\left(a + 2 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4} + a^{3} d + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a*d*x*cosh(d*x + c)^4 + 8*a*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a*d*x*sinh(d*x + c)^4 + 2*a*d*x + 4*((a + 2*b)*d*x - a - b)*cosh(d*x + c)^2 + 4*(3*a*d*x*cosh(d*x + c)^2 + (a + 2*b)*d*x - a - b)*sinh(d*x + c)^2 - (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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*(a*d*x*cosh(d*x + c)^3 + ((a + 2*b)*d*x - a - b)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4 + a^3*d + 2*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^2 + 2*(3*a^3*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b)*d)*sinh(d*x + c)^2 + 4*(a^3*d*cosh(d*x + c)^3 + (a^3 + 2*a^2*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
151,1,1846,0,0.472685," ","integrate(tanh(d*x+c)^2/(a+b*sech(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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 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)} 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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} - {\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\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} + 4 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\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 + 3 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 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)*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 + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*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 + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*d*x)*sinh(d*x + c)^2 + ((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 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + 4*((a^2 + 2*a*b)*cosh(d*x + c)^3 + (a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(2*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 + (a^2*b + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + a^3*b^2)*d*sinh(d*x + c)^4 + 2*(a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b + a^3*b^2)*d + 4*((a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*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 + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*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 + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*d*x)*sinh(d*x + c)^2 - ((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 + 4*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b)*cosh(d*x + c)^2 + a^2 + 4*a*b + 4*b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + 4*((a^2 + 2*a*b)*cosh(d*x + c)^3 + (a^2 + 4*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(2*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 + (a^2*b + 3*a*b^2 + 2*b^3 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + a^3*b^2)*d*sinh(d*x + c)^4 + 2*(a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b + a^3*b^2)*d + 4*((a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
152,1,476,0,0.417905," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, a d x \cosh\left(d x + c\right)^{4} + 8 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a d x \sinh\left(d x + c\right)^{4} + 2 \, a d x + 4 \, {\left({\left(a + 2 \, b\right)} d x - b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a d x \cosh\left(d x + c\right)^{2} + {\left(a + 2 \, b\right)} d x - b\right)} \sinh\left(d x + c\right)^{2} - {\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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 8 \, {\left(a d x \cosh\left(d x + c\right)^{3} + {\left({\left(a + 2 \, b\right)} d x - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4} + a^{3} d + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a*d*x*cosh(d*x + c)^4 + 8*a*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a*d*x*sinh(d*x + c)^4 + 2*a*d*x + 4*((a + 2*b)*d*x - b)*cosh(d*x + c)^2 + 4*(3*a*d*x*cosh(d*x + c)^2 + (a + 2*b)*d*x - b)*sinh(d*x + c)^2 - (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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*(a*d*x*cosh(d*x + c)^3 + ((a + 2*b)*d*x - b)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4 + a^3*d + 2*(a^3 + 2*a^2*b)*d*cosh(d*x + c)^2 + 2*(3*a^3*d*cosh(d*x + c)^2 + (a^3 + 2*a^2*b)*d)*sinh(d*x + c)^2 + 4*(a^3*d*cosh(d*x + c)^3 + (a^3 + 2*a^2*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
153,1,1690,0,0.461450," ","integrate(1/(a+b*sech(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} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, 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} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b + 4 \, {\left({\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, 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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 4 \, a b + 8 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{3} b\right)} d + 4 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 2 \, 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)} 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} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, 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} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b + 4 \, {\left({\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, 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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 2 \, a b + 4 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} d x + a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{3} b\right)} d + 4 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 2 \, 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)*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 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^2 + 4*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 + 2*(a^2 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*sinh(d*x + c)^2 + ((3*a^2 + 2*a*b)*cosh(d*x + c)^4 + 4*(3*a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 2*a*b)*sinh(d*x + c)^4 + 2*(3*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 4*b^2)*sinh(d*x + c)^2 + 3*a^2 + 2*a*b + 4*((3*a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 4*a*b + 8*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 + (2*(a^2 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^3*b)*d*sinh(d*x + c)^4 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + a^3*b)*d*cosh(d*x + c)^2 + (a^4 + 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + a^3*b)*d + 4*((a^4 + a^3*b)*d*cosh(d*x + c)^3 + (a^4 + 3*a^3*b + 2*a^2*b^2)*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 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 + 2*(a^2 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*sinh(d*x + c)^2 - ((3*a^2 + 2*a*b)*cosh(d*x + c)^4 + 4*(3*a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 2*a*b)*sinh(d*x + c)^4 + 2*(3*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 4*b^2)*sinh(d*x + c)^2 + 3*a^2 + 2*a*b + 4*((3*a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 2*a*b + 4*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 + (2*(a^2 + 3*a*b + 2*b^2)*d*x + a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^3*b)*d*sinh(d*x + c)^4 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + a^3*b)*d*cosh(d*x + c)^2 + (a^4 + 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + a^3*b)*d + 4*((a^4 + a^3*b)*d*cosh(d*x + c)^3 + (a^4 + 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
154,1,1031,0,0.550537," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{3} + 2 \, 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^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x - 4 \, {\left(a b^{2} + b^{3} - {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - a b^{2} - b^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\left(a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} \sinh\left(d x + c\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} 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) + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(a b^{2} + b^{3} - {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 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 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^3 + 2*a^2*b + a*b^2)*d*x*sinh(d*x + c)^4 + 2*(a^3 + 2*a^2*b + a*b^2)*d*x - 4*(a*b^2 + b^3 - (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x)*cosh(d*x + c)^2 + 4*(3*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^2 - a*b^2 - b^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x)*sinh(d*x + c)^2 - ((2*a^2*b + a*b^2)*cosh(d*x + c)^4 + 4*(2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b + a*b^2)*sinh(d*x + c)^4 + 2*a^2*b + a*b^2 + 2*(2*a^2*b + 5*a*b^2 + 2*b^3)*cosh(d*x + c)^2 + 2*(2*a^2*b + 5*a*b^2 + 2*b^3 + 3*(2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((2*a^2*b + a*b^2)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 + 2*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(a^3*cosh(d*x + c)^4 + 4*a^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*sinh(d*x + c)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(d*x + c)^2 + 2*(3*a^3*cosh(d*x + c)^2 + a^3 + 2*a^2*b)*sinh(d*x + c)^2 + 4*(a^3*cosh(d*x + c)^3 + (a^3 + 2*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))) + 8*((a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 - (a*b^2 + b^3 - (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 2*a^4*b + a^3*b^2)*d*sinh(d*x + c)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 2*a^4*b + a^3*b^2)*d + 4*((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
155,1,3624,0,0.508083," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 24 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \sinh\left(d x + c\right)^{6} - 4 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{3} + a b^{2} + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, a^{3} - 4 \, a b^{2} - 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x - 4 \, {\left(4 \, a^{3} + 8 \, a^{2} b + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 8 \, a^{2} b - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x - 6 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\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 + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, a^{2} b - 2 \, a b^{2} - {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{2} b - 22 \, a b^{2} - 8 \, b^{3} + 6 \, {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, 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 + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 8 \, a^{2} b + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, 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} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \sinh\left(d x + c\right)^{6} - 2 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{3} + a b^{2} + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, a^{3} - 2 \, a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x - 2 \, {\left(4 \, a^{3} + 8 \, a^{2} b + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 8 \, a^{2} b - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x - 6 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\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 + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, a^{2} b - 2 \, a b^{2} - {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{2} b - 22 \, a b^{2} - 8 \, b^{3} + 6 \, {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, 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 + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} b + 22 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} - a b^{2} - 2 \, b^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 8 \, a^{2} b + 2 \, b^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, 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 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^6 + 24*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(a^3 + 2*a^2*b + a*b^2)*d*x*sinh(d*x + c)^6 - 4*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^4 + 4*(15*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^2 - 2*a^3 + a*b^2 + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*sinh(d*x + c)^4 + 16*(5*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 - (2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*a^3 - 4*a*b^2 - 4*(a^3 + 2*a^2*b + a*b^2)*d*x - 4*(4*a^3 + 8*a^2*b + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^2 + 4*(15*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^4 - 4*a^3 - 8*a^2*b - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x - 6*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((5*a^2*b + 2*a*b^2)*cosh(d*x + c)^6 + 6*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 2*a*b^2)*sinh(d*x + c)^6 + (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + (5*a^2*b + 22*a*b^2 + 8*b^3 + 15*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*a^2*b - 2*a*b^2 - (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 - 5*a^2*b - 22*a*b^2 - 8*b^3 + 6*(5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + 2*(5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^3 - (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(3*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^5 - 2*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 8*a^2*b + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^6 + 6*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5 + 2*a^4*b + a^3*b^2)*d*sinh(d*x + c)^6 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^4 + (15*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d)*sinh(d*x + c)^4 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 6*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^2 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d)*sinh(d*x + c)^2 - (a^5 + 2*a^4*b + a^3*b^2)*d + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^5 + 2*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^6 + 12*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a^3 + 2*a^2*b + a*b^2)*d*x*sinh(d*x + c)^6 - 2*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^4 + 2*(15*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^2 - 2*a^3 + a*b^2 + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*sinh(d*x + c)^4 + 8*(5*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 - (2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*a^3 - 2*a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*d*x - 2*(4*a^3 + 8*a^2*b + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^2 + 2*(15*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^4 - 4*a^3 - 8*a^2*b - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x - 6*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((5*a^2*b + 2*a*b^2)*cosh(d*x + c)^6 + 6*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 2*a*b^2)*sinh(d*x + c)^6 + (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + (5*a^2*b + 22*a*b^2 + 8*b^3 + 15*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*a^2*b - 2*a*b^2 - (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 - 5*a^2*b - 22*a*b^2 - 8*b^3 + 6*(5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + 2*(5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c)^3 - (5*a^2*b + 22*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(3*(a^3 + 2*a^2*b + a*b^2)*d*x*cosh(d*x + c)^5 - 2*(2*a^3 - a*b^2 - 2*b^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 8*a^2*b + 2*b^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^6 + 6*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5 + 2*a^4*b + a^3*b^2)*d*sinh(d*x + c)^6 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^4 + (15*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d)*sinh(d*x + c)^4 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 + 6*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^2 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d)*sinh(d*x + c)^2 - (a^5 + 2*a^4*b + a^3*b^2)*d + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^5 + 2*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
156,1,3624,0,0.716349," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 2 \, b^{4} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 2 \, b^{4} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d x + 15 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 2 \, b^{4} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x + 4 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x + 6 \, {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 2 \, b^{4} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, 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^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a b^{3} + b^{4} + 7 \, {\left(3 \, a^{2} b^{2} + a 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^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{2} b^{2} - 13 \, a b^{3} - 4 \, b^{4} + 30 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} + a b^{3} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{3} + b^{4} - 3 \, {\left(3 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\left({\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 3 \, a^{3} b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 7 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} + 7 \, a^{3} b + 12 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{4} - a^{4} - 7 \, a^{3} b - 12 \, a^{2} b^{2} + 30 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 3 \, a^{3} b + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 7 \, a^{3} b + 12 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} - 3 \, {\left(a^{4} + 7 \, a^{3} b + 12 \, 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} + 3 \, a^{3} b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{4} + 7 \, a^{3} b + 12 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, 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(2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{4} + 6 \, a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 2 \, b^{4} - {\left(a^{4} + 7 \, a^{3} b + 15 \, a^{2} b^{2} + 13 \, a b^{3} + 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + a^{3} b - a b^{3} - b^{4} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d x\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{6} + 7 \, a^{5} b + 15 \, a^{4} b^{2} + 13 \, a^{3} b^{3} + 4 \, a^{2} b^{4}\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 7 \, a^{5} b + 15 \, a^{4} b^{2} + 13 \, a^{3} b^{3} + 4 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 7 \, a^{5} b + 15 \, a^{4} b^{2} + 13 \, a^{3} b^{3} + 4 \, a^{2} b^{4}\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{6} + 7 \, a^{5} b + 15 \, a^{4} b^{2} + 13 \, a^{3} b^{3} + 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\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 + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{6} + 7 \, a^{5} b + 15 \, a^{4} b^{2} + 13 \, a^{3} b^{3} + 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^8 + 16*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*sinh(d*x + c)^8 + 4*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^6 + 4*(14*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^2 + a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*sinh(d*x + c)^6 + 8*(14*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^3 + 3*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(2*a^4 + 6*a^3*b + 4*a^2*b^2 + 2*a*b^3 + 2*b^4 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*x)*cosh(d*x + c)^4 + 4*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^4 + 2*a^4 + 6*a^3*b + 4*a^2*b^2 + 2*a*b^3 + 2*b^4 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*x + 15*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^5 + 5*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^3 + (2*a^4 + 6*a^3*b + 4*a^2*b^2 + 2*a*b^3 + 2*b^4 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x + 4*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2 + 4*(14*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^6 + 15*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^4 + a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x + 6*(2*a^4 + 6*a^3*b + 4*a^2*b^2 + 2*a*b^3 + 2*b^4 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^2*b^2 + a*b^3)*cosh(d*x + c)^8 + 8*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b^2 + a*b^3)*sinh(d*x + c)^8 + 4*(3*a*b^3 + b^4)*cosh(d*x + c)^6 + 4*(3*a*b^3 + b^4 + 7*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)^3 + 3*(3*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2*b^2 + 13*a*b^3 + 4*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)^4 - 3*a^2*b^2 - 13*a*b^3 - 4*b^4 + 30*(3*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^2*b^2 + a*b^3 + 8*(7*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)^5 + 10*(3*a*b^3 + b^4)*cosh(d*x + c)^3 - (3*a^2*b^2 + 13*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a*b^3 + b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b^2 + a*b^3)*cosh(d*x + c)^6 + 15*(3*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a*b^3 + b^4 - 3*(3*a^2*b^2 + 13*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b^2 + a*b^3)*cosh(d*x + c)^7 + 3*(3*a*b^3 + b^4)*cosh(d*x + c)^5 - (3*a^2*b^2 + 13*a*b^3 + 4*b^4)*cosh(d*x + c)^3 + (3*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^4 + 3*a^3*b)*cosh(d*x + c)^8 + 8*(a^4 + 3*a^3*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 3*a^3*b)*sinh(d*x + c)^8 + 4*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^6 + 4*(a^3*b + 3*a^2*b^2 + 7*(a^4 + 3*a^3*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 3*a^3*b)*cosh(d*x + c)^3 + 3*(a^3*b + 3*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 + 7*a^3*b + 12*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*(a^4 + 3*a^3*b)*cosh(d*x + c)^4 - a^4 - 7*a^3*b - 12*a^2*b^2 + 30*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 3*a^3*b + 8*(7*(a^4 + 3*a^3*b)*cosh(d*x + c)^5 + 10*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 - (a^4 + 7*a^3*b + 12*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^4 + 3*a^3*b)*cosh(d*x + c)^6 + 15*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + a^3*b + 3*a^2*b^2 - 3*(a^4 + 7*a^3*b + 12*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 3*a^3*b)*cosh(d*x + c)^7 + 3*(a^3*b + 3*a^2*b^2)*cosh(d*x + c)^5 - (a^4 + 7*a^3*b + 12*a^2*b^2)*cosh(d*x + c)^3 + (a^3*b + 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*(2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^7 + 3*(a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*x)*cosh(d*x + c)^5 + 2*(2*a^4 + 6*a^3*b + 4*a^2*b^2 + 2*a*b^3 + 2*b^4 - (a^4 + 7*a^3*b + 15*a^2*b^2 + 13*a*b^3 + 4*b^4)*d*x)*cosh(d*x + c)^3 + (a^4 + a^3*b - a*b^3 - b^4 + 2*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*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)^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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)^6 - 2*(a^6 + 7*a^5*b + 15*a^4*b^2 + 13*a^3*b^3 + 4*a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 - (a^6 + 7*a^5*b + 15*a^4*b^2 + 13*a^3*b^3 + 4*a^2*b^4)*d)*sinh(d*x + c)^4 + 4*(a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 - (a^6 + 7*a^5*b + 15*a^4*b^2 + 13*a^3*b^3 + 4*a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 - 3*(a^6 + 7*a^5*b + 15*a^4*b^2 + 13*a^3*b^3 + 4*a^2*b^4)*d*cosh(d*x + c)^2 + (a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*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 + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^5 - (a^6 + 7*a^5*b + 15*a^4*b^2 + 13*a^3*b^3 + 4*a^2*b^4)*d*cosh(d*x + c)^3 + (a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
157,1,9849,0,0.612053," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{10} + 120 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 12 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \sinh\left(d x + c\right)^{10} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 12 \, {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a^{4} - 8 \, a^{3} b + a b^{3} + 2 \, b^{4} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 96 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 24 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} - a b^{3} - 3 \, b^{4} - {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(315 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x - 45 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 32 \, a^{4} - 80 \, a^{3} b - 12 \, a b^{3} + 32 \, {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x - 4 \, {\left(4 \, a^{4} + 36 \, a^{3} b + 80 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, b^{4} - 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(135 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 90 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 36 \, a^{3} b - 80 \, a^{2} b^{2} + 6 \, a b^{3} - 6 \, b^{4} + 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x + 12 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4} - 45 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 44 \, a b^{3} - 12 \, b^{4} - 14 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, 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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4} - 15 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 2 \, a b^{3} + 8 \, {\left(15 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4} + 12 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, 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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 26 \, 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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 18 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 36 \, a^{3} b + 80 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, b^{4} - 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{10} + 60 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \sinh\left(d x + c\right)^{10} - 6 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a^{4} - 8 \, a^{3} b + a b^{3} + 2 \, b^{4} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 48 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 12 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(105 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} - a b^{3} - 3 \, b^{4} - {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(315 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x - 45 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 16 \, a^{4} - 40 \, a^{3} b - 6 \, a b^{3} + 16 \, {\left(45 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x - 2 \, {\left(4 \, a^{4} + 36 \, a^{3} b + 80 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, b^{4} - 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(135 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 90 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 36 \, a^{3} b - 80 \, a^{2} b^{2} + 6 \, a b^{3} - 6 \, b^{4} + 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x + 12 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4} - 45 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 44 \, a b^{3} - 12 \, b^{4} - 14 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, 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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4} - 15 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 2 \, a b^{3} + 8 \, {\left(15 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4} + 12 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, 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} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} b^{2} - 26 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(7 \, a^{2} b^{2} + 44 \, a b^{3} + 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 26 \, 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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, {\left(15 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - a b^{3} - 2 \, b^{4} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 18 \, {\left(2 \, a^{4} + 10 \, a^{3} b + 16 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} + 38 \, a^{3} b + 72 \, a^{2} b^{2} + 9 \, b^{4} + 3 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 36 \, a^{3} b + 80 \, a^{2} b^{2} - 6 \, a b^{3} + 6 \, b^{4} - 3 \, {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^10 + 120*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 12*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*sinh(d*x + c)^10 - 12*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^8 + 12*(45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^2 - 4*a^4 - 8*a^3*b + a*b^3 + 2*b^4 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*sinh(d*x + c)^8 + 96*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^3 - (4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 24*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^6 + 24*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^4 - 2*a^4 - 10*a^3*b - 16*a^2*b^2 - a*b^3 - 3*b^4 - (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x - 14*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 48*(63*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^5 - 14*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^3 - 3*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^4 + 8*(315*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^6 - 105*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^4 + 2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x - 45*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 32*a^4 - 80*a^3*b - 12*a*b^3 + 32*(45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^7 - 21*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^5 - 15*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^3 + (2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 12*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x - 4*(4*a^4 + 36*a^3*b + 80*a^2*b^2 - 6*a*b^3 + 6*b^4 - 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^2 + 4*(135*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^8 - 84*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^6 - 90*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^4 - 4*a^4 - 36*a^3*b - 80*a^2*b^2 + 6*a*b^3 - 6*b^4 + 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x + 12*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^10 + 10*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (7*a^2*b^2 + 2*a*b^3)*sinh(d*x + c)^10 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^8 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4 - 45*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^6 + 2*(105*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 - 7*a^2*b^2 - 44*a*b^3 - 12*b^4 - 14*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^5 - 14*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^3 - 3*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 2*(105*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^6 - 35*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 + 44*a*b^3 + 12*b^4 - 15*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 7*a^2*b^2 - 2*a*b^3 + 8*(15*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^7 - 7*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^5 - 5*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + (45*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^8 - 28*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^6 - 30*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 - 26*a*b^3 - 8*b^4 + 12*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^9 - 4*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^7 - 6*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^5 + 4*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^9 - 12*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^7 - 18*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^5 + 4*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^3 - (4*a^4 + 36*a^3*b + 80*a^2*b^2 - 6*a*b^3 + 6*b^4 - 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d)*sinh(d*x + c)^8 - 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^2 - (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d)*sinh(d*x + c)^6 + 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^3 - 3*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^4 - 15*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d)*sinh(d*x + c)^4 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^5 - 5*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^3 + (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^6 - 30*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^4 + 12*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^7 - 6*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^5 + 4*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^3 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/6*(6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^10 + 60*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*sinh(d*x + c)^10 - 6*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^8 + 6*(45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^2 - 4*a^4 - 8*a^3*b + a*b^3 + 2*b^4 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*sinh(d*x + c)^8 + 48*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^3 - (4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 12*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^6 + 12*(105*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^4 - 2*a^4 - 10*a^3*b - 16*a^2*b^2 - a*b^3 - 3*b^4 - (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x - 14*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(63*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^5 - 14*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^3 - 3*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^4 + 4*(315*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^6 - 105*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^4 + 2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x - 45*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 16*a^4 - 40*a^3*b - 6*a*b^3 + 16*(45*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^7 - 21*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^5 - 15*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^3 + (2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x - 2*(4*a^4 + 36*a^3*b + 80*a^2*b^2 - 6*a*b^3 + 6*b^4 - 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^2 + 2*(135*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^8 - 84*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^6 - 90*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^4 - 4*a^4 - 36*a^3*b - 80*a^2*b^2 + 6*a*b^3 - 6*b^4 + 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x + 12*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^10 + 10*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (7*a^2*b^2 + 2*a*b^3)*sinh(d*x + c)^10 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^8 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4 - 45*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^6 + 2*(105*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 - 7*a^2*b^2 - 44*a*b^3 - 12*b^4 - 14*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^5 - 14*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^3 - 3*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 2*(105*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^6 - 35*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 + 44*a*b^3 + 12*b^4 - 15*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 7*a^2*b^2 - 2*a*b^3 + 8*(15*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^7 - 7*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^5 - 5*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + (45*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^8 - 28*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^6 - 30*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 - 26*a*b^3 - 8*b^4 + 12*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^9 - 4*(7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c)^7 - 6*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^5 + 4*(7*a^2*b^2 + 44*a*b^3 + 12*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 - 26*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 4*(15*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*x*cosh(d*x + c)^9 - 12*(4*a^4 + 8*a^3*b - a*b^3 - 2*b^4 + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*d*x)*cosh(d*x + c)^7 - 18*(2*a^4 + 10*a^3*b + 16*a^2*b^2 + a*b^3 + 3*b^4 + (a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^5 + 4*(2*a^4 + 38*a^3*b + 72*a^2*b^2 + 9*b^4 + 3*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*d*x)*cosh(d*x + c)^3 - (4*a^4 + 36*a^3*b + 80*a^2*b^2 - 6*a*b^3 + 6*b^4 - 3*(a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d)*sinh(d*x + c)^8 - 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^2 - (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d)*sinh(d*x + c)^6 + 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^3 - 3*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^4 - 15*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d)*sinh(d*x + c)^4 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^5 - 5*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^3 + (a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^6 - 30*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^4 + 12*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c)^7 - 6*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^5 + 4*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*d*cosh(d*x + c)^3 + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
158,1,5463,0,0.524439," ","integrate(tanh(d*x+c)^6/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{8} + 128 \, a^{2} b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, a^{2} b^{2} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{4} + a^{3} b + 20 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 16 \, a^{2} b^{2} d x + 8 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 15 \, a^{3} b + 18 \, a^{2} b^{2} + 72 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x - 15 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 12 \, a^{4} + 12 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, {\left(56 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(9 \, a^{4} + 13 \, a^{3} b - 28 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 13 \, a^{3} b + 28 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x - 6 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, 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} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, 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 + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, 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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b + 2 \, b^{2}\right)} \sqrt{\frac{a + b}{b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 13 \, a^{3} b - 28 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{5} b^{2} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} b^{2} d \sinh\left(d x + c\right)^{8} + a^{5} b^{2} d + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} b^{2} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{8} + 64 \, a^{2} b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, a^{2} b^{2} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{4} + a^{3} b + 20 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, a^{2} b^{2} d x + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 15 \, a^{3} b + 18 \, a^{2} b^{2} + 72 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x - 15 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a^{4} + 6 \, a^{3} b + 12 \, a^{2} b^{2} + 8 \, {\left(56 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(9 \, a^{4} + 13 \, a^{3} b - 28 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 13 \, a^{3} b + 28 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x - 6 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, 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} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, 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 + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} - 4 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, 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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 32 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 2 \, a^{3} b + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a + b}{b}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-\frac{a + b}{b}}}{2 \, {\left(a + b\right)}}\right) + 4 \, {\left(16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{4} - a^{3} b - 20 \, a^{2} b^{2} - 16 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 15 \, a^{3} b - 18 \, a^{2} b^{2} - 72 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 13 \, a^{3} b - 28 \, a^{2} b^{2} - 32 \, a b^{3} - 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{5} b^{2} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} b^{2} d \sinh\left(d x + c\right)^{8} + a^{5} b^{2} d + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{5} b^{2} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} b^{2} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*a^2*b^2*d*x*cosh(d*x + c)^8 + 128*a^2*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*a^2*b^2*d*x*sinh(d*x + c)^8 - 4*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^6 + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^2 - 3*a^4 + a^3*b + 20*a^2*b^2 + 16*a*b^3 + 16*(a^2*b^2 + 2*a*b^3)*d*x)*sinh(d*x + c)^6 + 16*a^2*b^2*d*x + 8*(112*a^2*b^2*d*x*cosh(d*x + c)^3 - 3*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^4 + 4*(280*a^2*b^2*d*x*cosh(d*x + c)^4 - 9*a^4 - 15*a^3*b + 18*a^2*b^2 + 72*a*b^3 + 48*b^4 + 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x - 15*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 12*a^4 + 12*a^3*b + 24*a^2*b^2 + 16*(56*a^2*b^2*d*x*cosh(d*x + c)^5 - 5*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(9*a^4 + 13*a^3*b - 28*a^2*b^2 - 32*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2 + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^6 - 15*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^4 - 9*a^4 - 13*a^3*b + 28*a^2*b^2 + 32*a*b^3 + 16*(a^2*b^2 + 2*a*b^3)*d*x - 6*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 - 4*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3 + 7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4 + 30*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 - 4*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 2*a^3*b + 16*a*b^3 + 3*(9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/b)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 2*b^2)*sqrt((a + b)/b))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(16*a^2*b^2*d*x*cosh(d*x + c)^7 - 3*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^5 - 2*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 13*a^3*b - 28*a^2*b^2 - 32*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a^5*b^2*d*cosh(d*x + c)^8 + 8*a^5*b^2*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*b^2*d*sinh(d*x + c)^8 + a^5*b^2*d + 4*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*a^5*b^2*d*cosh(d*x + c)^2 + (a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*a^5*b^2*d*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^5*b^2*d*cosh(d*x + c)^4 + 30*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*a^5*b^2*d*cosh(d*x + c)^5 + 10*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^5*b^2*d*cosh(d*x + c)^6 + 15*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^2 + 8*(a^5*b^2*d*cosh(d*x + c)^7 + 3*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + (a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*a^2*b^2*d*x*cosh(d*x + c)^8 + 64*a^2*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*a^2*b^2*d*x*sinh(d*x + c)^8 - 2*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^6 + 2*(112*a^2*b^2*d*x*cosh(d*x + c)^2 - 3*a^4 + a^3*b + 20*a^2*b^2 + 16*a*b^3 + 16*(a^2*b^2 + 2*a*b^3)*d*x)*sinh(d*x + c)^6 + 8*a^2*b^2*d*x + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^3 - 3*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^4 + 2*(280*a^2*b^2*d*x*cosh(d*x + c)^4 - 9*a^4 - 15*a^3*b + 18*a^2*b^2 + 72*a*b^3 + 48*b^4 + 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x - 15*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 6*a^4 + 6*a^3*b + 12*a^2*b^2 + 8*(56*a^2*b^2*d*x*cosh(d*x + c)^5 - 5*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(9*a^4 + 13*a^3*b - 28*a^2*b^2 - 32*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2 + 2*(112*a^2*b^2*d*x*cosh(d*x + c)^6 - 15*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^4 - 9*a^4 - 13*a^3*b + 28*a^2*b^2 + 32*a*b^3 + 16*(a^2*b^2 + 2*a*b^3)*d*x - 6*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 - 4*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3 + 7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4 + 30*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 - 4*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 2*a^3*b + 16*a*b^3 + 3*(9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 - 4*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 12*a^3*b + 16*a^2*b^2 + 32*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 2*a^3*b + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a + b)/b)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-(a + b)/b)/(a + b)) + 4*(16*a^2*b^2*d*x*cosh(d*x + c)^7 - 3*(3*a^4 - a^3*b - 20*a^2*b^2 - 16*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^5 - 2*(9*a^4 + 15*a^3*b - 18*a^2*b^2 - 72*a*b^3 - 48*b^4 - 8*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 13*a^3*b - 28*a^2*b^2 - 32*a*b^3 - 16*(a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a^5*b^2*d*cosh(d*x + c)^8 + 8*a^5*b^2*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*b^2*d*sinh(d*x + c)^8 + a^5*b^2*d + 4*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*a^5*b^2*d*cosh(d*x + c)^2 + (a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*a^5*b^2*d*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^5*b^2*d*cosh(d*x + c)^4 + 30*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*a^5*b^2*d*cosh(d*x + c)^5 + 10*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^5*b^2*d*cosh(d*x + c)^6 + 15*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^2 + 8*(a^5*b^2*d*cosh(d*x + c)^7 + 3*(a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + (a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
159,1,1741,0,0.459123," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \cosh\left(d x + c\right)^{8} + 16 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, a^{2} d x \sinh\left(d x + c\right)^{8} + 8 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} + 2 \, a b\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} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 8 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, a^{2} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x + 30 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 8 \, a b - 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} d x + 16 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 8 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b\right)} d x + 3 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 8 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 16 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 8 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, a b\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + a^{5} d + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} 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)^8 + 16*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*a^2*d*x*sinh(d*x + c)^8 + 8*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^6 + 8*(7*a^2*d*x*cosh(d*x + c)^2 + (a^2 + 2*a*b)*d*x - a^2 - a*b)*sinh(d*x + c)^6 + 16*(7*a^2*d*x*cosh(d*x + c)^3 + 3*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 8*a*b - 6*b^2)*cosh(d*x + c)^4 + 4*(35*a^2*d*x*cosh(d*x + c)^4 + (3*a^2 + 8*a*b + 8*b^2)*d*x + 30*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^2 - 2*a^2 - 8*a*b - 6*b^2)*sinh(d*x + c)^4 + 2*a^2*d*x + 16*(7*a^2*d*x*cosh(d*x + c)^5 + 10*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^3 + ((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 8*a*b - 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^2 + 8*(7*a^2*d*x*cosh(d*x + c)^6 + 15*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^4 + (a^2 + 2*a*b)*d*x + 3*((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 8*a*b - 6*b^2)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 16*(a^2*d*x*cosh(d*x + c)^7 + 3*((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c)^5 + ((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 8*a*b - 6*b^2)*cosh(d*x + c)^3 + ((a^2 + 2*a*b)*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^8 + 8*a^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*d*sinh(d*x + c)^8 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + 4*(7*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^6 + a^5*d + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^4 + 8*(7*a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^5*d*cosh(d*x + c)^4 + 30*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d)*sinh(d*x + c)^4 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + 8*(7*a^5*d*cosh(d*x + c)^5 + 10*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^5*d*cosh(d*x + c)^6 + 15*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^2 + 8*(a^5*d*cosh(d*x + c)^7 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
160,1,6464,0,0.573091," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(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^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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 + 28 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 4 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x + 15 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x + 4 \, {\left(3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 15 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x + 6 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3} + 7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, 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} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, 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 - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, 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 - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 8 \, {\left(16 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\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}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, 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} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(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^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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 + 14 \, a^{3} b^{2} + 12 \, a^{2} b^{3} + 2 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x + 15 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x + 2 \, {\left(3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 15 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x + 6 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3} + 7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, 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} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, 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 - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 4 \, a^{3} b - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, 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 - 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 4 \, a^{3} b - 48 \, a^{2} b^{2} - 96 \, a b^{3} - 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 16 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\right) + 4 \, {\left(16 \, {\left(a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} b + 13 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 29 \, a^{3} b^{2} + 82 \, a^{2} b^{3} + 104 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 16 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 23 \, a^{3} b^{2} + 52 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 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} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\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}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, 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} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{6} b^{2} + a^{5} b^{3}\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}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 11 \, a^{5} b^{3} + 16 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\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 + a^2*b^3)*d*x*cosh(d*x + c)^8 + 128*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^8 + 4*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^6 + 4*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 + 3*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*a^4*b + 28*a^3*b^2 + 24*a^2*b^3 + 4*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 + 3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x + 15*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(56*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 + 5*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^3 + (3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^3*b^2 + a^2*b^3)*d*x + 4*(3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 + 3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 15*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x + 6*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 4*a^3*b - 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^6 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3 + 7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4 + 30*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 4*a^3*b - 8*a^2*b^2 + 8*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^4 + a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3 + 3*(3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(16*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 + 3*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^5 + 2*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 + (3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^6*b^2 + a^5*b^3)*d + 8*((a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 + 64*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^8 + 2*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^6 + 2*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 + 3*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*a^4*b + 14*a^3*b^2 + 12*a^2*b^3 + 2*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 + 3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x + 15*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(56*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 + 5*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^3 + (3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^3*b^2 + a^2*b^3)*d*x + 2*(3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 + 3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 15*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x + 6*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 4*a^3*b - 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^6 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3 + 7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4 + 30*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 4*a^3*b - 8*a^2*b^2 + 8*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^4 + a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3 + 3*(3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 4*a^3*b - 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 4*a^3*b - 48*a^2*b^2 - 96*a*b^3 - 64*b^4)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 16*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 4*(16*(a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 + 3*(a^4*b + 13*a^3*b^2 + 28*a^2*b^3 + 16*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^5 + 2*(3*a^4*b + 29*a^3*b^2 + 82*a^2*b^3 + 104*a*b^4 + 48*b^5 + 8*(3*a^3*b^2 + 11*a^2*b^3 + 16*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 + (3*a^4*b + 23*a^3*b^2 + 52*a^2*b^3 + 32*a*b^4 + 16*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^6*b^2 + a^5*b^3)*d + 8*((a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 11*a^5*b^3 + 16*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
161,1,1753,0,0.447059," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \cosh\left(d x + c\right)^{8} + 16 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, a^{2} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a^{2} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, a^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 6 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, a^{2} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x + 15 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 6 \, a b - 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} d x + 16 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 6 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b\right)} d x + 6 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 6 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 8 \, {\left(2 \, a^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 2 \, a^{2} - 6 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} + 2 \, a b\right)} d x - a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + a^{5} d + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} 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)^8 + 16*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*a^2*d*x*sinh(d*x + c)^8 + 4*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^6 + 4*(14*a^2*d*x*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(14*a^2*d*x*cosh(d*x + c)^3 + 3*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 6*a*b - 6*b^2)*cosh(d*x + c)^4 + 4*(35*a^2*d*x*cosh(d*x + c)^4 + (3*a^2 + 8*a*b + 8*b^2)*d*x + 15*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^2 - 2*a^2 - 6*a*b - 6*b^2)*sinh(d*x + c)^4 + 2*a^2*d*x + 16*(7*a^2*d*x*cosh(d*x + c)^5 + 5*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^3 + ((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 6*a*b - 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^2 + 4*(14*a^2*d*x*cosh(d*x + c)^6 + 15*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^4 + 2*(a^2 + 2*a*b)*d*x + 6*((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 6*a*b - 6*b^2)*cosh(d*x + c)^2 - a^2 - 2*a*b)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*(2*a^2*d*x*cosh(d*x + c)^7 + 3*(2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c)^5 + 2*((3*a^2 + 8*a*b + 8*b^2)*d*x - 2*a^2 - 6*a*b - 6*b^2)*cosh(d*x + c)^3 + (2*(a^2 + 2*a*b)*d*x - a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^8 + 8*a^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*d*sinh(d*x + c)^8 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + 4*(7*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^6 + a^5*d + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^4 + 8*(7*a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^5*d*cosh(d*x + c)^4 + 30*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d)*sinh(d*x + c)^4 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + 8*(7*a^5*d*cosh(d*x + c)^5 + 10*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^5*d*cosh(d*x + c)^6 + 15*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^2 + 8*(a^5*d*cosh(d*x + c)^7 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
162,1,7158,0,0.568306," ","integrate(tanh(d*x+c)^2/(a+b*sech(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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, 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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, a^{4} b + 44 \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 4 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\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 + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x + 15 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 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^{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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\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 + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 15 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x + 6 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b + b^{2}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sqrt{a b + b^{2}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 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^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, 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 + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, a^{4} b + 22 \, a^{3} b^{2} + 12 \, a^{2} b^{3} + 2 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\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 + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x + 15 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 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^{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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\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 + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\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 + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 15 \, {\left(5 \, a^{4} b + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x + 6 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 12 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 60 \, a^{3} b + 144 \, a^{2} b^{2} + 160 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 18 \, a^{3} b + 32 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 + 2 \, b\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\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 + 25 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 16 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b + 73 \, a^{3} b^{2} + 146 \, a^{2} b^{3} + 136 \, a b^{4} + 48 \, b^{5} + 8 \, {\left(3 \, a^{4} b + 14 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 24 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 59 \, a^{3} b^{2} + 76 \, a^{2} b^{3} + 32 \, a b^{4} + 16 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 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^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^6 + 4*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*a^4*b + 44*a^3*b^2 + 24*a^2*b^3 + 4*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*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 + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x + 15*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*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 + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 15*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x + 6*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 12*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3 + 7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4 + 30*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 12*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3 + 3*(9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b + b^2)*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(a*b + b^2))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^5 + 2*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 2*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 + a^5*b^3)*d + 8*((a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^6 + 2*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*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 + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*a^4*b + 22*a^3*b^2 + 12*a^2*b^3 + 2*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*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 + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x + 15*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*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 + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*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 + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 15*(5*a^4*b + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x + 6*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 12*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3 + 7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4 + 30*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 12*a^3*b + 8*a^2*b^2 + 8*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3 + 3*(9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 12*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (9*a^4 + 60*a^3*b + 144*a^2*b^2 + 160*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (3*a^4 + 18*a^3*b + 32*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b - b^2)*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-a*b - b^2)/(a*b + b^2)) + 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 + 25*a^3*b^2 + 36*a^2*b^3 + 16*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^5 + 2*(15*a^4*b + 73*a^3*b^2 + 146*a^2*b^3 + 136*a*b^4 + 48*b^5 + 8*(3*a^4*b + 14*a^3*b^2 + 27*a^2*b^3 + 24*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + 59*a^3*b^2 + 76*a^2*b^3 + 32*a*b^4 + 16*(a^4*b + 4*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 2*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 + a^5*b^3)*d + 8*((a^7*b + 2*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
163,1,1666,0,0.453682," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \cosh\left(d x + c\right)^{8} + 16 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, a^{2} d x \sinh\left(d x + c\right)^{8} + 8 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 4 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, a^{2} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x + 30 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a b - 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} d x + 16 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, 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)^{3} + 8 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b\right)} d x + 3 \, {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 4 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\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 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) + 16 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} d x - 4 \, a b - 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, a b\right)} d x - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + a^{5} d + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} 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)^8 + 16*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*a^2*d*x*sinh(d*x + c)^8 + 8*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^6 + 8*(7*a^2*d*x*cosh(d*x + c)^2 + (a^2 + 2*a*b)*d*x - a*b)*sinh(d*x + c)^6 + 16*(7*a^2*d*x*cosh(d*x + c)^3 + 3*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 + 8*a*b + 8*b^2)*d*x - 4*a*b - 6*b^2)*cosh(d*x + c)^4 + 4*(35*a^2*d*x*cosh(d*x + c)^4 + (3*a^2 + 8*a*b + 8*b^2)*d*x + 30*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^2 - 4*a*b - 6*b^2)*sinh(d*x + c)^4 + 2*a^2*d*x + 16*(7*a^2*d*x*cosh(d*x + c)^5 + 10*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^3 + ((3*a^2 + 8*a*b + 8*b^2)*d*x - 4*a*b - 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^2 + 8*(7*a^2*d*x*cosh(d*x + c)^6 + 15*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^4 + (a^2 + 2*a*b)*d*x + 3*((3*a^2 + 8*a*b + 8*b^2)*d*x - 4*a*b - 6*b^2)*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^8 + 8*a^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 4*(7*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^6 + 8*(7*a^2*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(d*x + c)^4 + 8*(7*a^2*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 4*(7*a^2*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*(a^2*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b)*cosh(d*x + c)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 16*(a^2*d*x*cosh(d*x + c)^7 + 3*((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c)^5 + ((3*a^2 + 8*a*b + 8*b^2)*d*x - 4*a*b - 6*b^2)*cosh(d*x + c)^3 + ((a^2 + 2*a*b)*d*x - a*b)*cosh(d*x + c))*sinh(d*x + c))/(a^5*d*cosh(d*x + c)^8 + 8*a^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*d*sinh(d*x + c)^8 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^6 + 4*(7*a^5*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^6 + a^5*d + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^4 + 8*(7*a^5*d*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^5*d*cosh(d*x + c)^4 + 30*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d)*sinh(d*x + c)^4 + 4*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^2 + 8*(7*a^5*d*cosh(d*x + c)^5 + 10*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^5*d*cosh(d*x + c)^6 + 15*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 + 2*a^4*b)*d)*sinh(d*x + c)^2 + 8*(a^5*d*cosh(d*x + c)^7 + 3*(a^5 + 2*a^4*b)*d*cosh(d*x + c)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
164,1,6538,0,0.570400," ","integrate(1/(a+b*sech(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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} d x + 15 \, {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 36 \, a^{3} b + 24 \, a^{2} b^{2} + 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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x + 6 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} d x + 15 \, {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 18 \, a^{3} b + 12 \, a^{2} b^{2} + 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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x + 6 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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 + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3} + 7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4} + 30 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} + 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 180 \, a^{3} b + 304 \, a^{2} b^{2} + 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 50 \, a^{3} b + 48 \, a^{2} b^{2} + 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{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 + 28 \, a^{2} b^{2} + 16 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(27 \, a^{3} b + 90 \, a^{2} b^{2} + 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x + 15*(9*a^3*b + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 36*a^3*b + 24*a^2*b^2 + 16*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x + 6*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 20*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3 + 7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4 + 30*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 20*a^3*b + 8*a^2*b^2 + 8*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3 + 3*(45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 + 3*(9*a^3*b + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^5 + 2*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 + 30*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 + 15*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 + 2*a^6*b + a^5*b^2)*d + 8*((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x + 15*(9*a^3*b + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 18*a^3*b + 12*a^2*b^2 + 8*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*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 + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x + 6*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 20*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^6 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3 + 7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 + 3*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4 + 30*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 20*a^3*b + 8*a^2*b^2 + 8*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 + 10*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^3 + (45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 + 15*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^4 + 15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3 + 3*(45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 + 3*(15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c)^5 + (45*a^4 + 180*a^3*b + 304*a^2*b^2 + 224*a*b^3 + 64*b^4)*cosh(d*x + c)^3 + (15*a^4 + 50*a^3*b + 48*a^2*b^2 + 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/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 + 28*a^2*b^2 + 16*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c)^5 + 2*(27*a^3*b + 90*a^2*b^2 + 120*a*b^3 + 48*b^4 + 8*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3 + 16*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 + 30*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 + 15*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 + 2*a^6*b + a^5*b^2)*d + 8*((a^7 + 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
165,1,4132,0,0.847459," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 14 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\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} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 6 \, b^{5} - {\left(3 \, a^{5} + 17 \, a^{4} b + 41 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 6 \, a^{3} b^{2} - 20 \, a^{2} b^{3} - 20 \, a b^{4} - 6 \, b^{5} + {\left(3 \, a^{5} + 17 \, a^{4} b + 41 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} d x - 15 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 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(7 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 6 \, b^{5} - {\left(3 \, a^{5} + 17 \, a^{4} b + 41 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x - 4 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 3 \, a^{3} b^{2} - 5 \, a^{2} b^{3} - 2 \, a b^{4} - 15 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x - 6 \, {\left(6 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 6 \, b^{5} - {\left(3 \, a^{5} + 17 \, a^{4} b + 41 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\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 + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(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)^{7} + {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4} + 7 \, {\left(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)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + 2 \, {\left(9 \, a^{4} b + 33 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(9 \, a^{4} b + 33 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5} + 35 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b + 33 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4} + 15 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(9 \, a^{4} b + 33 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, 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 + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} b + 33 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\left(a^{5} \cosh\left(d x + c\right)^{8} + 8 \, a^{5} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{5} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{5} \cosh\left(d x + c\right)^{2} + a^{5} + 2 \, a^{4} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{5} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + a^{5} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{5} \cosh\left(d x + c\right)^{4} + 3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{5} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{5} \cosh\left(d x + c\right)^{6} + a^{5} + 2 \, a^{4} b + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{5} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{4} 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) + 8 \, {\left(2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 6 \, b^{5} - {\left(3 \, a^{5} + 17 \, a^{4} b + 41 \, a^{3} b^{2} + 51 \, a^{2} b^{3} + 32 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 2 \, a b^{4} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 9 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, 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} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 8 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 17 \, a^{7} b + 41 \, a^{6} b^{2} + 51 \, a^{5} b^{3} + 32 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 + 16*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^8 - 4*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^6 - 4*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 14*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*sinh(d*x + c)^6 + 8*(14*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 - 3*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(6*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 6*b^5 - (3*a^5 + 17*a^4*b + 41*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 + 4*(35*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 - 6*a^3*b^2 - 20*a^2*b^3 - 20*a*b^4 - 6*b^5 + (3*a^5 + 17*a^4*b + 41*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*d*x - 15*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(7*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 - 5*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^3 - (6*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 6*b^5 - (3*a^5 + 17*a^4*b + 41*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x - 4*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^2 + 4*(14*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 - 3*a^3*b^2 - 5*a^2*b^3 - 2*a*b^4 - 15*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^4 + 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x - 6*(6*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 6*b^5 - (3*a^5 + 17*a^4*b + 41*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^8 + 8*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(d*x + c)^8 + 4*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^6 + 4*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4 + 7*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^3 + 3*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + 2*(9*a^4*b + 33*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*cosh(d*x + c)^4 + 2*(9*a^4*b + 33*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5 + 35*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^4 + 30*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^5 + 10*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^3 + (9*a^4*b + 33*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^6 + 3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4 + 15*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^4 + 3*(9*a^4*b + 33*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^7 + 3*(3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c)^5 + (9*a^4*b + 33*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*cosh(d*x + c)^3 + (3*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(a^5*cosh(d*x + c)^8 + 8*a^5*cosh(d*x + c)*sinh(d*x + c)^7 + a^5*sinh(d*x + c)^8 + 4*(a^5 + 2*a^4*b)*cosh(d*x + c)^6 + 4*(7*a^5*cosh(d*x + c)^2 + a^5 + 2*a^4*b)*sinh(d*x + c)^6 + 8*(7*a^5*cosh(d*x + c)^3 + 3*(a^5 + 2*a^4*b)*cosh(d*x + c))*sinh(d*x + c)^5 + a^5 + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(d*x + c)^4 + 2*(35*a^5*cosh(d*x + c)^4 + 3*a^5 + 8*a^4*b + 8*a^3*b^2 + 30*(a^5 + 2*a^4*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a^5*cosh(d*x + c)^5 + 10*(a^5 + 2*a^4*b)*cosh(d*x + c)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^5 + 2*a^4*b)*cosh(d*x + c)^2 + 4*(7*a^5*cosh(d*x + c)^6 + a^5 + 2*a^4*b + 15*(a^5 + 2*a^4*b)*cosh(d*x + c)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^5*cosh(d*x + c)^7 + 3*(a^5 + 2*a^4*b)*cosh(d*x + c)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(d*x + c)^3 + (a^5 + 2*a^4*b)*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 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 - 3*(3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c)^5 - 2*(6*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 6*b^5 - (3*a^5 + 17*a^4*b + 41*a^3*b^2 + 51*a^2*b^3 + 32*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 - (3*a^3*b^2 + 5*a^2*b^3 + 2*a*b^4 - 2*(a^5 + 5*a^4*b + 9*a^3*b^2 + 7*a^2*b^3 + 2*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 8*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^8 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 30*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 10*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^3 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 15*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d)*sinh(d*x + c)^2 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d + 8*((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 3*(a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c)^5 + (3*a^8 + 17*a^7*b + 41*a^6*b^2 + 51*a^5*b^3 + 32*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 5*a^7*b + 9*a^6*b^2 + 7*a^5*b^3 + 2*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
166,1,11606,0,0.629672," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{10} + 160 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{10} - 4 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 4 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 180 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 32 \, {\left(60 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 8 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(420 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 16 \, a^{5} - 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 68 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\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} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 32 \, a^{5} - 52 \, a^{3} b^{2} - 24 \, a^{2} b^{3} - 8 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(420 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 24 \, a^{5} - 64 \, a^{4} b - 64 \, a^{3} b^{2} - 15 \, a^{2} b^{3} - 60 \, a b^{4} - 24 \, b^{5} - 35 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x - 15 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\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} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 7 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x - 8 \, {\left(16 \, a^{5} + 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 16 \, a b^{4} + 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(90 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 16 \, a^{5} - 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 16 \, a b^{4} - 15 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x - 6 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4} + 45 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 35 \, a^{4} b - 28 \, a^{3} b^{2} - 8 \, a^{2} b^{3} - 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, a^{4} b - 168 \, a^{3} b^{2} - 400 \, a^{2} b^{3} - 256 \, a b^{4} - 64 \, b^{5} + 35 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, 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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 105 \, a^{4} b - 364 \, a^{3} b^{2} - 248 \, a^{2} b^{3} - 64 \, a b^{4} + 30 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, 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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a 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{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \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) + 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} + 3 \, a b + 2 \, b^{2}\right)} \sqrt{\frac{b}{a + b}}}{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 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \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}\right) + 16 \, {\left(10 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 2 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} + 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 16 \, a b^{4} + 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{10} + 80 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{10} - 2 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 180 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(60 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(420 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 16 \, a^{5} - 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 68 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\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} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 16 \, a^{5} - 26 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(420 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 24 \, a^{5} - 64 \, a^{4} b - 64 \, a^{3} b^{2} - 15 \, a^{2} b^{3} - 60 \, a b^{4} - 24 \, b^{5} - 35 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x - 15 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\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} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 7 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x - 4 \, {\left(16 \, a^{5} + 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 16 \, a b^{4} + 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(90 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 14 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 16 \, a^{5} - 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 16 \, a b^{4} - 15 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x - 6 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4} + 45 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 35 \, a^{4} b - 28 \, a^{3} b^{2} - 8 \, a^{2} b^{3} - 2 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, a^{4} b - 168 \, a^{3} b^{2} - 400 \, a^{2} b^{3} - 256 \, a b^{4} - 64 \, b^{5} + 35 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, 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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 105 \, a^{4} b - 364 \, a^{3} b^{2} - 248 \, a^{2} b^{3} - 64 \, a b^{4} + 30 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, 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 + 28 \, a^{3} b^{2} + 8 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(35 \, a^{4} b + 168 \, a^{3} b^{2} + 400 \, a^{2} b^{3} + 256 \, a b^{4} + 64 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 364 \, a^{3} b^{2} + 248 \, a^{2} b^{3} + 64 \, a 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(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 + 2 \, b\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 8 \, {\left(10 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 2 \, {\left(8 \, a^{5} - 13 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 16 \, a b^{4} - 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(16 \, a^{5} + 32 \, a^{4} b - 13 \, a^{3} b^{2} - 43 \, a^{2} b^{3} - 68 \, a b^{4} - 24 \, b^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 64 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 60 \, a b^{4} + 24 \, b^{5} + 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} + 32 \, a^{4} b + 13 \, a^{3} b^{2} + 43 \, a^{2} b^{3} + 16 \, a b^{4} + 2 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^10 + 160*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 16*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^10 - 4*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^8 - 4*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 180*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*sinh(d*x + c)^8 + 32*(60*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 - (8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 8*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^6 + 8*(420*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 - 16*a^5 - 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 68*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(252*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^3 - 3*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 32*a^5 - 52*a^3*b^2 - 24*a^2*b^3 - 8*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 + 8*(420*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 - 24*a^5 - 64*a^4*b - 64*a^3*b^2 - 15*a^2*b^3 - 60*a*b^4 - 24*b^5 - 35*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^4 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x - 15*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(60*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 - 7*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^5 - 5*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 - (24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 16*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x - 8*(16*a^5 + 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 16*a*b^4 + 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^2 + 8*(90*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^6 - 16*a^5 - 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 16*a*b^4 - 15*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 - 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x - 6*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^10 + 10*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*sinh(d*x + c)^10 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^8 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4 + 45*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^3 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^6 + 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5 + 105*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^4 + 14*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^5 + 14*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^3 + 3*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 35*a^4*b - 28*a^3*b^2 - 8*a^2*b^3 - 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^6 - 35*a^4*b - 168*a^3*b^2 - 400*a^2*b^3 - 256*a*b^4 - 64*b^5 + 35*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^4 + 15*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^7 + 7*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^5 + 5*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^3 - (35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^2 + (45*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^8 + 28*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^6 - 105*a^4*b - 364*a^3*b^2 - 248*a^2*b^3 - 64*a*b^4 + 30*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^4 - 12*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^9 + 4*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^7 + 6*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^5 - 4*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^3 - (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log((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 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 + 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 + (a^2 + 2*a*b)*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 + 3*a*b + 2*b^2)*sqrt(b/(a + b)))/(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 + 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 + (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 16*(10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^9 - 2*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^7 - 3*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^5 - 2*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 - (16*a^5 + 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 16*a*b^4 + 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^10 + 10*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^10 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^8 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^8 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^6 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^3 + 3*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 35*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^4 + 15*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 7*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^5 + 5*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 28*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^6 + 30*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 - 12*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^2 - (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d + 2*(5*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^9 + 4*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^7 + 6*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^5 - 4*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^10 + 80*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 8*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^10 - 2*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^8 - 2*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 180*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*sinh(d*x + c)^8 + 16*(60*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 - (8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^6 + 4*(420*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 - 16*a^5 - 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 68*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(252*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^3 - 3*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 16*a^5 - 26*a^3*b^2 - 12*a^2*b^3 - 4*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 + 4*(420*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 - 24*a^5 - 64*a^4*b - 64*a^3*b^2 - 15*a^2*b^3 - 60*a*b^4 - 24*b^5 - 35*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^4 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x - 15*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(60*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 - 7*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^5 - 5*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 - (24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x - 4*(16*a^5 + 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 16*a*b^4 + 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^2 + 4*(90*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 - 14*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^6 - 16*a^5 - 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 16*a*b^4 - 15*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^4 - 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x - 6*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^10 + 10*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*sinh(d*x + c)^10 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^8 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4 + 45*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^3 + (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^6 + 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5 + 105*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^4 + 14*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^5 + 14*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^3 + 3*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 35*a^4*b - 28*a^3*b^2 - 8*a^2*b^3 - 2*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^6 - 35*a^4*b - 168*a^3*b^2 - 400*a^2*b^3 - 256*a*b^4 - 64*b^5 + 35*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^4 + 15*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^7 + 7*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^5 + 5*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^3 - (35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^2 + (45*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^8 + 28*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^6 - 105*a^4*b - 364*a^3*b^2 - 248*a^2*b^3 - 64*a*b^4 + 30*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^4 - 12*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 28*a^3*b^2 + 8*a^2*b^3)*cosh(d*x + c)^9 + 4*(105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c)^7 + 6*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^5 - 4*(35*a^4*b + 168*a^3*b^2 + 400*a^2*b^3 + 256*a*b^4 + 64*b^5)*cosh(d*x + c)^3 - (105*a^4*b + 364*a^3*b^2 + 248*a^2*b^3 + 64*a*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a + 2*b)*sqrt(-b/(a + b))/b) + 8*(10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^9 - 2*(8*a^5 - 13*a^3*b^2 - 36*a^2*b^3 - 16*a*b^4 - 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c)^7 - 3*(16*a^5 + 32*a^4*b - 13*a^3*b^2 - 43*a^2*b^3 - 68*a*b^4 - 24*b^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^5 - 2*(24*a^5 + 64*a^4*b + 64*a^3*b^2 + 15*a^2*b^3 + 60*a*b^4 + 24*b^5 + 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*d*x)*cosh(d*x + c)^3 - (16*a^5 + 32*a^4*b + 13*a^3*b^2 + 43*a^2*b^3 + 16*a*b^4 + 2*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^10 + 10*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*sinh(d*x + c)^10 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^8 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^2 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^8 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^3 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^4 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^6 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^5 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^3 + 3*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^6 + 35*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^4 + 15*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d)*sinh(d*x + c)^4 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^7 + 7*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^5 + 5*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^8 + 28*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^6 + 30*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^4 - 12*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^2 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d)*sinh(d*x + c)^2 - (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d + 2*(5*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*d*cosh(d*x + c)^9 + 4*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c)^7 + 6*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^5 - 4*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*d*cosh(d*x + c)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
167,1,10255,0,1.341334," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + 33 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(495 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x + 90 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(231 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{6} + 3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} + 105 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} d x + 7 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\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} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} + 70 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x + 60 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\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} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x + 4 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + 30 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x + 3 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\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} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sinh\left(d x + c\right)^{12} + 2 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5} + 33 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\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} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6} - 495 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} - 90 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{4} b^{2} - 28 \, a^{3} b^{3} - 65 \, a^{2} b^{4} - 36 \, a b^{5} - 8 \, b^{6} + 105 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 7 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + 8 \, {\left(99 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 95 \, a^{2} b^{4} + 64 \, a b^{5} + 16 \, b^{6} - 70 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, 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} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5} - 30 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, 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} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - {\left(6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + a + 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}}\right) - 2 \, {\left({\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{6} + 4 \, a^{5} b\right)} \sinh\left(d x + c\right)^{12} + 2 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2} + 33 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{8} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3} - 495 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{4} - 90 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{6} - a^{6} - 8 \, a^{5} b - 24 \, a^{4} b^{2} - 32 \, a^{3} b^{3} + 105 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + a^{6} + 4 \, a^{5} b + 8 \, {\left(99 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{6} - a^{6} - 4 \, a^{5} b + 16 \, a^{4} b^{2} + 64 \, a^{3} b^{3} - 70 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{6} + a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2} - 30 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{6} + 4 \, a^{5} b\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} + 8 \, a^{5} b + 24 \, a^{4} b^{2} + 32 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{6} + 4 \, a^{5} b - 16 \, a^{4} b^{2} - 64 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 8 \, a^{5} b + 16 \, a^{4} 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(3 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d x \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\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} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 12 \, a^{3} b^{3} + 20 \, a^{2} b^{4} + 22 \, a b^{5} + 6 \, b^{6} - {\left(a^{6} + 8 \, a^{5} b + 30 \, a^{4} b^{2} + 60 \, a^{3} b^{3} + 65 \, a^{2} b^{4} + 36 \, a b^{5} + 8 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 28 \, a^{2} b^{4} - 40 \, a b^{5} - 12 \, b^{6} - {\left(a^{6} + 4 \, a^{5} b - 10 \, a^{4} b^{2} - 60 \, a^{3} b^{3} - 95 \, a^{2} b^{4} - 64 \, a b^{5} - 16 \, b^{6}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} + a^{5} b - 4 \, a^{3} b^{3} - 6 \, a^{2} b^{4} - 2 \, a b^{5} + {\left(a^{6} + 8 \, a^{5} b + 22 \, a^{4} b^{2} + 28 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 4 \, a b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \sinh\left(d x + c\right)^{12} + 2 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 2 \, {\left(33 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{10} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, 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} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 90 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(231 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 105 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(99 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 7 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(495 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} - 70 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(55 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} - 14 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} - 14 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d + 4 \, {\left(3 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} d \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{9} - 2 \, {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{9} + 8 \, a^{8} b + 30 \, a^{7} b^{2} + 60 \, a^{6} b^{3} + 65 \, a^{5} b^{4} + 36 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{9} + 4 \, a^{8} b - 10 \, a^{7} b^{2} - 60 \, a^{6} b^{3} - 95 \, a^{5} b^{4} - 64 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 8 \, a^{8} b + 22 \, a^{7} b^{2} + 28 \, a^{6} b^{3} + 17 \, a^{5} b^{4} + 4 \, 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 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^12 + 24*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*sinh(d*x + c)^12 + 4*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^10 + 4*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + 33*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^2 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*sinh(d*x + c)^10 + 40*(11*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^3 + (a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^8 + 2*(495*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^4 + 8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x + 90*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^5 + 30*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^3 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 8*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c)^6 + 8*(231*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^6 + 3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 + 105*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^4 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x + 7*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(99*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^7 + 63*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^5 + 7*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^3 + 3*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^8 + 420*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^6 + 8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 + 70*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^4 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x + 60*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(55*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^9 + 60*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^7 + 14*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^5 + 20*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c)^3 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x + 4*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^10 + 45*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^8 + 14*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^6 + a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + 30*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c)^4 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x + 3*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^12 + 12*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)*sinh(d*x + c)^11 + (6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sinh(d*x + c)^12 + 2*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^10 + 2*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5 + 33*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^3 + (6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^9 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^8 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6 - 495*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^4 - 90*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^5 + 30*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^3 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c)^6 + 4*(231*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^6 - 6*a^4*b^2 - 28*a^3*b^3 - 65*a^2*b^4 - 36*a*b^5 - 8*b^6 + 105*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^4 - 7*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + 8*(99*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^7 + 63*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^5 - 7*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^3 - 3*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c))*sinh(d*x + c)^5 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^4 + (495*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^8 + 420*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^6 - 6*a^4*b^2 - 4*a^3*b^3 + 95*a^2*b^4 + 64*a*b^5 + 16*b^6 - 70*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^4 - 60*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^9 + 60*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^7 - 14*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^5 - 20*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c)^3 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^2 + 2*(33*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^10 + 45*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^8 - 14*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^6 + 6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5 - 30*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c)^4 - 3*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*cosh(d*x + c)^11 + 5*(6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c)^9 - 2*(6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^7 - 6*(6*a^4*b^2 + 28*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*cosh(d*x + c)^5 - (6*a^4*b^2 + 4*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*cosh(d*x + c)^3 + (6*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^6 + 4*a^5*b)*cosh(d*x + c)^12 + 12*(a^6 + 4*a^5*b)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^6 + 4*a^5*b)*sinh(d*x + c)^12 + 2*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^10 + 2*(a^6 + 8*a^5*b + 16*a^4*b^2 + 33*(a^6 + 4*a^5*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^6 + 4*a^5*b)*cosh(d*x + c)^3 + (a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^8 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3 - 495*(a^6 + 4*a^5*b)*cosh(d*x + c)^4 - 90*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^6 + 4*a^5*b)*cosh(d*x + c)^5 + 30*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^3 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c)^6 + 4*(231*(a^6 + 4*a^5*b)*cosh(d*x + c)^6 - a^6 - 8*a^5*b - 24*a^4*b^2 - 32*a^3*b^3 + 105*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^4 - 7*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + a^6 + 4*a^5*b + 8*(99*(a^6 + 4*a^5*b)*cosh(d*x + c)^7 + 63*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^5 - 7*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^3 - 3*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^4 + (495*(a^6 + 4*a^5*b)*cosh(d*x + c)^8 + 420*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^6 - a^6 - 4*a^5*b + 16*a^4*b^2 + 64*a^3*b^3 - 70*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^4 - 60*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^6 + 4*a^5*b)*cosh(d*x + c)^9 + 60*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^7 - 14*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^5 - 20*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c)^3 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^2 + 2*(33*(a^6 + 4*a^5*b)*cosh(d*x + c)^10 + 45*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^8 - 14*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^6 + a^6 + 8*a^5*b + 16*a^4*b^2 - 30*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c)^4 - 3*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(a^6 + 4*a^5*b)*cosh(d*x + c)^11 + 5*(a^6 + 8*a^5*b + 16*a^4*b^2)*cosh(d*x + c)^9 - 2*(a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^7 - 6*(a^6 + 8*a^5*b + 24*a^4*b^2 + 32*a^3*b^3)*cosh(d*x + c)^5 - (a^6 + 4*a^5*b - 16*a^4*b^2 - 64*a^3*b^3)*cosh(d*x + c)^3 + (a^6 + 8*a^5*b + 16*a^4*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*(3*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*x*cosh(d*x + c)^11 + 5*(a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c)^9 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^7 + 6*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 12*a^3*b^3 + 20*a^2*b^4 + 22*a*b^5 + 6*b^6 - (a^6 + 8*a^5*b + 30*a^4*b^2 + 60*a^3*b^3 + 65*a^2*b^4 + 36*a*b^5 + 8*b^6)*d*x)*cosh(d*x + c)^5 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 28*a^2*b^4 - 40*a*b^5 - 12*b^6 - (a^6 + 4*a^5*b - 10*a^4*b^2 - 60*a^3*b^3 - 95*a^2*b^4 - 64*a*b^5 - 16*b^6)*d*x)*cosh(d*x + c)^3 + (a^6 + a^5*b - 4*a^3*b^3 - 6*a^2*b^4 - 2*a*b^5 + (a^6 + 8*a^5*b + 22*a^4*b^2 + 28*a^3*b^3 + 17*a^2*b^4 + 4*a*b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^12 + 12*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^11 + (a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*sinh(d*x + c)^12 + 2*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^10 + 2*(33*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^2 + (a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d)*sinh(d*x + c)^10 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^8 + 20*(11*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^3 + (a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^9 + (495*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^4 + 90*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^2 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d)*sinh(d*x + c)^8 - 4*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c)^6 + 8*(99*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^5 + 30*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^3 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^6 + 105*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^4 - 7*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^2 - (a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d)*sinh(d*x + c)^6 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^4 + 8*(99*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^7 + 63*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^5 - 7*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^3 - 3*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (495*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^8 + 420*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^6 - 70*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^4 - 60*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c)^2 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d)*sinh(d*x + c)^4 + 2*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^2 + 4*(55*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^9 + 60*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^7 - 14*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^5 - 20*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c)^3 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(33*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^10 + 45*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^8 - 14*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^6 - 30*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c)^4 - 3*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d)*sinh(d*x + c)^2 + (a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d + 4*(3*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*d*cosh(d*x + c)^11 + 5*(a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c)^9 - 2*(a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^7 - 6*(a^9 + 8*a^8*b + 30*a^7*b^2 + 60*a^6*b^3 + 65*a^5*b^4 + 36*a^4*b^5 + 8*a^3*b^6)*d*cosh(d*x + c)^5 - (a^9 + 4*a^8*b - 10*a^7*b^2 - 60*a^6*b^3 - 95*a^5*b^4 - 64*a^4*b^5 - 16*a^3*b^6)*d*cosh(d*x + c)^3 + (a^9 + 8*a^8*b + 22*a^7*b^2 + 28*a^6*b^3 + 17*a^5*b^4 + 4*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
168,-1,0,0,0.000000," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate(1/(a+b*sech(d*x+c)^2)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,1,183,0,0.670619," ","integrate((1-sech(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{x \cosh\left(x\right)^{4} + 4 \, x \cosh\left(x\right) \sinh\left(x\right)^{3} + x \sinh\left(x\right)^{4} + 2 \, {\left(x - 1\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, x \cosh\left(x\right)^{2} + x - 1\right)} \sinh\left(x\right)^{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)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left(x \cosh\left(x\right)^{3} + {\left(x - 1\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + x}{\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,"-(x*cosh(x)^4 + 4*x*cosh(x)*sinh(x)^3 + x*sinh(x)^4 + 2*(x - 1)*cosh(x)^2 + 2*(3*x*cosh(x)^2 + x - 1)*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)*log(2*cosh(x)/(cosh(x) - sinh(x))) + 4*(x*cosh(x)^3 + (x - 1)*cosh(x))*sinh(x) + 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
171,1,18,0,0.773230," ","integrate((1-sech(x)^2)^(1/2),x, algorithm=""fricas"")","-x + \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-x + log(2*cosh(x)/(cosh(x) - sinh(x)))","A",0
172,1,18,0,0.534117," ","integrate(1/(1-sech(x)^2)^(1/2),x, algorithm=""fricas"")","-x + \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-x + log(2*sinh(x)/(cosh(x) - sinh(x)))","A",0
173,1,1,0,0.678579," ","integrate((-1+sech(x)^2)^(3/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
174,1,1,0,0.512774," ","integrate((-1+sech(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
175,1,1,0,0.491812," ","integrate(1/(-1+sech(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
176,1,4594,0,1.326016," ","integrate((a+b*sech(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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 10 \, a b - 15 \, b^{2} + 8 \, {\left({\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, \sqrt{2} {\left({\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 10 \, a b - 15 \, b^{2} + 8 \, {\left({\left(2 \, a^{2} + 10 \, a b - 15 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{2} + 26 \, a b - 29 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 9 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((2*a^2 + 10*a*b - 15*b^2)*cosh(x)^8 + 8*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)*sinh(x)^7 + (2*a^2 + 10*a*b - 15*b^2)*sinh(x)^8 + 4*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^6 + 4*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^2 + 2*a^2 + 9*a*b - 5*b^2)*sinh(x)^6 + 8*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^3 + 3*(2*a^2 + 9*a*b - 5*b^2)*cosh(x))*sinh(x)^5 + 2*(6*a^2 + 26*a*b - 29*b^2)*cosh(x)^4 + 2*(35*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^4 + 30*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^2 + 6*a^2 + 26*a*b - 29*b^2)*sinh(x)^4 + 8*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^5 + 10*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^3 + (6*a^2 + 26*a*b - 29*b^2)*cosh(x))*sinh(x)^3 + 4*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^2 + 4*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^6 + 15*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^4 + 3*(6*a^2 + 26*a*b - 29*b^2)*cosh(x)^2 + 2*a^2 + 9*a*b - 5*b^2)*sinh(x)^2 + 2*a^2 + 10*a*b - 15*b^2 + 8*((2*a^2 + 10*a*b - 15*b^2)*cosh(x)^7 + 3*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^5 + (6*a^2 + 26*a*b - 29*b^2)*cosh(x)^3 + (2*a^2 + 9*a*b - 5*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*sqrt(2)*((2*a^2 + 10*a*b - 15*b^2)*cosh(x)^8 + 8*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)*sinh(x)^7 + (2*a^2 + 10*a*b - 15*b^2)*sinh(x)^8 + 4*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^6 + 4*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^2 + 2*a^2 + 9*a*b - 5*b^2)*sinh(x)^6 + 8*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^3 + 3*(2*a^2 + 9*a*b - 5*b^2)*cosh(x))*sinh(x)^5 + 2*(6*a^2 + 26*a*b - 29*b^2)*cosh(x)^4 + 2*(35*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^4 + 30*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^2 + 6*a^2 + 26*a*b - 29*b^2)*sinh(x)^4 + 8*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^5 + 10*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^3 + (6*a^2 + 26*a*b - 29*b^2)*cosh(x))*sinh(x)^3 + 4*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^2 + 4*(7*(2*a^2 + 10*a*b - 15*b^2)*cosh(x)^6 + 15*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^4 + 3*(6*a^2 + 26*a*b - 29*b^2)*cosh(x)^2 + 2*a^2 + 9*a*b - 5*b^2)*sinh(x)^2 + 2*a^2 + 10*a*b - 15*b^2 + 8*((2*a^2 + 10*a*b - 15*b^2)*cosh(x)^7 + 3*(2*a^2 + 9*a*b - 5*b^2)*cosh(x)^5 + (6*a^2 + 26*a*b - 29*b^2)*cosh(x)^3 + (2*a^2 + 9*a*b - 5*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
177,1,8852,0,1.218403," ","integrate((a+b*sech(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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2} + 8 \, {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b + 5 \, b^{2} + 2 \, {\left(3 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2} + 8 \, {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 6 \, a b - 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b + 5 \, b^{2} + 2 \, {\left(3 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2} + 8 \, {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b + 5 \, b^{2} + 2 \, {\left(3 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 6 \, a b - 3 \, b^{2} + 8 \, {\left({\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 6 \, a b - 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - \sqrt{2} {\left({\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b + 5 \, b^{2} + 2 \, {\left(3 \, {\left(a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 6*a*b - 3*b^2)*cosh(x)^8 + 8*(a^2 + 6*a*b - 3*b^2)*cosh(x)*sinh(x)^7 + (a^2 + 6*a*b - 3*b^2)*sinh(x)^8 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^6 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 30*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 3*a^2 + 18*a*b - 9*b^2)*sinh(x)^4 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 10*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 15*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 9*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^2 + a^2 + 6*a*b - 3*b^2 + 8*((a^2 + 6*a*b - 3*b^2)*cosh(x)^7 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + (a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*(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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 2*sqrt(2)*((a*b - 5*b^2)*cosh(x)^6 + 6*(a*b - 5*b^2)*cosh(x)*sinh(x)^5 + (a*b - 5*b^2)*sinh(x)^6 + (a*b + 3*b^2)*cosh(x)^4 + (15*(a*b - 5*b^2)*cosh(x)^2 + a*b + 3*b^2)*sinh(x)^4 + 4*(5*(a*b - 5*b^2)*cosh(x)^3 + (a*b + 3*b^2)*cosh(x))*sinh(x)^3 - (a*b + 3*b^2)*cosh(x)^2 + (15*(a*b - 5*b^2)*cosh(x)^4 + 6*(a*b + 3*b^2)*cosh(x)^2 - a*b - 3*b^2)*sinh(x)^2 - a*b + 5*b^2 + 2*(3*(a*b - 5*b^2)*cosh(x)^5 + 2*(a*b + 3*b^2)*cosh(x)^3 - (a*b + 3*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 6*a*b - 3*b^2)*cosh(x)^8 + 8*(a^2 + 6*a*b - 3*b^2)*cosh(x)*sinh(x)^7 + (a^2 + 6*a*b - 3*b^2)*sinh(x)^8 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^6 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 30*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 3*a^2 + 18*a*b - 9*b^2)*sinh(x)^4 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 10*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 15*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 9*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^2 + a^2 + 6*a*b - 3*b^2 + 8*((a^2 + 6*a*b - 3*b^2)*cosh(x)^7 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + (a^2 + 6*a*b - 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - sqrt(2)*((a*b - 5*b^2)*cosh(x)^6 + 6*(a*b - 5*b^2)*cosh(x)*sinh(x)^5 + (a*b - 5*b^2)*sinh(x)^6 + (a*b + 3*b^2)*cosh(x)^4 + (15*(a*b - 5*b^2)*cosh(x)^2 + a*b + 3*b^2)*sinh(x)^4 + 4*(5*(a*b - 5*b^2)*cosh(x)^3 + (a*b + 3*b^2)*cosh(x))*sinh(x)^3 - (a*b + 3*b^2)*cosh(x)^2 + (15*(a*b - 5*b^2)*cosh(x)^4 + 6*(a*b + 3*b^2)*cosh(x)^2 - a*b - 3*b^2)*sinh(x)^2 - a*b + 5*b^2 + 2*(3*(a*b - 5*b^2)*cosh(x)^5 + 2*(a*b + 3*b^2)*cosh(x)^3 - (a*b + 3*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((a^2 + 6*a*b - 3*b^2)*cosh(x)^8 + 8*(a^2 + 6*a*b - 3*b^2)*cosh(x)*sinh(x)^7 + (a^2 + 6*a*b - 3*b^2)*sinh(x)^8 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^6 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 30*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 3*a^2 + 18*a*b - 9*b^2)*sinh(x)^4 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 10*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 15*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 9*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^2 + a^2 + 6*a*b - 3*b^2 + 8*((a^2 + 6*a*b - 3*b^2)*cosh(x)^7 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + (a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*b - 5*b^2)*cosh(x)^6 + 6*(a*b - 5*b^2)*cosh(x)*sinh(x)^5 + (a*b - 5*b^2)*sinh(x)^6 + (a*b + 3*b^2)*cosh(x)^4 + (15*(a*b - 5*b^2)*cosh(x)^2 + a*b + 3*b^2)*sinh(x)^4 + 4*(5*(a*b - 5*b^2)*cosh(x)^3 + (a*b + 3*b^2)*cosh(x))*sinh(x)^3 - (a*b + 3*b^2)*cosh(x)^2 + (15*(a*b - 5*b^2)*cosh(x)^4 + 6*(a*b + 3*b^2)*cosh(x)^2 - a*b - 3*b^2)*sinh(x)^2 - a*b + 5*b^2 + 2*(3*(a*b - 5*b^2)*cosh(x)^5 + 2*(a*b + 3*b^2)*cosh(x)^3 - (a*b + 3*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + ((a^2 + 6*a*b - 3*b^2)*cosh(x)^8 + 8*(a^2 + 6*a*b - 3*b^2)*cosh(x)*sinh(x)^7 + (a^2 + 6*a*b - 3*b^2)*sinh(x)^8 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^6 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 30*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 3*a^2 + 18*a*b - 9*b^2)*sinh(x)^4 + 8*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 10*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + 4*(7*(a^2 + 6*a*b - 3*b^2)*cosh(x)^6 + 15*(a^2 + 6*a*b - 3*b^2)*cosh(x)^4 + 9*(a^2 + 6*a*b - 3*b^2)*cosh(x)^2 + a^2 + 6*a*b - 3*b^2)*sinh(x)^2 + a^2 + 6*a*b - 3*b^2 + 8*((a^2 + 6*a*b - 3*b^2)*cosh(x)^7 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^5 + 3*(a^2 + 6*a*b - 3*b^2)*cosh(x)^3 + (a^2 + 6*a*b - 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - sqrt(2)*((a*b - 5*b^2)*cosh(x)^6 + 6*(a*b - 5*b^2)*cosh(x)*sinh(x)^5 + (a*b - 5*b^2)*sinh(x)^6 + (a*b + 3*b^2)*cosh(x)^4 + (15*(a*b - 5*b^2)*cosh(x)^2 + a*b + 3*b^2)*sinh(x)^4 + 4*(5*(a*b - 5*b^2)*cosh(x)^3 + (a*b + 3*b^2)*cosh(x))*sinh(x)^3 - (a*b + 3*b^2)*cosh(x)^2 + (15*(a*b - 5*b^2)*cosh(x)^4 + 6*(a*b + 3*b^2)*cosh(x)^2 - a*b - 3*b^2)*sinh(x)^2 - a*b + 5*b^2 + 2*(3*(a*b - 5*b^2)*cosh(x)^5 + 2*(a*b + 3*b^2)*cosh(x)^3 - (a*b + 3*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
178,1,2394,0,0.729814," ","integrate((a+b*sech(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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a - 3 \, b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, \sqrt{2} {\left({\left(a - 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a - 3 \, b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a - 3*b)*cosh(x)^4 + 4*(a - 3*b)*cosh(x)*sinh(x)^3 + (a - 3*b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a - 3*b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a - 3*b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a - 3*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*sqrt(2)*((a - 3*b)*cosh(x)^4 + 4*(a - 3*b)*cosh(x)*sinh(x)^3 + (a - 3*b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a - 3*b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a - 3*b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a - 3*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
179,1,4316,0,0.889116," ","integrate((a+b*sech(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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 - 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)) + (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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - (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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((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)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + ((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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
180,1,1608,0,0.486125," ","integrate((a+b*sech(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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
181,1,2949,0,0.583642," ","integrate((a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 - 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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \frac{1}{4} \, \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \frac{1}{2} \, \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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}{2} \, \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right)\right]"," ",0,"[1/4*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 1/4*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) - 1/2*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 1/2*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)), -1/2*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) - 1/2*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + sqrt(b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a))]","B",0
182,1,3597,0,0.616107," ","integrate(coth(x)*(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \frac{1}{4} \, \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \frac{1}{2} \, \sqrt{a + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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}{2} \, \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right)\right]"," ",0,"[1/4*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 1/4*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) - 1/2*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 1/2*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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)), -1/2*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) - 1/2*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a))]","B",0
183,1,1303,0,0.522679," ","integrate(coth(x)^2*(a+b*sech(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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
184,1,5247,0,0.634349," ","integrate(coth(x)^3*(a+b*sech(x)^2)^(1/2),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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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)^{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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{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{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 - 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{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{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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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 + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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 + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{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{{\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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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 - 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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\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*(((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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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)^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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*(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 - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + ((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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*(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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((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 + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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 + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*(((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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((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 - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
185,1,2341,0,0.621967," ","integrate(coth(x)^4*(a+b*sech(x)^2)^(1/2),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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(4 \, a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, a + 3 \, b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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\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)}}, -\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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} {\left({\left(4 \, a + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(4 \, a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, a + 3 \, b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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\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)}}\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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((4*a + 3*b)*cosh(x)^4 + 4*(4*a + 3*b)*cosh(x)*sinh(x)^3 + (4*a + 3*b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(4*a + 3*b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((4*a + 3*b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 4*a + 3*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((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), -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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*((4*a + 3*b)*cosh(x)^4 + 4*(4*a + 3*b)*cosh(x)*sinh(x)^3 + (4*a + 3*b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(4*a + 3*b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((4*a + 3*b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 4*a + 3*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((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)]","B",0
186,-1,0,0,0.000000," ","integrate(coth(x)^5*(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,1,4226,0,2.145864," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b \cosh\left(x\right)^{10} + 10 \, a b \cosh\left(x\right) \sinh\left(x\right)^{9} + a b \sinh\left(x\right)^{10} + 5 \, a b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{8} + 10 \, a b \cosh\left(x\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{4} + 14 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 10 \, a b \cosh\left(x\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(x\right)^{5} + 70 \, a b \cosh\left(x\right)^{3} + 15 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{6} + 35 \, a b \cosh\left(x\right)^{4} + 15 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} + 5 \, a b \cosh\left(x\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{7} + 7 \, a b \cosh\left(x\right)^{5} + 5 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{8} + 28 \, a b \cosh\left(x\right)^{6} + 30 \, a b \cosh\left(x\right)^{4} + 12 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 10 \, {\left(a b \cosh\left(x\right)^{9} + 4 \, a b \cosh\left(x\right)^{7} + 6 \, a b \cosh\left(x\right)^{5} + 4 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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(a b \cosh\left(x\right)^{10} + 10 \, a b \cosh\left(x\right) \sinh\left(x\right)^{9} + a b \sinh\left(x\right)^{10} + 5 \, a b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{8} + 10 \, a b \cosh\left(x\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{4} + 14 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 10 \, a b \cosh\left(x\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(x\right)^{5} + 70 \, a b \cosh\left(x\right)^{3} + 15 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{6} + 35 \, a b \cosh\left(x\right)^{4} + 15 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} + 5 \, a b \cosh\left(x\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{7} + 7 \, a b \cosh\left(x\right)^{5} + 5 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{8} + 28 \, a b \cosh\left(x\right)^{6} + 30 \, a b \cosh\left(x\right)^{4} + 12 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 10 \, {\left(a b \cosh\left(x\right)^{9} + 4 \, a b \cosh\left(x\right)^{7} + 6 \, a b \cosh\left(x\right)^{5} + 4 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} - 20 \, a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 20 \, a b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 20 \, a b + 8 \, {\left({\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(a b \cosh\left(x\right)^{10} + 10 \, a b \cosh\left(x\right) \sinh\left(x\right)^{9} + a b \sinh\left(x\right)^{10} + 5 \, a b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{8} + 10 \, a b \cosh\left(x\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{4} + 14 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 10 \, a b \cosh\left(x\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(x\right)^{5} + 70 \, a b \cosh\left(x\right)^{3} + 15 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{6} + 35 \, a b \cosh\left(x\right)^{4} + 15 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} + 5 \, a b \cosh\left(x\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{7} + 7 \, a b \cosh\left(x\right)^{5} + 5 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{8} + 28 \, a b \cosh\left(x\right)^{6} + 30 \, a b \cosh\left(x\right)^{4} + 12 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 10 \, {\left(a b \cosh\left(x\right)^{9} + 4 \, a b \cosh\left(x\right)^{7} + 6 \, a b \cosh\left(x\right)^{5} + 4 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 15 \, {\left(a b \cosh\left(x\right)^{10} + 10 \, a b \cosh\left(x\right) \sinh\left(x\right)^{9} + a b \sinh\left(x\right)^{10} + 5 \, a b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{8} + 10 \, a b \cosh\left(x\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{4} + 14 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 10 \, a b \cosh\left(x\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(x\right)^{5} + 70 \, a b \cosh\left(x\right)^{3} + 15 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(x\right)^{6} + 35 \, a b \cosh\left(x\right)^{4} + 15 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} + 5 \, a b \cosh\left(x\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(x\right)^{7} + 7 \, a b \cosh\left(x\right)^{5} + 5 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(x\right)^{8} + 28 \, a b \cosh\left(x\right)^{6} + 30 \, a b \cosh\left(x\right)^{4} + 12 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 10 \, {\left(a b \cosh\left(x\right)^{9} + 4 \, a b \cosh\left(x\right)^{7} + 6 \, a b \cosh\left(x\right)^{5} + 4 \, a b \cosh\left(x\right)^{3} + a b \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, \sqrt{2} {\left({\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 20 \, a b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 20 \, a b + 8 \, {\left({\left(3 \, a^{2} - 20 \, a b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} - 36 \, a b + 4 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 14 \, a b - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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*cosh(x)^10 + 10*a*b*cosh(x)*sinh(x)^9 + a*b*sinh(x)^10 + 5*a*b*cosh(x)^8 + 5*(9*a*b*cosh(x)^2 + a*b)*sinh(x)^8 + 10*a*b*cosh(x)^6 + 40*(3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^7 + 10*(21*a*b*cosh(x)^4 + 14*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 10*a*b*cosh(x)^4 + 4*(63*a*b*cosh(x)^5 + 70*a*b*cosh(x)^3 + 15*a*b*cosh(x))*sinh(x)^5 + 10*(21*a*b*cosh(x)^6 + 35*a*b*cosh(x)^4 + 15*a*b*cosh(x)^2 + a*b)*sinh(x)^4 + 5*a*b*cosh(x)^2 + 40*(3*a*b*cosh(x)^7 + 7*a*b*cosh(x)^5 + 5*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^3 + 5*(9*a*b*cosh(x)^8 + 28*a*b*cosh(x)^6 + 30*a*b*cosh(x)^4 + 12*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 10*(a*b*cosh(x)^9 + 4*a*b*cosh(x)^7 + 6*a*b*cosh(x)^5 + 4*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*cosh(x)^10 + 10*a*b*cosh(x)*sinh(x)^9 + a*b*sinh(x)^10 + 5*a*b*cosh(x)^8 + 5*(9*a*b*cosh(x)^2 + a*b)*sinh(x)^8 + 10*a*b*cosh(x)^6 + 40*(3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^7 + 10*(21*a*b*cosh(x)^4 + 14*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 10*a*b*cosh(x)^4 + 4*(63*a*b*cosh(x)^5 + 70*a*b*cosh(x)^3 + 15*a*b*cosh(x))*sinh(x)^5 + 10*(21*a*b*cosh(x)^6 + 35*a*b*cosh(x)^4 + 15*a*b*cosh(x)^2 + a*b)*sinh(x)^4 + 5*a*b*cosh(x)^2 + 40*(3*a*b*cosh(x)^7 + 7*a*b*cosh(x)^5 + 5*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^3 + 5*(9*a*b*cosh(x)^8 + 28*a*b*cosh(x)^6 + 30*a*b*cosh(x)^4 + 12*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 10*(a*b*cosh(x)^9 + 4*a*b*cosh(x)^7 + 6*a*b*cosh(x)^5 + 4*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((3*a^2 - 20*a*b)*cosh(x)^8 + 8*(3*a^2 - 20*a*b)*cosh(x)*sinh(x)^7 + (3*a^2 - 20*a*b)*sinh(x)^8 + 4*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 20*a*b)*cosh(x)^2 + 3*a^2 - 14*a*b - 5*b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 20*a*b)*cosh(x)^3 + 3*(3*a^2 - 14*a*b - 5*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 - 36*a*b + 4*b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 20*a*b)*cosh(x)^4 + 30*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^2 + 9*a^2 - 36*a*b + 4*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 20*a*b)*cosh(x)^5 + 10*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^3 + (9*a^2 - 36*a*b + 4*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 20*a*b)*cosh(x)^6 + 15*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^4 + 3*(9*a^2 - 36*a*b + 4*b^2)*cosh(x)^2 + 3*a^2 - 14*a*b - 5*b^2)*sinh(x)^2 + 3*a^2 - 20*a*b + 8*((3*a^2 - 20*a*b)*cosh(x)^7 + 3*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^5 + (9*a^2 - 36*a*b + 4*b^2)*cosh(x)^3 + (3*a^2 - 14*a*b - 5*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^10 + 10*a*b*cosh(x)*sinh(x)^9 + a*b*sinh(x)^10 + 5*a*b*cosh(x)^8 + 5*(9*a*b*cosh(x)^2 + a*b)*sinh(x)^8 + 10*a*b*cosh(x)^6 + 40*(3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^7 + 10*(21*a*b*cosh(x)^4 + 14*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 10*a*b*cosh(x)^4 + 4*(63*a*b*cosh(x)^5 + 70*a*b*cosh(x)^3 + 15*a*b*cosh(x))*sinh(x)^5 + 10*(21*a*b*cosh(x)^6 + 35*a*b*cosh(x)^4 + 15*a*b*cosh(x)^2 + a*b)*sinh(x)^4 + 5*a*b*cosh(x)^2 + 40*(3*a*b*cosh(x)^7 + 7*a*b*cosh(x)^5 + 5*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^3 + 5*(9*a*b*cosh(x)^8 + 28*a*b*cosh(x)^6 + 30*a*b*cosh(x)^4 + 12*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 10*(a*b*cosh(x)^9 + 4*a*b*cosh(x)^7 + 6*a*b*cosh(x)^5 + 4*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + 15*(a*b*cosh(x)^10 + 10*a*b*cosh(x)*sinh(x)^9 + a*b*sinh(x)^10 + 5*a*b*cosh(x)^8 + 5*(9*a*b*cosh(x)^2 + a*b)*sinh(x)^8 + 10*a*b*cosh(x)^6 + 40*(3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^7 + 10*(21*a*b*cosh(x)^4 + 14*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 10*a*b*cosh(x)^4 + 4*(63*a*b*cosh(x)^5 + 70*a*b*cosh(x)^3 + 15*a*b*cosh(x))*sinh(x)^5 + 10*(21*a*b*cosh(x)^6 + 35*a*b*cosh(x)^4 + 15*a*b*cosh(x)^2 + a*b)*sinh(x)^4 + 5*a*b*cosh(x)^2 + 40*(3*a*b*cosh(x)^7 + 7*a*b*cosh(x)^5 + 5*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x)^3 + 5*(9*a*b*cosh(x)^8 + 28*a*b*cosh(x)^6 + 30*a*b*cosh(x)^4 + 12*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 10*(a*b*cosh(x)^9 + 4*a*b*cosh(x)^7 + 6*a*b*cosh(x)^5 + 4*a*b*cosh(x)^3 + a*b*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*sqrt(2)*((3*a^2 - 20*a*b)*cosh(x)^8 + 8*(3*a^2 - 20*a*b)*cosh(x)*sinh(x)^7 + (3*a^2 - 20*a*b)*sinh(x)^8 + 4*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 20*a*b)*cosh(x)^2 + 3*a^2 - 14*a*b - 5*b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 20*a*b)*cosh(x)^3 + 3*(3*a^2 - 14*a*b - 5*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 - 36*a*b + 4*b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 20*a*b)*cosh(x)^4 + 30*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^2 + 9*a^2 - 36*a*b + 4*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 20*a*b)*cosh(x)^5 + 10*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^3 + (9*a^2 - 36*a*b + 4*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 20*a*b)*cosh(x)^6 + 15*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^4 + 3*(9*a^2 - 36*a*b + 4*b^2)*cosh(x)^2 + 3*a^2 - 14*a*b - 5*b^2)*sinh(x)^2 + 3*a^2 - 20*a*b + 8*((3*a^2 - 20*a*b)*cosh(x)^7 + 3*(3*a^2 - 14*a*b - 5*b^2)*cosh(x)^5 + (9*a^2 - 36*a*b + 4*b^2)*cosh(x)^3 + (3*a^2 - 14*a*b - 5*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
188,1,8582,0,1.152718," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 18 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(5 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, a b - 7 \, b^{2}\right)} \sinh\left(x\right)^{2} - 5 \, a b + b^{2} + 2 \, {\left(3 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} + 4 \, b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, b \cosh\left(x\right)^{4} + 2 \, {\left(35 \, b \cosh\left(x\right)^{4} + 30 \, b \cosh\left(x\right)^{2} + 3 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b \cosh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, b \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b \cosh\left(x\right)^{6} + 15 \, b \cosh\left(x\right)^{4} + 9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b \cosh\left(x\right)^{7} + 3 \, b \cosh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{{\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 18 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 6 \, a b - 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \sqrt{2} {\left({\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(5 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, a b - 7 \, b^{2}\right)} \sinh\left(x\right)^{2} - 5 \, a b + b^{2} + 2 \, {\left(3 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} + 4 \, b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, b \cosh\left(x\right)^{4} + 2 \, {\left(35 \, b \cosh\left(x\right)^{4} + 30 \, b \cosh\left(x\right)^{2} + 3 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b \cosh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, b \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b \cosh\left(x\right)^{6} + 15 \, b \cosh\left(x\right)^{4} + 9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b \cosh\left(x\right)^{7} + 3 \, b \cosh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{8 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 8 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) - {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 18 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(5 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, a b - 7 \, b^{2}\right)} \sinh\left(x\right)^{2} - 5 \, a b + b^{2} + 2 \, {\left(3 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} + 4 \, b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, b \cosh\left(x\right)^{4} + 2 \, {\left(35 \, b \cosh\left(x\right)^{4} + 30 \, b \cosh\left(x\right)^{2} + 3 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b \cosh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, b \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b \cosh\left(x\right)^{6} + 15 \, b \cosh\left(x\right)^{4} + 9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b \cosh\left(x\right)^{7} + 3 \, b \cosh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{4 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 18 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 6 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 6 \, a b - 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 4 \, {\left(a b \cosh\left(x\right)^{8} + 8 \, a b \cosh\left(x\right) \sinh\left(x\right)^{7} + a b \sinh\left(x\right)^{8} + 4 \, a b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{6} + 6 \, a b \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b \cosh\left(x\right)^{4} + 30 \, a b \cosh\left(x\right)^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a b \cosh\left(x\right)^{5} + 10 \, a b \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b \cosh\left(x\right)^{6} + 15 \, a b \cosh\left(x\right)^{4} + 9 \, a b \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{2} + a b + 8 \, {\left(a b \cosh\left(x\right)^{7} + 3 \, a b \cosh\left(x\right)^{5} + 3 \, a b \cosh\left(x\right)^{3} + a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{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{2} {\left({\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(5 \, a b - b^{2}\right)} \sinh\left(x\right)^{6} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, a b - 7 \, b^{2}\right)} \sinh\left(x\right)^{2} - 5 \, a b + b^{2} + 2 \, {\left(3 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(5 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} + 4 \, b \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, b \cosh\left(x\right)^{4} + 2 \, {\left(35 \, b \cosh\left(x\right)^{4} + 30 \, b \cosh\left(x\right)^{2} + 3 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b \cosh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, b \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b \cosh\left(x\right)^{6} + 15 \, b \cosh\left(x\right)^{4} + 9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b \cosh\left(x\right)^{7} + 3 \, b \cosh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}\right]"," ",0,"[1/16*(4*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 - 6*a*b - b^2)*cosh(x)^8 + 8*(3*a^2 - 6*a*b - b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 6*a*b - b^2)*sinh(x)^8 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 30*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 9*a^2 - 18*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 10*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 15*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 9*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^2 + 3*a^2 - 6*a*b - b^2 + 8*((3*a^2 - 6*a*b - b^2)*cosh(x)^7 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + (3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((5*a*b - b^2)*cosh(x)^6 + 6*(5*a*b - b^2)*cosh(x)*sinh(x)^5 + (5*a*b - b^2)*sinh(x)^6 + (5*a*b + 7*b^2)*cosh(x)^4 + (15*(5*a*b - b^2)*cosh(x)^2 + 5*a*b + 7*b^2)*sinh(x)^4 + 4*(5*(5*a*b - b^2)*cosh(x)^3 + (5*a*b + 7*b^2)*cosh(x))*sinh(x)^3 - (5*a*b + 7*b^2)*cosh(x)^2 + (15*(5*a*b - b^2)*cosh(x)^4 + 6*(5*a*b + 7*b^2)*cosh(x)^2 - 5*a*b - 7*b^2)*sinh(x)^2 - 5*a*b + b^2 + 2*(3*(5*a*b - b^2)*cosh(x)^5 + 2*(5*a*b + 7*b^2)*cosh(x)^3 - (5*a*b + 7*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 + 4*b*cosh(x)^6 + 4*(7*b*cosh(x)^2 + b)*sinh(x)^6 + 8*(7*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^5 + 6*b*cosh(x)^4 + 2*(35*b*cosh(x)^4 + 30*b*cosh(x)^2 + 3*b)*sinh(x)^4 + 8*(7*b*cosh(x)^5 + 10*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 4*b*cosh(x)^2 + 4*(7*b*cosh(x)^6 + 15*b*cosh(x)^4 + 9*b*cosh(x)^2 + b)*sinh(x)^2 + 8*(b*cosh(x)^7 + 3*b*cosh(x)^5 + 3*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/8*(((3*a^2 - 6*a*b - b^2)*cosh(x)^8 + 8*(3*a^2 - 6*a*b - b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 6*a*b - b^2)*sinh(x)^8 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 30*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 9*a^2 - 18*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 10*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 15*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 9*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^2 + 3*a^2 - 6*a*b - b^2 + 8*((3*a^2 - 6*a*b - b^2)*cosh(x)^7 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + (3*a^2 - 6*a*b - 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + sqrt(2)*((5*a*b - b^2)*cosh(x)^6 + 6*(5*a*b - b^2)*cosh(x)*sinh(x)^5 + (5*a*b - b^2)*sinh(x)^6 + (5*a*b + 7*b^2)*cosh(x)^4 + (15*(5*a*b - b^2)*cosh(x)^2 + 5*a*b + 7*b^2)*sinh(x)^4 + 4*(5*(5*a*b - b^2)*cosh(x)^3 + (5*a*b + 7*b^2)*cosh(x))*sinh(x)^3 - (5*a*b + 7*b^2)*cosh(x)^2 + (15*(5*a*b - b^2)*cosh(x)^4 + 6*(5*a*b + 7*b^2)*cosh(x)^2 - 5*a*b - 7*b^2)*sinh(x)^2 - 5*a*b + b^2 + 2*(3*(5*a*b - b^2)*cosh(x)^5 + 2*(5*a*b + 7*b^2)*cosh(x)^3 - (5*a*b + 7*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 + 4*b*cosh(x)^6 + 4*(7*b*cosh(x)^2 + b)*sinh(x)^6 + 8*(7*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^5 + 6*b*cosh(x)^4 + 2*(35*b*cosh(x)^4 + 30*b*cosh(x)^2 + 3*b)*sinh(x)^4 + 8*(7*b*cosh(x)^5 + 10*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 4*b*cosh(x)^2 + 4*(7*b*cosh(x)^6 + 15*b*cosh(x)^4 + 9*b*cosh(x)^2 + b)*sinh(x)^2 + 8*(b*cosh(x)^7 + 3*b*cosh(x)^5 + 3*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/16*(8*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + 8*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) - ((3*a^2 - 6*a*b - b^2)*cosh(x)^8 + 8*(3*a^2 - 6*a*b - b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 6*a*b - b^2)*sinh(x)^8 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 30*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 9*a^2 - 18*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 10*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 15*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 9*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^2 + 3*a^2 - 6*a*b - b^2 + 8*((3*a^2 - 6*a*b - b^2)*cosh(x)^7 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + (3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)*((5*a*b - b^2)*cosh(x)^6 + 6*(5*a*b - b^2)*cosh(x)*sinh(x)^5 + (5*a*b - b^2)*sinh(x)^6 + (5*a*b + 7*b^2)*cosh(x)^4 + (15*(5*a*b - b^2)*cosh(x)^2 + 5*a*b + 7*b^2)*sinh(x)^4 + 4*(5*(5*a*b - b^2)*cosh(x)^3 + (5*a*b + 7*b^2)*cosh(x))*sinh(x)^3 - (5*a*b + 7*b^2)*cosh(x)^2 + (15*(5*a*b - b^2)*cosh(x)^4 + 6*(5*a*b + 7*b^2)*cosh(x)^2 - 5*a*b - 7*b^2)*sinh(x)^2 - 5*a*b + b^2 + 2*(3*(5*a*b - b^2)*cosh(x)^5 + 2*(5*a*b + 7*b^2)*cosh(x)^3 - (5*a*b + 7*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 + 4*b*cosh(x)^6 + 4*(7*b*cosh(x)^2 + b)*sinh(x)^6 + 8*(7*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^5 + 6*b*cosh(x)^4 + 2*(35*b*cosh(x)^4 + 30*b*cosh(x)^2 + 3*b)*sinh(x)^4 + 8*(7*b*cosh(x)^5 + 10*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 4*b*cosh(x)^2 + 4*(7*b*cosh(x)^6 + 15*b*cosh(x)^4 + 9*b*cosh(x)^2 + b)*sinh(x)^2 + 8*(b*cosh(x)^7 + 3*b*cosh(x)^5 + 3*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/8*(4*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((3*a^2 - 6*a*b - b^2)*cosh(x)^8 + 8*(3*a^2 - 6*a*b - b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 6*a*b - b^2)*sinh(x)^8 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 30*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 9*a^2 - 18*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 10*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 6*a*b - b^2)*cosh(x)^6 + 15*(3*a^2 - 6*a*b - b^2)*cosh(x)^4 + 9*(3*a^2 - 6*a*b - b^2)*cosh(x)^2 + 3*a^2 - 6*a*b - b^2)*sinh(x)^2 + 3*a^2 - 6*a*b - b^2 + 8*((3*a^2 - 6*a*b - b^2)*cosh(x)^7 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^5 + 3*(3*a^2 - 6*a*b - b^2)*cosh(x)^3 + (3*a^2 - 6*a*b - 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 4*(a*b*cosh(x)^8 + 8*a*b*cosh(x)*sinh(x)^7 + a*b*sinh(x)^8 + 4*a*b*cosh(x)^6 + 4*(7*a*b*cosh(x)^2 + a*b)*sinh(x)^6 + 6*a*b*cosh(x)^4 + 8*(7*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^5 + 2*(35*a*b*cosh(x)^4 + 30*a*b*cosh(x)^2 + 3*a*b)*sinh(x)^4 + 4*a*b*cosh(x)^2 + 8*(7*a*b*cosh(x)^5 + 10*a*b*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 4*(7*a*b*cosh(x)^6 + 15*a*b*cosh(x)^4 + 9*a*b*cosh(x)^2 + a*b)*sinh(x)^2 + a*b + 8*(a*b*cosh(x)^7 + 3*a*b*cosh(x)^5 + 3*a*b*cosh(x)^3 + a*b*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + sqrt(2)*((5*a*b - b^2)*cosh(x)^6 + 6*(5*a*b - b^2)*cosh(x)*sinh(x)^5 + (5*a*b - b^2)*sinh(x)^6 + (5*a*b + 7*b^2)*cosh(x)^4 + (15*(5*a*b - b^2)*cosh(x)^2 + 5*a*b + 7*b^2)*sinh(x)^4 + 4*(5*(5*a*b - b^2)*cosh(x)^3 + (5*a*b + 7*b^2)*cosh(x))*sinh(x)^3 - (5*a*b + 7*b^2)*cosh(x)^2 + (15*(5*a*b - b^2)*cosh(x)^4 + 6*(5*a*b + 7*b^2)*cosh(x)^2 - 5*a*b - 7*b^2)*sinh(x)^2 - 5*a*b + b^2 + 2*(3*(5*a*b - b^2)*cosh(x)^5 + 2*(5*a*b + 7*b^2)*cosh(x)^3 - (5*a*b + 7*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 + 4*b*cosh(x)^6 + 4*(7*b*cosh(x)^2 + b)*sinh(x)^6 + 8*(7*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^5 + 6*b*cosh(x)^4 + 2*(35*b*cosh(x)^4 + 30*b*cosh(x)^2 + 3*b)*sinh(x)^4 + 8*(7*b*cosh(x)^5 + 10*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 4*b*cosh(x)^2 + 4*(7*b*cosh(x)^6 + 15*b*cosh(x)^4 + 9*b*cosh(x)^2 + b)*sinh(x)^2 + 8*(b*cosh(x)^7 + 3*b*cosh(x)^5 + 3*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)]","B",0
189,1,2312,0,0.841991," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x),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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{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} + {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, a \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 8 \, \sqrt{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} + {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, a \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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*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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + (2*a + b)*cosh(x)^2 + (6*a*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 2*(2*a*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 8*sqrt(2)*(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + (2*a + b)*cosh(x)^2 + (6*a*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 2*(2*a*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
190,1,4140,0,1.850553," ","integrate((a+b*sech(x)^2)^(3/2),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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 3 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + b\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 3 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) - {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 3 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + b\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + b\right)} \cosh\left(x\right)^{2} + 3 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{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{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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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*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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)^4 + 4*(3*a + b)*cosh(x)*sinh(x)^3 + (3*a + b)*sinh(x)^4 + 2*(3*a + b)*cosh(x)^2 + 2*(3*(3*a + b)*cosh(x)^2 + 3*a + b)*sinh(x)^2 + 4*((3*a + b)*cosh(x)^3 + (3*a + b)*cosh(x))*sinh(x) + 3*a + b)*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + b)*cosh(x)^4 + 4*(3*a + b)*cosh(x)*sinh(x)^3 + (3*a + b)*sinh(x)^4 + 2*(3*a + b)*cosh(x)^2 + 2*(3*(3*a + b)*cosh(x)^2 + 3*a + b)*sinh(x)^2 + 4*((3*a + b)*cosh(x)^3 + (3*a + b)*cosh(x))*sinh(x) + 3*a + b)*sqrt(b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) - ((3*a + b)*cosh(x)^4 + 4*(3*a + b)*cosh(x)*sinh(x)^3 + (3*a + b)*sinh(x)^4 + 2*(3*a + b)*cosh(x)^2 + 2*(3*(3*a + b)*cosh(x)^2 + 3*a + b)*sinh(x)^2 + 4*((3*a + b)*cosh(x)^3 + (3*a + b)*cosh(x))*sinh(x) + 3*a + b)*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) - ((3*a + b)*cosh(x)^4 + 4*(3*a + b)*cosh(x)*sinh(x)^3 + (3*a + b)*sinh(x)^4 + 2*(3*a + b)*cosh(x)^2 + 2*(3*(3*a + b)*cosh(x)^2 + 3*a + b)*sinh(x)^2 + 4*((3*a + b)*cosh(x)^3 + (3*a + b)*cosh(x))*sinh(x) + 3*a + b)*sqrt(b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) - sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
191,1,4123,0,1.306826," ","integrate(coth(x)*(a+b*sech(x)^2)^(3/2),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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 + 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(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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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({\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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(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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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({\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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(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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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({\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 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{-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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, \sqrt{2} b \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*b*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*b*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 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)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*sqrt(2)*b*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
192,1,3349,0,4.041295," ","integrate(coth(x)^2*(a+b*sech(x)^2)^(3/2),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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 - 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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\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 - 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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 + b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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(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(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) - (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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 + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 2*sqrt(2)*(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
193,-1,0,0,0.000000," ","integrate((a+b*sech(d*x+c)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,1,2678,0,0.613093," ","integrate(tanh(x)^5/(a+b*sech(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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + 3 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + 3 \, a b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{4} + 6 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a b^{2} \cosh\left(x\right)^{5} + 2 \, a b^{2} \cosh\left(x\right)^{3} + a b^{2} \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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 4 \, \sqrt{2} {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + 3 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + 3 \, a b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{4} + 6 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a b^{2} \cosh\left(x\right)^{5} + 2 \, a b^{2} \cosh\left(x\right)^{3} + a b^{2} \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)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 8*sqrt(2)*((a^2 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 2*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + 3*a*b^2*cosh(x)^4 + 3*a*b^2*cosh(x)^2 + 3*(5*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + 3*a*b^2*cosh(x))*sinh(x)^3 + a*b^2 + 3*(5*a*b^2*cosh(x)^4 + 6*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 6*(a*b^2*cosh(x)^5 + 2*a*b^2*cosh(x)^3 + a*b^2*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)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 4*sqrt(2)*((a^2 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 2*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + 3*a*b^2*cosh(x)^4 + 3*a*b^2*cosh(x)^2 + 3*(5*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + 3*a*b^2*cosh(x))*sinh(x)^3 + a*b^2 + 3*(5*a*b^2*cosh(x)^4 + 6*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 6*(a*b^2*cosh(x)^5 + 2*a*b^2*cosh(x)^3 + a*b^2*cosh(x))*sinh(x))]","B",0
195,1,4569,0,0.657797," ","integrate(tanh(x)^4/(a+b*sech(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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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(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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + 2 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + a b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + 2 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + a b^{2} \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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + 2 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + a b^{2} \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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 3 \, a b + 4 \, {\left({\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 3 \, a b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{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{2} {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + 2 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + a b^{2} \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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 3*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 3*a*b)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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)) + (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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 2*sqrt(2)*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + 2*a*b^2*cosh(x)^2 + a*b^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + a*b^2*cosh(x))*sinh(x)), -1/4*(2*((a^2 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 3*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 3*a*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - (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)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + 2*a*b^2*cosh(x)^2 + a*b^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + a*b^2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + ((a^2 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 3*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 3*a*b)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + 2*a*b^2*cosh(x)^2 + a*b^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + a*b^2*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)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((a^2 + 3*a*b)*cosh(x)^4 + 4*(a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (a^2 + 3*a*b)*sinh(x)^4 + 2*(a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(a^2 + 3*a*b)*cosh(x)^2 + a^2 + 3*a*b)*sinh(x)^2 + a^2 + 3*a*b + 4*((a^2 + 3*a*b)*cosh(x)^3 + (a^2 + 3*a*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) - sqrt(2)*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + 2*a*b^2*cosh(x)^2 + a*b^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + a*b^2*cosh(x))*sinh(x))]","B",0
196,1,1650,0,0.523726," ","integrate(tanh(x)^3/(a+b*sech(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} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} + a b\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} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, \sqrt{2} a \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} + a b\right)}}\right]"," ",0,"[1/4*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*a*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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), -1/2*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*sqrt(2)*a*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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",0
197,1,2856,0,0.562194," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 \, a \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, a b}, -\frac{4 \, a \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - \sqrt{a} b \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, a b}, -\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a} b \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + a \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 \, a b}, -\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, a \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + \sqrt{-a} b \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right)}{2 \, a b}\right]"," ",0,"[1/4*(sqrt(a)*b*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b), -1/4*(4*a*sqrt(b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - sqrt(a)*b*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + sqrt(-a)*b*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + a*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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), -1/2*(sqrt(-a)*b*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + 2*a*sqrt(b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + sqrt(-a)*b*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)))/(a*b)]","B",0
198,1,1430,0,0.464961," ","integrate(tanh(x)/(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, a}, -\frac{\sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right)}{2 \, a}\right]"," ",0,"[1/4*(sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/a, -1/2*(sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)))/a]","B",0
199,1,1059,0,0.453042," ","integrate(1/(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, a}, -\frac{\sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right)}{2 \, a}\right]"," ",0,"[1/4*(sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/a, -1/2*(sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)))/a]","B",0
200,1,3663,0,0.574081," ","integrate(coth(x)/(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a + b\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 \, \sqrt{a + b} 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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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 + b\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left(a + b\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 + b\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{\sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - \sqrt{a + b} 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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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{\sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right)}{2 \, {\left(a^{2} + a b\right)}}\right]"," ",0,"[1/4*((a + b)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), 1/4*(4*a*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (a + b)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), -1/2*(sqrt(-a)*(a + b)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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*(sqrt(-a)*(a + b)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*a*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)))/(a^2 + a*b)]","B",0
201,1,1365,0,0.510281," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(1/2),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} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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({\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} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 2 \, \sqrt{2} a \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*a*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 2*sqrt(2)*a*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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
202,1,6475,0,0.734164," ","integrate(coth(x)^3/(a+b*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{-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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + 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} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + 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{-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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + 4 \, {\left({\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + 3*a*b)*cosh(x)^4 + 4*(2*a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (2*a^2 + 3*a*b)*sinh(x)^4 - 2*(2*a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(x)^2 - 2*a^2 - 3*a*b)*sinh(x)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(x)^3 - (2*a^2 + 3*a*b)*cosh(x))*sinh(x))*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 + 2*a^2*b + a*b^2 - 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 2*a^2*b + a*b^2)*cosh(x))*sinh(x)), 1/4*(2*((2*a^2 + 3*a*b)*cosh(x)^4 + 4*(2*a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (2*a^2 + 3*a*b)*sinh(x)^4 - 2*(2*a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(x)^2 - 2*a^2 - 3*a*b)*sinh(x)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(x)^3 - (2*a^2 + 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + ((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 + 2*a^2*b + a*b^2 - 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 2*a^2*b + a*b^2)*cosh(x))*sinh(x)), -1/4*(2*((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + 2*((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((2*a^2 + 3*a*b)*cosh(x)^4 + 4*(2*a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (2*a^2 + 3*a*b)*sinh(x)^4 - 2*(2*a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(x)^2 - 2*a^2 - 3*a*b)*sinh(x)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(x)^3 - (2*a^2 + 3*a*b)*cosh(x))*sinh(x))*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 + 2*a^2*b + a*b^2 - 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 2*a^2*b + a*b^2)*cosh(x))*sinh(x)), -1/2*(((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - ((2*a^2 + 3*a*b)*cosh(x)^4 + 4*(2*a^2 + 3*a*b)*cosh(x)*sinh(x)^3 + (2*a^2 + 3*a*b)*sinh(x)^4 - 2*(2*a^2 + 3*a*b)*cosh(x)^2 + 2*(3*(2*a^2 + 3*a*b)*cosh(x)^2 - 2*a^2 - 3*a*b)*sinh(x)^2 + 2*a^2 + 3*a*b + 4*((2*a^2 + 3*a*b)*cosh(x)^3 - (2*a^2 + 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 + 2*a^2*b + a*b^2 - 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 2*a^2*b + a*b^2)*cosh(x))*sinh(x))]","B",0
203,1,3360,0,0.675722," ","integrate(tanh(x)^5/(a+b*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} + 4 \, b^{3} + 6 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} + 4 \, b^{3} + 6 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2} + 3 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{6} + 6 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{3} b^{2} \sinh\left(x\right)^{6} + a^{3} b^{2} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a^{3} b^{2} \cosh\left(x\right)^{2} + 3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{3} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 6 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left(a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} + 4 \, b^{3} + 6 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a b^{2} \cosh\left(x\right)^{2} + 3 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a b^{2} \cosh\left(x\right)^{4} + 3 \, a b^{2} + 4 \, b^{3} + 6 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} + 4 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} {\left({\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2} + 3 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{6} + 6 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{3} b^{2} \sinh\left(x\right)^{6} + a^{3} b^{2} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(15 \, a^{3} b^{2} \cosh\left(x\right)^{2} + 3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{3} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 6 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + (3*a*b^2 + 4*b^3)*cosh(x)^4 + (15*a*b^2*cosh(x)^2 + 3*a*b^2 + 4*b^3)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 + a*b^2 + (3*a*b^2 + 4*b^3)*cosh(x)^2 + (15*a*b^2*cosh(x)^4 + 3*a*b^2 + 4*b^3 + 6*(3*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a*b^2*cosh(x)^5 + 2*(3*a*b^2 + 4*b^3)*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + (3*a*b^2 + 4*b^3)*cosh(x)^4 + (15*a*b^2*cosh(x)^2 + 3*a*b^2 + 4*b^3)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 + a*b^2 + (3*a*b^2 + 4*b^3)*cosh(x)^2 + (15*a*b^2*cosh(x)^4 + 3*a*b^2 + 4*b^3 + 6*(3*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a*b^2*cosh(x)^5 + 2*(3*a*b^2 + 4*b^3)*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(2*a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (2*a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + 2*a^3 + 2*a^2*b + a*b^2 + 2*(2*a^3 + 4*a^2*b + a*b^2)*cosh(x)^2 + 2*(2*a^3 + 4*a^2*b + a*b^2 + 3*(2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (2*a^3 + 4*a^2*b + a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^6 + 6*a^3*b^2*cosh(x)*sinh(x)^5 + a^3*b^2*sinh(x)^6 + a^3*b^2 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + (15*a^3*b^2*cosh(x)^2 + 3*a^3*b^2 + 4*a^2*b^3)*sinh(x)^4 + 4*(5*a^3*b^2*cosh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2 + (15*a^3*b^2*cosh(x)^4 + 3*a^3*b^2 + 4*a^2*b^3 + 6*(3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a^3*b^2*cosh(x)^5 + 2*(3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)), -1/2*((a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + (3*a*b^2 + 4*b^3)*cosh(x)^4 + (15*a*b^2*cosh(x)^2 + 3*a*b^2 + 4*b^3)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 + a*b^2 + (3*a*b^2 + 4*b^3)*cosh(x)^2 + (15*a*b^2*cosh(x)^4 + 3*a*b^2 + 4*b^3 + 6*(3*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a*b^2*cosh(x)^5 + 2*(3*a*b^2 + 4*b^3)*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 + (3*a*b^2 + 4*b^3)*cosh(x)^4 + (15*a*b^2*cosh(x)^2 + 3*a*b^2 + 4*b^3)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 + (3*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 + a*b^2 + (3*a*b^2 + 4*b^3)*cosh(x)^2 + (15*a*b^2*cosh(x)^4 + 3*a*b^2 + 4*b^3 + 6*(3*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a*b^2*cosh(x)^5 + 2*(3*a*b^2 + 4*b^3)*cosh(x)^3 + (3*a*b^2 + 4*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*((2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(2*a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (2*a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + 2*a^3 + 2*a^2*b + a*b^2 + 2*(2*a^3 + 4*a^2*b + a*b^2)*cosh(x)^2 + 2*(2*a^3 + 4*a^2*b + a*b^2 + 3*(2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (2*a^3 + 4*a^2*b + a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^6 + 6*a^3*b^2*cosh(x)*sinh(x)^5 + a^3*b^2*sinh(x)^6 + a^3*b^2 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + (15*a^3*b^2*cosh(x)^2 + 3*a^3*b^2 + 4*a^2*b^3)*sinh(x)^4 + 4*(5*a^3*b^2*cosh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2 + (15*a^3*b^2*cosh(x)^4 + 3*a^3*b^2 + 4*a^2*b^3 + 6*(3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*a^3*b^2*cosh(x)^5 + 2*(3*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 + (3*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x))]","B",0
204,1,5170,0,0.699500," ","integrate(tanh(x)^4/(a+b*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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 b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{4} + 4 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b^{2} \sinh\left(x\right)^{4} + a^{3} b^{2} + 2 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{2} + a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{4 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{4} + 4 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b^{2} \sinh\left(x\right)^{4} + a^{3} b^{2} + 2 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{2} + a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-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 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + a + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{4} + 4 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b^{2} \sinh\left(x\right)^{4} + a^{3} b^{2} + 2 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{2} + a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a b^{2} \cosh\left(x\right)^{4} + 4 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{2} \sinh\left(x\right)^{4} + a b^{2} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(x\right)^{2} + a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(x\right)^{3} + {\left(a b^{2} + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} \cosh\left(x\right)^{4} + 4 \, a^{3} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b^{2} \sinh\left(x\right)^{4} + a^{3} b^{2} + 2 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} \cosh\left(x\right)^{2} + a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b^{2} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^4 + 4*a^3*b^2*cosh(x)*sinh(x)^3 + a^3*b^2*sinh(x)^4 + a^3*b^2 + 2*(a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(3*a^3*b^2*cosh(x)^2 + a^3*b^2 + 2*a^2*b^3)*sinh(x)^2 + 4*(a^3*b^2*cosh(x)^3 + (a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), 1/4*(4*(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^4 + 4*a^3*b^2*cosh(x)*sinh(x)^3 + a^3*b^2*sinh(x)^4 + a^3*b^2 + 2*(a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(3*a^3*b^2*cosh(x)^2 + a^3*b^2 + 2*a^2*b^3)*sinh(x)^2 + 4*(a^3*b^2*cosh(x)^3 + (a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), -1/2*((a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + (a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))*sqrt(-b)*log(-((a - b)*cosh(x)^4 + 4*(a - b)*cosh(x)*sinh(x)^3 + (a - b)*sinh(x)^4 + 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a - b)*cosh(x)^2 + a + 3*b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a - b)*cosh(x)^3 + (a + 3*b)*cosh(x))*sinh(x) + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^4 + 4*a^3*b^2*cosh(x)*sinh(x)^3 + a^3*b^2*sinh(x)^4 + a^3*b^2 + 2*(a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(3*a^3*b^2*cosh(x)^2 + a^3*b^2 + 2*a^2*b^3)*sinh(x)^2 + 4*(a^3*b^2*cosh(x)^3 + (a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), -1/2*((a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*b^2*cosh(x)^4 + 4*a*b^2*cosh(x)*sinh(x)^3 + a*b^2*sinh(x)^4 + a*b^2 + 2*(a*b^2 + 2*b^3)*cosh(x)^2 + 2*(3*a*b^2*cosh(x)^2 + a*b^2 + 2*b^3)*sinh(x)^2 + 4*(a*b^2*cosh(x)^3 + (a*b^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2*cosh(x)^4 + 4*a^3*b^2*cosh(x)*sinh(x)^3 + a^3*b^2*sinh(x)^4 + a^3*b^2 + 2*(a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(3*a^3*b^2*cosh(x)^2 + a^3*b^2 + 2*a^2*b^3)*sinh(x)^2 + 4*(a^3*b^2*cosh(x)^3 + (a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x))]","B",0
205,1,2194,0,0.537299," ","integrate(tanh(x)^3/(a+b*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(x\right)^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a b + 4 \, {\left(a b \cosh\left(x\right)^{3} + {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(x\right)^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a b + 4 \, {\left(a b \cosh\left(x\right)^{3} + {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 \cosh\left(x\right)^{4} + 4 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b \sinh\left(x\right)^{4} + a^{3} b + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b \cosh\left(x\right)^{2} + a^{3} b + 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b \cosh\left(x\right)^{3} + {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left(a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(x\right)^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a b + 4 \, {\left(a b \cosh\left(x\right)^{3} + {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(x\right)^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a b + 4 \, {\left(a b \cosh\left(x\right)^{3} + {\left(a b + 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 \cosh\left(x\right)^{4} + 4 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} b \sinh\left(x\right)^{4} + a^{3} b + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} b \cosh\left(x\right)^{2} + a^{3} b + 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} b \cosh\left(x\right)^{3} + {\left(a^{3} b + 2 \, a^{2} b^{2}\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 + 2*b^2)*cosh(x)^2 + 2*(3*a*b*cosh(x)^2 + a*b + 2*b^2)*sinh(x)^2 + a*b + 4*(a*b*cosh(x)^3 + (a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + 2*b^2)*cosh(x)^2 + 2*(3*a*b*cosh(x)^2 + a*b + 2*b^2)*sinh(x)^2 + a*b + 4*(a*b*cosh(x)^3 + (a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b*cosh(x)^4 + 4*a^3*b*cosh(x)*sinh(x)^3 + a^3*b*sinh(x)^4 + a^3*b + 2*(a^3*b + 2*a^2*b^2)*cosh(x)^2 + 2*(3*a^3*b*cosh(x)^2 + a^3*b + 2*a^2*b^2)*sinh(x)^2 + 4*(a^3*b*cosh(x)^3 + (a^3*b + 2*a^2*b^2)*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 + 2*b^2)*cosh(x)^2 + 2*(3*a*b*cosh(x)^2 + a*b + 2*b^2)*sinh(x)^2 + a*b + 4*(a*b*cosh(x)^3 + (a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*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 + 2*b^2)*cosh(x)^2 + 2*(3*a*b*cosh(x)^2 + a*b + 2*b^2)*sinh(x)^2 + a*b + 4*(a*b*cosh(x)^3 + (a*b + 2*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b*cosh(x)^4 + 4*a^3*b*cosh(x)*sinh(x)^3 + a^3*b*sinh(x)^4 + a^3*b + 2*(a^3*b + 2*a^2*b^2)*cosh(x)^2 + 2*(3*a^3*b*cosh(x)^2 + a^3*b + 2*a^2*b^2)*sinh(x)^2 + 4*(a^3*b*cosh(x)^3 + (a^3*b + 2*a^2*b^2)*cosh(x))*sinh(x))]","B",0
206,1,1733,0,0.542445," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(3/2),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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x)), -1/2*((a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))]","B",0
207,1,2034,0,0.518588," ","integrate(tanh(x)/(a+b*sech(x)^2)^(3/2),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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\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 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x)), -1/2*((a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + (a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))]","B",0
208,1,2095,0,0.549627," ","integrate(1/(a+b*sech(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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + a^{3} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} + a^{3} b\right)} \sinh\left(x\right)^{4} + a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + 3 \, a b + 2 \, b^{2}\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} + 3 \, a b + 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + a^{3} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} + a^{3} b\right)} \sinh\left(x\right)^{4} + a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\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 + 3*a*b + 2*b^2)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 + 3*a*b + 2*b^2)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 + 3*a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 3*a*b + 2*b^2)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 + 3*a*b + 2*b^2)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 + 3*a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^4 + a^3*b)*cosh(x)^4 + 4*(a^4 + a^3*b)*cosh(x)*sinh(x)^3 + (a^4 + a^3*b)*sinh(x)^4 + a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*cosh(x)^2 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2 + 3*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 + a^3*b)*cosh(x)^3 + (a^4 + 3*a^3*b + 2*a^2*b^2)*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 + 3*a*b + 2*b^2)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 + 3*a*b + 2*b^2)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 + 3*a*b + 2*b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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 + 3*a*b + 2*b^2)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 + 3*a*b + 2*b^2)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 + 3*a*b + 2*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^4 + a^3*b)*cosh(x)^4 + 4*(a^4 + a^3*b)*cosh(x)*sinh(x)^3 + (a^4 + a^3*b)*sinh(x)^4 + a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*cosh(x)^2 + 2*(a^4 + 3*a^3*b + 2*a^2*b^2 + 3*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 + a^3*b)*cosh(x)^3 + (a^4 + 3*a^3*b + 2*a^2*b^2)*cosh(x))*sinh(x))]","B",0
209,1,6939,0,0.738270," ","integrate(coth(x)/(a+b*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{4 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \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 + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + 3 \, 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 + b} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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 + 3 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 2 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^3 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + 3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), 1/4*(4*(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + ((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^3 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + 3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - (a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*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 + 3*b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a + 3*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a + 3*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^3 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + 3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*cosh(x)^2 + 2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3 + 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 5*a*b^2 + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 2*(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + a^3 + 2*(a^3 + 2*a^2*b)*cosh(x)^2 + 2*(3*a^3*cosh(x)^2 + a^3 + 2*a^2*b)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + (a^3 + 2*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 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*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 4*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^3 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^4 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x)^2 + 2*(a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3 + 3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 4*a^4*b + 5*a^3*b^2 + 2*a^2*b^3)*cosh(x))*sinh(x))]","B",0
210,1,3941,0,0.670176," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} + 15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} - 6 \, a^{2} b - 9 \, a b^{2} - 4 \, b^{3} + 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} + 15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} - 6 \, a^{2} b - 9 \, a b^{2} - 4 \, b^{3} + 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + a b^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{6} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} + 15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} - 6 \, a^{2} b - 9 \, a b^{2} - 4 \, b^{3} + 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} + 15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} - 6 \, a^{2} b - 9 \, a b^{2} - 4 \, b^{3} + 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + a b^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b - a b^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{6} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^6 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^4 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 + 15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 - a^3 - 2*a^2*b - a*b^2 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2 + (15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 - a^3 - 6*a^2*b - 9*a*b^2 - 4*b^3 + 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 2*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 2*a^2*b + a*b^2)*cosh(x)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^6 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^4 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 + 15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 - a^3 - 2*a^2*b - a*b^2 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2 + (15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 - a^3 - 6*a^2*b - 9*a*b^2 - 4*b^3 + 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 2*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a^3 + a*b^2)*cosh(x)^4 + 4*(a^3 + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + a*b^2)*sinh(x)^4 + a^3 + a*b^2 + 2*(a^3 + 2*a^2*b - a*b^2)*cosh(x)^2 + 2*(a^3 + 2*a^2*b - a*b^2 + 3*(a^3 + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a*b^2)*cosh(x)^3 + (a^3 + 2*a^2*b - a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + 6*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^5 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^6 - a^5 - 2*a^4*b - a^3*b^2 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3 + 15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3 - 15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 6*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 2*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^6 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^4 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 + 15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 - a^3 - 2*a^2*b - a*b^2 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2 + (15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 - a^3 - 6*a^2*b - 9*a*b^2 - 4*b^3 + 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 2*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + ((a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^6 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^4 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 + 15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x))*sinh(x)^3 - a^3 - 2*a^2*b - a*b^2 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2 + (15*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 - a^3 - 6*a^2*b - 9*a*b^2 - 4*b^3 + 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 2*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*cosh(x)^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*((a^3 + a*b^2)*cosh(x)^4 + 4*(a^3 + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + a*b^2)*sinh(x)^4 + a^3 + a*b^2 + 2*(a^3 + 2*a^2*b - a*b^2)*cosh(x)^2 + 2*(a^3 + 2*a^2*b - a*b^2 + 3*(a^3 + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a*b^2)*cosh(x)^3 + (a^3 + 2*a^2*b - a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + 6*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^5 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^6 - a^5 - 2*a^4*b - a^3*b^2 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3 + 15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3 - 15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 6*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 2*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x))*sinh(x))]","B",0
211,-1,0,0,0.000000," ","integrate(tanh(x)^6/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,1,5184,0,0.764096," ","integrate(tanh(x)^5/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b^{2} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{2} + a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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^{2} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b^{2} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{2} + a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + 5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a^{5} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{5} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} b^{2} \sinh\left(x\right)^{8} + a^{5} b^{2} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{2} + a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4} + 30 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{6} + a^{5} b^{2} + 2 \, a^{4} b^{3} + 15 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b^{2} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{2} + a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b^{2} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{2} + a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} + 8 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} + 2 \, a 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) - 4 \, \sqrt{2} {\left({\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + 5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} - a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a^{5} b^{2} \cosh\left(x\right)^{8} + 8 \, a^{5} b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} b^{2} \sinh\left(x\right)^{8} + a^{5} b^{2} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{2} + a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} b^{2} \cosh\left(x\right)^{4} + 3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4} + 30 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} b^{2} \cosh\left(x\right)^{6} + a^{5} b^{2} + 2 \, a^{4} b^{3} + 15 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} b^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*(a^2*b^2*cosh(x)^8 + 8*a^2*b^2*cosh(x)*sinh(x)^7 + a^2*b^2*sinh(x)^8 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(7*a^2*b^2*cosh(x)^2 + a^2*b^2 + 2*a*b^3)*sinh(x)^6 + 8*(7*a^2*b^2*cosh(x)^3 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*a^2*b^2*cosh(x)^4 + 3*a^2*b^2 + 8*a*b^3 + 8*b^4 + 30*(a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(x)^5 + 10*(a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*a^2*b^2*cosh(x)^6 + 15*(a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^2*b^2 + 2*a*b^3 + 3*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b^2*cosh(x)^7 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^3 + (a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*cosh(x)^8 + 8*a^2*b^2*cosh(x)*sinh(x)^7 + a^2*b^2*sinh(x)^8 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(7*a^2*b^2*cosh(x)^2 + a^2*b^2 + 2*a*b^3)*sinh(x)^6 + 8*(7*a^2*b^2*cosh(x)^3 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*a^2*b^2*cosh(x)^4 + 3*a^2*b^2 + 8*a*b^3 + 8*b^4 + 30*(a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(x)^5 + 10*(a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*a^2*b^2*cosh(x)^6 + 15*(a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^2*b^2 + 2*a*b^3 + 3*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b^2*cosh(x)^7 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^3 + (a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 8*sqrt(2)*((a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^6 + 6*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)*sinh(x)^5 + (a^4 - a^3*b - 2*a^2*b^2)*sinh(x)^6 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^4 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 + 5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 - a^3*b - 2*a^2*b^2 + 4*(5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^3 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^2 + 3*(5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^4 + a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 + 6*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^5 + 2*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^3 + (a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*b^2*cosh(x)^8 + 8*a^5*b^2*cosh(x)*sinh(x)^7 + a^5*b^2*sinh(x)^8 + a^5*b^2 + 4*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^6 + 4*(7*a^5*b^2*cosh(x)^2 + a^5*b^2 + 2*a^4*b^3)*sinh(x)^6 + 8*(7*a^5*b^2*cosh(x)^3 + 3*(a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^4 + 2*(35*a^5*b^2*cosh(x)^4 + 3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4 + 30*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*b^2*cosh(x)^5 + 10*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^3 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^2 + 4*(7*a^5*b^2*cosh(x)^6 + a^5*b^2 + 2*a^4*b^3 + 15*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^4 + 3*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*b^2*cosh(x)^7 + 3*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^5 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^3 + (a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x)), -1/6*(3*(a^2*b^2*cosh(x)^8 + 8*a^2*b^2*cosh(x)*sinh(x)^7 + a^2*b^2*sinh(x)^8 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(7*a^2*b^2*cosh(x)^2 + a^2*b^2 + 2*a*b^3)*sinh(x)^6 + 8*(7*a^2*b^2*cosh(x)^3 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*a^2*b^2*cosh(x)^4 + 3*a^2*b^2 + 8*a*b^3 + 8*b^4 + 30*(a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(x)^5 + 10*(a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*a^2*b^2*cosh(x)^6 + 15*(a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^2*b^2 + 2*a*b^3 + 3*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b^2*cosh(x)^7 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^3 + (a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*(a^2*b^2*cosh(x)^8 + 8*a^2*b^2*cosh(x)*sinh(x)^7 + a^2*b^2*sinh(x)^8 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(7*a^2*b^2*cosh(x)^2 + a^2*b^2 + 2*a*b^3)*sinh(x)^6 + 8*(7*a^2*b^2*cosh(x)^3 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*a^2*b^2*cosh(x)^4 + 3*a^2*b^2 + 8*a*b^3 + 8*b^4 + 30*(a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(x)^5 + 10*(a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*a^2*b^2*cosh(x)^6 + 15*(a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^2*b^2 + 2*a*b^3 + 3*(3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b^2*cosh(x)^7 + 3*(a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^2*b^2 + 8*a*b^3 + 8*b^4)*cosh(x)^3 + (a^2*b^2 + 2*a*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) - 4*sqrt(2)*((a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^6 + 6*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)*sinh(x)^5 + (a^4 - a^3*b - 2*a^2*b^2)*sinh(x)^6 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^4 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 + 5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 - a^3*b - 2*a^2*b^2 + 4*(5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^3 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^2 + 3*(5*(a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^4 + a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 + 6*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 - a^3*b - 2*a^2*b^2)*cosh(x)^5 + 2*(a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x)^3 + (a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*b^2*cosh(x)^8 + 8*a^5*b^2*cosh(x)*sinh(x)^7 + a^5*b^2*sinh(x)^8 + a^5*b^2 + 4*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^6 + 4*(7*a^5*b^2*cosh(x)^2 + a^5*b^2 + 2*a^4*b^3)*sinh(x)^6 + 8*(7*a^5*b^2*cosh(x)^3 + 3*(a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^4 + 2*(35*a^5*b^2*cosh(x)^4 + 3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4 + 30*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*b^2*cosh(x)^5 + 10*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^3 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^2 + 4*(7*a^5*b^2*cosh(x)^6 + a^5*b^2 + 2*a^4*b^3 + 15*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^4 + 3*(3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*b^2*cosh(x)^7 + 3*(a^5*b^2 + 2*a^4*b^3)*cosh(x)^5 + (3*a^5*b^2 + 8*a^4*b^3 + 8*a^3*b^4)*cosh(x)^3 + (a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x))]","B",0
213,1,3559,0,0.695669," ","integrate(tanh(x)^4/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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^{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \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 b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} - 3 \, a b \cosh\left(x\right)^{2} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{4} + 6 \, a b \cosh\left(x\right)^{2} - a b\right)} \sinh\left(x\right)^{2} - a^{2} + 6 \, {\left(a^{2} \cosh\left(x\right)^{5} + 2 \, a b \cosh\left(x\right)^{3} - a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a^{5} \cosh\left(x\right)^{8} + 8 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{2} + a^{5} + 2 \, a^{4} b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} \cosh\left(x\right)^{4} + 3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{6} + a^{5} + 2 \, a^{4} b + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 8 \, \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 b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a b\right)} \sinh\left(x\right)^{4} - 3 \, a b \cosh\left(x\right)^{2} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{4} + 6 \, a b \cosh\left(x\right)^{2} - a b\right)} \sinh\left(x\right)^{2} - a^{2} + 6 \, {\left(a^{2} \cosh\left(x\right)^{5} + 2 \, a b \cosh\left(x\right)^{3} - a b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a^{5} \cosh\left(x\right)^{8} + 8 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{2} + a^{5} + 2 \, a^{4} b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} \cosh\left(x\right)^{4} + 3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{6} + a^{5} + 2 \, a^{4} b + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a*b*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a*b)*sinh(x)^4 - 3*a*b*cosh(x)^2 + 4*(5*a^2*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 3*(5*a^2*cosh(x)^4 + 6*a*b*cosh(x)^2 - a*b)*sinh(x)^2 - a^2 + 6*(a^2*cosh(x)^5 + 2*a*b*cosh(x)^3 - a*b*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*cosh(x)^8 + 8*a^5*cosh(x)*sinh(x)^7 + a^5*sinh(x)^8 + 4*(a^5 + 2*a^4*b)*cosh(x)^6 + 4*(7*a^5*cosh(x)^2 + a^5 + 2*a^4*b)*sinh(x)^6 + 8*(7*a^5*cosh(x)^3 + 3*(a^5 + 2*a^4*b)*cosh(x))*sinh(x)^5 + a^5 + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^4 + 2*(35*a^5*cosh(x)^4 + 3*a^5 + 8*a^4*b + 8*a^3*b^2 + 30*(a^5 + 2*a^4*b)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*cosh(x)^5 + 10*(a^5 + 2*a^4*b)*cosh(x)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^5 + 2*a^4*b)*cosh(x)^2 + 4*(7*a^5*cosh(x)^6 + a^5 + 2*a^4*b + 15*(a^5 + 2*a^4*b)*cosh(x)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*cosh(x)^7 + 3*(a^5 + 2*a^4*b)*cosh(x)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^3 + (a^5 + 2*a^4*b)*cosh(x))*sinh(x)), -1/6*(3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 8*sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a*b*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a*b)*sinh(x)^4 - 3*a*b*cosh(x)^2 + 4*(5*a^2*cosh(x)^3 + 3*a*b*cosh(x))*sinh(x)^3 + 3*(5*a^2*cosh(x)^4 + 6*a*b*cosh(x)^2 - a*b)*sinh(x)^2 - a^2 + 6*(a^2*cosh(x)^5 + 2*a*b*cosh(x)^3 - a*b*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*cosh(x)^8 + 8*a^5*cosh(x)*sinh(x)^7 + a^5*sinh(x)^8 + 4*(a^5 + 2*a^4*b)*cosh(x)^6 + 4*(7*a^5*cosh(x)^2 + a^5 + 2*a^4*b)*sinh(x)^6 + 8*(7*a^5*cosh(x)^3 + 3*(a^5 + 2*a^4*b)*cosh(x))*sinh(x)^5 + a^5 + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^4 + 2*(35*a^5*cosh(x)^4 + 3*a^5 + 8*a^4*b + 8*a^3*b^2 + 30*(a^5 + 2*a^4*b)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*cosh(x)^5 + 10*(a^5 + 2*a^4*b)*cosh(x)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^5 + 2*a^4*b)*cosh(x)^2 + 4*(7*a^5*cosh(x)^6 + a^5 + 2*a^4*b + 15*(a^5 + 2*a^4*b)*cosh(x)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*cosh(x)^7 + 3*(a^5 + 2*a^4*b)*cosh(x)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^3 + (a^5 + 2*a^4*b)*cosh(x))*sinh(x))]","B",0
214,1,4644,0,0.726392," ","integrate(tanh(x)^3/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b \cosh\left(x\right)^{8} + 8 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{2} + a^{2} b + 2 \, a b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b \cosh\left(x\right)^{4} + 3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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^{2} b \cosh\left(x\right)^{8} + 8 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{2} + a^{2} b + 2 \, a b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b \cosh\left(x\right)^{4} + 3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 4 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 6 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a^{5} b \cosh\left(x\right)^{8} + 8 \, a^{5} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{2} + a^{5} b + 2 \, a^{4} b^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 8 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} b \cosh\left(x\right)^{4} + 3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3} + 30 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{6} + a^{5} b + 2 \, a^{4} b^{2} + 15 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left(a^{2} b \cosh\left(x\right)^{8} + 8 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{2} + a^{2} b + 2 \, a b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b \cosh\left(x\right)^{4} + 3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(a^{2} b \cosh\left(x\right)^{8} + 8 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{2} + a^{2} b + 2 \, a b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} b \cosh\left(x\right)^{4} + 3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 4 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} b \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{2} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b + 2 \, a 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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 2 \, \sqrt{2} {\left({\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 4 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 6 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a^{5} b \cosh\left(x\right)^{8} + 8 \, a^{5} b \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} b \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{2} + a^{5} b + 2 \, a^{4} b^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 8 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} b \cosh\left(x\right)^{4} + 3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3} + 30 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} b \cosh\left(x\right)^{6} + a^{5} b + 2 \, a^{4} b^{2} + 15 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} b \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*(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 + 2*a*b^2)*cosh(x)^6 + 4*(7*a^2*b*cosh(x)^2 + a^2*b + 2*a*b^2)*sinh(x)^6 + 8*(7*a^2*b*cosh(x)^3 + 3*(a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*a^2*b*cosh(x)^4 + 3*a^2*b + 8*a*b^2 + 8*b^3 + 30*(a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^2*b*cosh(x)^5 + 10*(a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 4*(a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*a^2*b*cosh(x)^6 + 15*(a^2*b + 2*a*b^2)*cosh(x)^4 + a^2*b + 2*a*b^2 + 3*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b*cosh(x)^7 + 3*(a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^3 + (a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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)^8 + 8*a^2*b*cosh(x)*sinh(x)^7 + a^2*b*sinh(x)^8 + 4*(a^2*b + 2*a*b^2)*cosh(x)^6 + 4*(7*a^2*b*cosh(x)^2 + a^2*b + 2*a*b^2)*sinh(x)^6 + 8*(7*a^2*b*cosh(x)^3 + 3*(a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*a^2*b*cosh(x)^4 + 3*a^2*b + 8*a*b^2 + 8*b^3 + 30*(a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^2*b*cosh(x)^5 + 10*(a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 4*(a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*a^2*b*cosh(x)^6 + 15*(a^2*b + 2*a*b^2)*cosh(x)^4 + a^2*b + 2*a*b^2 + 3*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b*cosh(x)^7 + 3*(a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^3 + (a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a^3 + 4*a^2*b)*cosh(x)^6 + 6*(a^3 + 4*a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + 4*a^2*b)*sinh(x)^6 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^4 + 3*(a^3 + 4*a^2*b + 4*a*b^2 + 5*(a^3 + 4*a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 4*a^2*b)*cosh(x)^3 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 4*a^2*b + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2 + 3*(5*(a^3 + 4*a^2*b)*cosh(x)^4 + a^3 + 4*a^2*b + 4*a*b^2 + 6*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 + 4*a^2*b)*cosh(x)^5 + 2*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*b*cosh(x)^8 + 8*a^5*b*cosh(x)*sinh(x)^7 + a^5*b*sinh(x)^8 + 4*(a^5*b + 2*a^4*b^2)*cosh(x)^6 + 4*(7*a^5*b*cosh(x)^2 + a^5*b + 2*a^4*b^2)*sinh(x)^6 + a^5*b + 8*(7*a^5*b*cosh(x)^3 + 3*(a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^4 + 2*(35*a^5*b*cosh(x)^4 + 3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3 + 30*(a^5*b + 2*a^4*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*b*cosh(x)^5 + 10*(a^5*b + 2*a^4*b^2)*cosh(x)^3 + (3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x))*sinh(x)^3 + 4*(a^5*b + 2*a^4*b^2)*cosh(x)^2 + 4*(7*a^5*b*cosh(x)^6 + a^5*b + 2*a^4*b^2 + 15*(a^5*b + 2*a^4*b^2)*cosh(x)^4 + 3*(3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*b*cosh(x)^7 + 3*(a^5*b + 2*a^4*b^2)*cosh(x)^5 + (3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^3 + (a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)), -1/6*(3*(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 + 2*a*b^2)*cosh(x)^6 + 4*(7*a^2*b*cosh(x)^2 + a^2*b + 2*a*b^2)*sinh(x)^6 + 8*(7*a^2*b*cosh(x)^3 + 3*(a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*a^2*b*cosh(x)^4 + 3*a^2*b + 8*a*b^2 + 8*b^3 + 30*(a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^2*b*cosh(x)^5 + 10*(a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 4*(a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*a^2*b*cosh(x)^6 + 15*(a^2*b + 2*a*b^2)*cosh(x)^4 + a^2*b + 2*a*b^2 + 3*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b*cosh(x)^7 + 3*(a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^3 + (a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*(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 + 2*a*b^2)*cosh(x)^6 + 4*(7*a^2*b*cosh(x)^2 + a^2*b + 2*a*b^2)*sinh(x)^6 + 8*(7*a^2*b*cosh(x)^3 + 3*(a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*a^2*b*cosh(x)^4 + 3*a^2*b + 8*a*b^2 + 8*b^3 + 30*(a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^2*b*cosh(x)^5 + 10*(a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 4*(a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*a^2*b*cosh(x)^6 + 15*(a^2*b + 2*a*b^2)*cosh(x)^4 + a^2*b + 2*a*b^2 + 3*(3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^2*b*cosh(x)^7 + 3*(a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^2*b + 8*a*b^2 + 8*b^3)*cosh(x)^3 + (a^2*b + 2*a*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 2*sqrt(2)*((a^3 + 4*a^2*b)*cosh(x)^6 + 6*(a^3 + 4*a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + 4*a^2*b)*sinh(x)^6 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^4 + 3*(a^3 + 4*a^2*b + 4*a*b^2 + 5*(a^3 + 4*a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + 4*a^2*b)*cosh(x)^3 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 4*a^2*b + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2 + 3*(5*(a^3 + 4*a^2*b)*cosh(x)^4 + a^3 + 4*a^2*b + 4*a*b^2 + 6*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 + 4*a^2*b)*cosh(x)^5 + 2*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^3 + (a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*b*cosh(x)^8 + 8*a^5*b*cosh(x)*sinh(x)^7 + a^5*b*sinh(x)^8 + 4*(a^5*b + 2*a^4*b^2)*cosh(x)^6 + 4*(7*a^5*b*cosh(x)^2 + a^5*b + 2*a^4*b^2)*sinh(x)^6 + a^5*b + 8*(7*a^5*b*cosh(x)^3 + 3*(a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^4 + 2*(35*a^5*b*cosh(x)^4 + 3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3 + 30*(a^5*b + 2*a^4*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*b*cosh(x)^5 + 10*(a^5*b + 2*a^4*b^2)*cosh(x)^3 + (3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x))*sinh(x)^3 + 4*(a^5*b + 2*a^4*b^2)*cosh(x)^2 + 4*(7*a^5*b*cosh(x)^6 + a^5*b + 2*a^4*b^2 + 15*(a^5*b + 2*a^4*b^2)*cosh(x)^4 + 3*(3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*b*cosh(x)^7 + 3*(a^5*b + 2*a^4*b^2)*cosh(x)^5 + (3*a^5*b + 8*a^4*b^2 + 8*a^3*b^3)*cosh(x)^3 + (a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x))]","B",0
215,1,4989,0,0.770082," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\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} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 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} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, a^{3} - 4 \, a^{2} b - 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} - 4 \, a^{2} b - 4 \, a b^{2} + 6 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + a^{5} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + a^{5} b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} + 7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + a^{5} b + 8 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3} + 35 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{6} + a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} + 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\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} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\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} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 3 \, {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} + 11 \, a^{2} b + 16 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2} + 5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, a^{3} - 4 \, a^{2} b - 3 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} - 4 \, a^{2} b - 4 \, a b^{2} + 6 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 4 \, a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 4 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + a^{5} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + a^{5} b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} + 7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + a^{5} b + 8 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3} + 35 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{6} + a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} + 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + a^{5} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 11 \, a^{5} b + 16 \, a^{4} b^{2} + 8 \, a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((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 + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^6 + 4*(a^3 + 3*a^2*b + 2*a*b^2 + 7*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + a^2*b)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*(a^3 + a^2*b)*cosh(x)^4 + 3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3 + 30*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + a^2*b)*cosh(x)^5 + 10*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^3 + a^2*b + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*(a^3 + a^2*b)*cosh(x)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^4 + a^3 + 3*a^2*b + 2*a*b^2 + 3*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + a^2*b)*cosh(x)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^3 + (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 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 + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^6 + 4*(a^3 + 3*a^2*b + 2*a*b^2 + 7*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + a^2*b)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*(a^3 + a^2*b)*cosh(x)^4 + 3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3 + 30*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + a^2*b)*cosh(x)^5 + 10*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^3 + a^2*b + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*(a^3 + a^2*b)*cosh(x)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^4 + a^3 + 3*a^2*b + 2*a*b^2 + 3*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + a^2*b)*cosh(x)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^3 + (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^3 + 4*a^2*b)*cosh(x)^6 + 6*(3*a^3 + 4*a^2*b)*cosh(x)*sinh(x)^5 + (3*a^3 + 4*a^2*b)*sinh(x)^6 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^4 + 3*(a^3 + 4*a^2*b + 4*a*b^2 + 5*(3*a^3 + 4*a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 4*a^2*b)*cosh(x)^3 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x)^3 - 3*a^3 - 4*a^2*b - 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2 + 3*(5*(3*a^3 + 4*a^2*b)*cosh(x)^4 - a^3 - 4*a^2*b - 4*a*b^2 + 6*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 4*a^2*b)*cosh(x)^5 + 2*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^3 - (a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + a^5*b)*cosh(x)^8 + 8*(a^6 + a^5*b)*cosh(x)*sinh(x)^7 + (a^6 + a^5*b)*sinh(x)^8 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^6 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 + 7*(a^6 + a^5*b)*cosh(x)^2)*sinh(x)^6 + a^6 + a^5*b + 8*(7*(a^6 + a^5*b)*cosh(x)^3 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^4 + 2*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3 + 35*(a^6 + a^5*b)*cosh(x)^4 + 30*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + a^5*b)*cosh(x)^5 + 10*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^3 + (3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x))*sinh(x)^3 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^2 + 4*(7*(a^6 + a^5*b)*cosh(x)^6 + a^6 + 3*a^5*b + 2*a^4*b^2 + 15*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^4 + 3*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + a^5*b)*cosh(x)^7 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^5 + (3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^3 + (a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)), -1/6*(3*((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 + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^6 + 4*(a^3 + 3*a^2*b + 2*a*b^2 + 7*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + a^2*b)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*(a^3 + a^2*b)*cosh(x)^4 + 3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3 + 30*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + a^2*b)*cosh(x)^5 + 10*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^3 + a^2*b + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*(a^3 + a^2*b)*cosh(x)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^4 + a^3 + 3*a^2*b + 2*a*b^2 + 3*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + a^2*b)*cosh(x)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^3 + (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*((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 + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^6 + 4*(a^3 + 3*a^2*b + 2*a*b^2 + 7*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + a^2*b)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^4 + 2*(35*(a^3 + a^2*b)*cosh(x)^4 + 3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3 + 30*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + a^2*b)*cosh(x)^5 + 10*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^3 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x))*sinh(x)^3 + a^3 + a^2*b + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 + 4*(7*(a^3 + a^2*b)*cosh(x)^6 + 15*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^4 + a^3 + 3*a^2*b + 2*a*b^2 + 3*(3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + a^2*b)*cosh(x)^7 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^5 + (3*a^3 + 11*a^2*b + 16*a*b^2 + 8*b^3)*cosh(x)^3 + (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 2*sqrt(2)*((3*a^3 + 4*a^2*b)*cosh(x)^6 + 6*(3*a^3 + 4*a^2*b)*cosh(x)*sinh(x)^5 + (3*a^3 + 4*a^2*b)*sinh(x)^6 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^4 + 3*(a^3 + 4*a^2*b + 4*a*b^2 + 5*(3*a^3 + 4*a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 4*a^2*b)*cosh(x)^3 + 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x)^3 - 3*a^3 - 4*a^2*b - 3*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2 + 3*(5*(3*a^3 + 4*a^2*b)*cosh(x)^4 - a^3 - 4*a^2*b - 4*a*b^2 + 6*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 4*a^2*b)*cosh(x)^5 + 2*(a^3 + 4*a^2*b + 4*a*b^2)*cosh(x)^3 - (a^3 + 4*a^2*b + 4*a*b^2)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + a^5*b)*cosh(x)^8 + 8*(a^6 + a^5*b)*cosh(x)*sinh(x)^7 + (a^6 + a^5*b)*sinh(x)^8 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^6 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 + 7*(a^6 + a^5*b)*cosh(x)^2)*sinh(x)^6 + a^6 + a^5*b + 8*(7*(a^6 + a^5*b)*cosh(x)^3 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^4 + 2*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3 + 35*(a^6 + a^5*b)*cosh(x)^4 + 30*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + a^5*b)*cosh(x)^5 + 10*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^3 + (3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x))*sinh(x)^3 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^2 + 4*(7*(a^6 + a^5*b)*cosh(x)^6 + a^6 + 3*a^5*b + 2*a^4*b^2 + 15*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^4 + 3*(3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + a^5*b)*cosh(x)^7 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x)^5 + (3*a^6 + 11*a^5*b + 16*a^4*b^2 + 8*a^3*b^3)*cosh(x)^3 + (a^6 + 3*a^5*b + 2*a^4*b^2)*cosh(x))*sinh(x))]","B",0
216,1,3994,0,0.702719," ","integrate(tanh(x)/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\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} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3} + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b + 3 \, {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \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} + 2 \, 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^{2} + 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^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + 5 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 14 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b\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^{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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \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 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \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 \, a^{2} \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} + 6 \, {\left(a^{2} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a^{5} \cosh\left(x\right)^{8} + 8 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{2} + a^{5} + 2 \, a^{4} b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} \cosh\left(x\right)^{4} + 3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{6} + a^{5} + 2 \, a^{4} b + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\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 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b\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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}\right) + 8 \, \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 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \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 \, a^{2} \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} + 6 \, {\left(a^{2} \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{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a^{5} \cosh\left(x\right)^{8} + 8 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{5} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{2} + a^{5} + 2 \, a^{4} b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a^{5} \cosh\left(x\right)^{4} + 3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 30 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{5} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a^{5} \cosh\left(x\right)^{6} + a^{5} + 2 \, a^{4} b + 15 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{5} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 2 \, a^{4} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(a)*log(((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 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^6 + 2*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3 + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 6*a^3 + 14*a^2*b + 9*a*b^2 + 30*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^3 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(2*a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^4 + 2*a^3 + 3*a^2*b + 3*(6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^2)*sinh(x)^2 + 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 + 2*a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + (3*a^2 + 4*a*b)*cosh(x)^2 + (15*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 3*a^2 + 4*a*b)*sinh(x)^2 + a^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (3*a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(2*a^3 + 5*a^2*b + 4*a*b^2 + b^3)*cosh(x)^5 + (6*a^3 + 14*a^2*b + 9*a*b^2)*cosh(x)^3 + (2*a^3 + 3*a^2*b)*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*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*a*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + b*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2 + a*b)*sinh(x)^4 + 4*(5*a^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*cosh(x)^4 + 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 + a^2 + 6*(a^2*cosh(x)^5 + 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*cosh(x)^8 + 8*a^5*cosh(x)*sinh(x)^7 + a^5*sinh(x)^8 + 4*(a^5 + 2*a^4*b)*cosh(x)^6 + 4*(7*a^5*cosh(x)^2 + a^5 + 2*a^4*b)*sinh(x)^6 + 8*(7*a^5*cosh(x)^3 + 3*(a^5 + 2*a^4*b)*cosh(x))*sinh(x)^5 + a^5 + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^4 + 2*(35*a^5*cosh(x)^4 + 3*a^5 + 8*a^4*b + 8*a^3*b^2 + 30*(a^5 + 2*a^4*b)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*cosh(x)^5 + 10*(a^5 + 2*a^4*b)*cosh(x)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^5 + 2*a^4*b)*cosh(x)^2 + 4*(7*a^5*cosh(x)^6 + a^5 + 2*a^4*b + 15*(a^5 + 2*a^4*b)*cosh(x)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*cosh(x)^7 + 3*(a^5 + 2*a^4*b)*cosh(x)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^3 + (a^5 + 2*a^4*b)*cosh(x))*sinh(x)), -1/6*(3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 3*a*b)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + 3*a*b)*sinh(x)^2 + a^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 + 4*(a^2 + 2*a*b)*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^6 + 8*(7*a^2*cosh(x)^3 + 3*(a^2 + 2*a*b)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^4 + 2*(35*a^2*cosh(x)^4 + 30*(a^2 + 2*a*b)*cosh(x)^2 + 3*a^2 + 8*a*b + 8*b^2)*sinh(x)^4 + 8*(7*a^2*cosh(x)^5 + 10*(a^2 + 2*a*b)*cosh(x)^3 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 + 2*a*b)*cosh(x)^2 + 4*(7*a^2*cosh(x)^6 + 15*(a^2 + 2*a*b)*cosh(x)^4 + 3*(3*a^2 + 8*a*b + 8*b^2)*cosh(x)^2 + a^2 + 2*a*b)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 + 3*(a^2 + 2*a*b)*cosh(x)^5 + (3*a^2 + 8*a*b + 8*b^2)*cosh(x)^3 + (a^2 + 2*a*b)*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*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 + 2*b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*(a*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a)) + 8*sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2 + a*b)*sinh(x)^4 + 4*(5*a^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*cosh(x)^4 + 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 + a^2 + 6*(a^2*cosh(x)^5 + 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5*cosh(x)^8 + 8*a^5*cosh(x)*sinh(x)^7 + a^5*sinh(x)^8 + 4*(a^5 + 2*a^4*b)*cosh(x)^6 + 4*(7*a^5*cosh(x)^2 + a^5 + 2*a^4*b)*sinh(x)^6 + 8*(7*a^5*cosh(x)^3 + 3*(a^5 + 2*a^4*b)*cosh(x))*sinh(x)^5 + a^5 + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^4 + 2*(35*a^5*cosh(x)^4 + 3*a^5 + 8*a^4*b + 8*a^3*b^2 + 30*(a^5 + 2*a^4*b)*cosh(x)^2)*sinh(x)^4 + 8*(7*a^5*cosh(x)^5 + 10*(a^5 + 2*a^4*b)*cosh(x)^3 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^5 + 2*a^4*b)*cosh(x)^2 + 4*(7*a^5*cosh(x)^6 + a^5 + 2*a^4*b + 15*(a^5 + 2*a^4*b)*cosh(x)^4 + 3*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 8*(a^5*cosh(x)^7 + 3*(a^5 + 2*a^4*b)*cosh(x)^5 + (3*a^5 + 8*a^4*b + 8*a^3*b^2)*cosh(x)^3 + (a^5 + 2*a^4*b)*cosh(x))*sinh(x))]","B",0
217,1,6299,0,0.800578," ","integrate(1/(a+b*sech(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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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 + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} b - 4 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sinh\left(x\right)^{8} + a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4} + 35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4} + 30 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\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} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} + 14 \, a^{3} b + 27 \, a^{2} b^{2} + 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 4 \, \sqrt{2} {\left({\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3} + 5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} b - 4 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b + 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sinh\left(x\right)^{8} + a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4} + 35 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 7 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 8*sqrt(2)*((3*a^3*b + 2*a^2*b^2)*cosh(x)^6 + 6*(3*a^3*b + 2*a^2*b^2)*cosh(x)*sinh(x)^5 + (3*a^3*b + 2*a^2*b^2)*sinh(x)^6 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3 + 5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^2)*sinh(x)^4 - 3*a^3*b - 2*a^2*b^2 + 4*(5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^3 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^3 - 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 3*(5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^4 - a^3*b - 4*a^2*b^2 - 2*a*b^3 + 6*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3*b + 2*a^2*b^2)*cosh(x)^5 + 2*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^3 - (a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^8 + 8*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)*sinh(x)^7 + (a^7 + 2*a^6*b + a^5*b^2)*sinh(x)^8 + a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^6 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3 + 7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^3 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^4 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4 + 35*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^4 + 30*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^5 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^3 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3 + 7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^6 + 15*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^4 + 3*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^7 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^5 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^3 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^6 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4 + 30*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*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 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^3 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x)^5 + (3*a^4 + 14*a^3*b + 27*a^2*b^2 + 24*a*b^3 + 8*b^4)*cosh(x)^3 + (a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 4*sqrt(2)*((3*a^3*b + 2*a^2*b^2)*cosh(x)^6 + 6*(3*a^3*b + 2*a^2*b^2)*cosh(x)*sinh(x)^5 + (3*a^3*b + 2*a^2*b^2)*sinh(x)^6 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^4 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3 + 5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^2)*sinh(x)^4 - 3*a^3*b - 2*a^2*b^2 + 4*(5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^3 + 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x)^3 - 3*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^2 + 3*(5*(3*a^3*b + 2*a^2*b^2)*cosh(x)^4 - a^3*b - 4*a^2*b^2 - 2*a*b^3 + 6*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3*b + 2*a^2*b^2)*cosh(x)^5 + 2*(a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x)^3 - (a^3*b + 4*a^2*b^2 + 2*a*b^3)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^8 + 8*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)*sinh(x)^7 + (a^7 + 2*a^6*b + a^5*b^2)*sinh(x)^8 + a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^6 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3 + 7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^3 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^4 + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4 + 35*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^4 + 30*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^5 + 10*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^3 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3 + 7*(a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^6 + 15*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^4 + 3*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^7 + 2*a^6*b + a^5*b^2)*cosh(x)^7 + 3*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x)^5 + (3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*cosh(x)^3 + (a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*cosh(x))*sinh(x))]","B",0
218,-1,0,0,0.000000," ","integrate(coth(x)/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,1,11205,0,4.181714," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\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)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4} + 45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} - a^{5} - 7 \, a^{4} b - 23 \, a^{3} b^{2} - 37 \, a^{2} b^{3} - 28 \, a b^{4} - 8 \, b^{5} + 35 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 17 \, a^{4} b - 33 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 8 \, a b^{4} + 30 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(x\right)^{8} + 8 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{2} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{4} + {\left(70 \, a b^{2} \cosh\left(x\right)^{4} + a^{3} + 4 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\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} + 4 \, a b\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} - 4 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} + 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} + 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b\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} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\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)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4} + 45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} - a^{5} - 7 \, a^{4} b - 23 \, a^{3} b^{2} - 37 \, a^{2} b^{3} - 28 \, a b^{4} - 8 \, b^{5} + 35 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 17 \, a^{4} b - 33 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 8 \, a b^{4} + 30 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a + 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} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{\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} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4} + 7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 6 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 24 \, a^{4} b + 15 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 12 \, a b^{4} + 35 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4} + 45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} - a^{8} - 3 \, a^{7} b - 3 \, a^{6} b^{2} - a^{5} b^{3} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5} - 105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{4} - 15 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 17 \, a^{7} b - 33 \, a^{6} b^{2} - 27 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 28 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\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)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4} + 45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} - a^{5} - 7 \, a^{4} b - 23 \, a^{3} b^{2} - 37 \, a^{2} b^{3} - 28 \, a b^{4} - 8 \, b^{5} + 35 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 17 \, a^{4} b - 33 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 8 \, a b^{4} + 30 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \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\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a b \cosh\left(x\right)^{4} + 4 \, a b \cosh\left(x\right) \sinh\left(x\right)^{3} + a b \sinh\left(x\right)^{4} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)^{2} + {\left(6 \, a b \cosh\left(x\right)^{2} - a^{2} - 3 \, a b\right)} \sinh\left(x\right)^{2} - a^{2} + 2 \, {\left(2 \, a b \cosh\left(x\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\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)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4} + 45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} - a^{5} - 7 \, a^{4} b - 23 \, a^{3} b^{2} - 37 \, a^{2} b^{3} - 28 \, a b^{4} - 8 \, b^{5} + 35 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 17 \, a^{4} b - 33 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 8 \, a b^{4} + 30 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 7 \, a^{4} b + 23 \, a^{3} b^{2} + 37 \, a^{2} b^{3} + 28 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 17 \, a^{4} b + 33 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 8 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4} + 7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 6 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 24 \, a^{4} b + 15 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 12 \, a b^{4} + 35 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 5 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 6 \, a^{4} b + 8 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + a + 2 \, 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} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4} + 45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} - a^{8} - 3 \, a^{7} b - 3 \, a^{6} b^{2} - a^{5} b^{3} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5} - 105 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{4} - 15 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 17 \, a^{7} b - 33 \, a^{6} b^{2} - 27 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 28 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^10 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^8 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x)^7 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^6 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^3 + 3*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 - a^5 - 7*a^4*b - 23*a^3*b^2 - 37*a^2*b^3 - 28*a*b^4 - 8*b^5 + 35*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^4 + 15*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^7 + 7*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^5 + 5*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^8 + 28*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^6 - 3*a^5 - 17*a^4*b - 33*a^3*b^2 - 27*a^2*b^3 - 8*a*b^4 + 30*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 - 12*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^9 + 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^7 + 6*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x))*sqrt(a)*log((a*b^2*cosh(x)^8 + 8*a*b^2*cosh(x)*sinh(x)^7 + a*b^2*sinh(x)^8 - 2*(a*b^2 - b^3)*cosh(x)^6 + 2*(14*a*b^2*cosh(x)^2 - a*b^2 + b^3)*sinh(x)^6 + 4*(14*a*b^2*cosh(x)^3 - 3*(a*b^2 - b^3)*cosh(x))*sinh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^4 + (70*a*b^2*cosh(x)^4 + a^3 + 4*a^2*b + 9*a*b^2 - 30*(a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*a*b^2*cosh(x)^5 - 10*(a*b^2 - b^3)*cosh(x)^3 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*(a^3 + 3*a^2*b)*cosh(x)^2 + 2*(14*a*b^2*cosh(x)^6 - 15*(a*b^2 - b^3)*cosh(x)^4 + a^3 + 3*a^2*b + 3*(a^3 + 4*a^2*b + 9*a*b^2)*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 + 4*a*b)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 - 4*a*b)*sinh(x)^2 - a^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 + 4*a*b)*cosh(x))*sinh(x))*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*a*b^2*cosh(x)^7 - 3*(a*b^2 - b^3)*cosh(x)^5 + (a^3 + 4*a^2*b + 9*a*b^2)*cosh(x)^3 + (a^3 + 3*a^2*b)*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 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^10 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^8 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x)^7 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^6 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^3 + 3*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 - a^5 - 7*a^4*b - 23*a^3*b^2 - 37*a^2*b^3 - 28*a*b^4 - 8*b^5 + 35*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^4 + 15*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^7 + 7*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^5 + 5*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^8 + 28*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^6 - 3*a^5 - 17*a^4*b - 33*a^3*b^2 - 27*a^2*b^3 - 8*a*b^4 + 30*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 - 12*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^9 + 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^7 + 6*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x))*sqrt(a)*log(-(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(a*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^8 + 8*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)*sinh(x)^7 + (3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*sinh(x)^8 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^6 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4 + 7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 + 3*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x)^5 + 3*a^5 + 9*a^3*b^2 + 4*a^2*b^3 + 6*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^4 + 2*(9*a^5 + 24*a^4*b + 15*a^3*b^2 - 36*a^2*b^3 - 12*a*b^4 + 35*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + 30*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^5 + 10*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + 3*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x))*sinh(x)^3 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^2 + 4*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^6 + 3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4 + 15*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 9*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^7 + 3*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^5 + 3*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^3 + (3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^10 + 10*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)*sinh(x)^9 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*sinh(x)^10 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^8 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4 + 45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^2)*sinh(x)^8 - a^8 - 3*a^7*b - 3*a^6*b^2 - a^5*b^3 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^3 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x))*sinh(x)^7 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^6 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5 + 105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^4 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^5 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^3 + 3*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x))*sinh(x)^5 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^4 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5 - 105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^6 - 35*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^4 - 15*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^7 + 7*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^5 + 5*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^3 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^2 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^8 - 3*a^8 - 17*a^7*b - 33*a^6*b^2 - 27*a^5*b^3 - 8*a^4*b^4 + 28*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^6 + 30*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^4 - 12*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^9 + 4*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^7 + 6*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^5 - 4*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x))*sinh(x)), -1/6*(3*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^10 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^8 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x)^7 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^6 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^3 + 3*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 - a^5 - 7*a^4*b - 23*a^3*b^2 - 37*a^2*b^3 - 28*a*b^4 - 8*b^5 + 35*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^4 + 15*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^7 + 7*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^5 + 5*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^8 + 28*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^6 - 3*a^5 - 17*a^4*b - 33*a^3*b^2 - 27*a^2*b^3 - 8*a*b^4 + 30*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 - 12*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^9 + 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^7 + 6*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*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 - (a^2 + 3*a*b)*cosh(x)^2 + (6*a*b*cosh(x)^2 - a^2 - 3*a*b)*sinh(x)^2 - a^2 + 2*(2*a*b*cosh(x)^3 - (a^2 + 3*a*b)*cosh(x))*sinh(x))) + 3*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^10 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^8 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x)^7 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^6 + 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 14*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^3 + 3*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 - a^5 - 7*a^4*b - 23*a^3*b^2 - 37*a^2*b^3 - 28*a*b^4 - 8*b^5 + 35*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^4 + 15*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^7 + 7*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^5 + 5*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^8 + 28*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^6 - 3*a^5 - 17*a^4*b - 33*a^3*b^2 - 27*a^2*b^3 - 8*a*b^4 + 30*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^4 - 12*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^9 + 4*(3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x)^7 + 6*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^5 - 4*(a^5 + 7*a^4*b + 23*a^3*b^2 + 37*a^2*b^3 + 28*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 17*a^4*b + 33*a^3*b^2 + 27*a^2*b^3 + 8*a*b^4)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)) + 2*sqrt(2)*((3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^8 + 8*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)*sinh(x)^7 + (3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*sinh(x)^8 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^6 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4 + 7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^3 + 3*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x)^5 + 3*a^5 + 9*a^3*b^2 + 4*a^2*b^3 + 6*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^4 + 2*(9*a^5 + 24*a^4*b + 15*a^3*b^2 - 36*a^2*b^3 - 12*a*b^4 + 35*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^4 + 30*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^5 + 10*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + 3*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x))*sinh(x)^3 + 4*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^2 + 4*(7*(3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^6 + 3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4 + 15*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 9*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 9*a^3*b^2 + 4*a^2*b^3)*cosh(x)^7 + 3*(3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x)^5 + 3*(3*a^5 + 8*a^4*b + 5*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4)*cosh(x)^3 + (3*a^5 + 6*a^4*b + 8*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x))*sqrt((a*cosh(x)^2 + a*sinh(x)^2 + a + 2*b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^10 + 10*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)*sinh(x)^9 + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*sinh(x)^10 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^8 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4 + 45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^2)*sinh(x)^8 - a^8 - 3*a^7*b - 3*a^6*b^2 - a^5*b^3 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^3 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x))*sinh(x)^7 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^6 + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5 + 105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^4 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^5 + 14*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^3 + 3*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x))*sinh(x)^5 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^4 - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5 - 105*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^6 - 35*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^4 - 15*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^7 + 7*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^5 + 5*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^3 - (a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^2 + (45*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^8 - 3*a^8 - 17*a^7*b - 33*a^6*b^2 - 27*a^5*b^3 - 8*a^4*b^4 + 28*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^6 + 30*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^4 - 12*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*cosh(x)^9 + 4*(3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x)^7 + 6*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^5 - 4*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*cosh(x)^3 - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*cosh(x))*sinh(x))]","B",0
220,-1,0,0,0.000000," ","integrate(1/(a+b*sech(d*x+c)^2)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
