1,1,1574,0,0.469465," ","integrate((b*coth(d*x+c))^(7/2),x, algorithm=""fricas"")","\left[-\frac{10 \, {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 5 \, {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 16 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b^{3} \sinh\left(d x + c\right)^{4} - 4 \, b^{3} \cosh\left(d x + c\right)^{2} + 3 \, b^{3} + 2 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} - 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} - 2 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{20 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}, \frac{10 \, {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 5 \, {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) - 16 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b^{3} \sinh\left(d x + c\right)^{4} - 4 \, b^{3} \cosh\left(d x + c\right)^{2} + 3 \, b^{3} + 2 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} - 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} - 2 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{20 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}\right]"," ",0,"[-1/20*(10*(b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 - 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 5*(b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 - 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 16*(3*b^3*cosh(d*x + c)^4 + 12*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b^3*sinh(d*x + c)^4 - 4*b^3*cosh(d*x + c)^2 + 3*b^3 + 2*(9*b^3*cosh(d*x + c)^2 - 2*b^3)*sinh(d*x + c)^2 + 4*(3*b^3*cosh(d*x + c)^3 - 2*b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(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), 1/20*(10*(b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 - 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 5*(b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 - 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) - 16*(3*b^3*cosh(d*x + c)^4 + 12*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b^3*sinh(d*x + c)^4 - 4*b^3*cosh(d*x + c)^2 + 3*b^3 + 2*(9*b^3*cosh(d*x + c)^2 - 2*b^3)*sinh(d*x + c)^2 + 4*(3*b^3*cosh(d*x + c)^3 - 2*b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(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
2,1,988,0,0.466490," ","integrate((b*coth(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{12 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2} - d\right)}}, -\frac{6 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{12 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2} - d\right)}}\right]"," ",0,"[-1/12*(6*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 3*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2)*sqrt(b*cosh(d*x + c)/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), -1/12*(6*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 3*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) + 8*(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2)*sqrt(b*cosh(d*x + c)/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
3,1,637,0,0.439499," ","integrate((b*coth(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b} b \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{-b} b \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, b \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, d}, \frac{2 \, b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + b^{\frac{3}{2}} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) - 8 \, b \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, d}\right]"," ",0,"[-1/4*(2*sqrt(-b)*b*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*b*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*b*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/d, 1/4*(2*b^(3/2)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + b^(3/2)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) - 8*b*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/d]","B",0
4,1,594,0,0.436381," ","integrate((b*coth(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, d}, -\frac{2 \, \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right)}{4 \, d}\right]"," ",0,"[-1/4*(2*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/d, -1/4*(2*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b))/d]","B",0
5,1,598,0,0.428378," ","integrate(1/(b*coth(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, b d}, \frac{2 \, \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right)}{4 \, b d}\right]"," ",0,"[-1/4*(2*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/(b*d), 1/4*(2*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b))/(b*d)]","B",0
6,1,923,0,0.436904," ","integrate(1/(b*coth(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + {\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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, {\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 \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}, -\frac{2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - {\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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) + 8 \, {\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 \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}\right]"," ",0,"[-1/4*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d), -1/4*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) + 8*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d)]","B",0
7,1,1428,0,0.457420," ","integrate(1/(b*coth(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\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{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, {\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{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{12 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4} + 2 \, b^{3} d \cosh\left(d x + c\right)^{2} + b^{3} d + 2 \, {\left(3 \, b^{3} d \cosh\left(d x + c\right)^{2} + b^{3} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} d \cosh\left(d x + c\right)^{3} + b^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\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{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) - 8 \, {\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{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{12 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4} + 2 \, b^{3} d \cosh\left(d x + c\right)^{2} + b^{3} d + 2 \, {\left(3 \, b^{3} d \cosh\left(d x + c\right)^{2} + b^{3} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} d \cosh\left(d x + c\right)^{3} + b^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/12*(6*(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(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 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(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*(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(b*cosh(d*x + c)/sinh(d*x + c)))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4 + 2*b^3*d*cosh(d*x + c)^2 + b^3*d + 2*(3*b^3*d*cosh(d*x + c)^2 + b^3*d)*sinh(d*x + c)^2 + 4*(b^3*d*cosh(d*x + c)^3 + b^3*d*cosh(d*x + c))*sinh(d*x + c)), 1/12*(6*(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(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 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(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) - 8*(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(b*cosh(d*x + c)/sinh(d*x + c)))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4 + 2*b^3*d*cosh(d*x + c)^2 + b^3*d + 2*(3*b^3*d*cosh(d*x + c)^2 + b^3*d)*sinh(d*x + c)^2 + 4*(b^3*d*cosh(d*x + c)^3 + b^3*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
8,1,2132,0,0.486607," ","integrate(1/(b*coth(d*x+c))^(7/2),x, algorithm=""fricas"")","\left[-\frac{10 \, {\left(\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 3 \, \cosh\left(d x + c\right)^{4} + 4 \, {\left(5 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right)^{2} + 6 \, {\left(\cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 5 \, {\left(\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 3 \, \cosh\left(d x + c\right)^{4} + 4 \, {\left(5 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right)^{2} + 6 \, {\left(\cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 16 \, {\left(3 \, \cosh\left(d x + c\right)^{6} + 18 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, \sinh\left(d x + c\right)^{6} + {\left(45 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, \cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 3\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{20 \, {\left(b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{4} d \sinh\left(d x + c\right)^{6} + 3 \, b^{4} d \cosh\left(d x + c\right)^{4} + 3 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d + 3 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{4} + 6 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b^{4} d \cosh\left(d x + c\right)^{5} + 2 \, b^{4} d \cosh\left(d x + c\right)^{3} + b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{10 \, {\left(\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 3 \, \cosh\left(d x + c\right)^{4} + 4 \, {\left(5 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right)^{2} + 6 \, {\left(\cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 5 \, {\left(\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 3 \, \cosh\left(d x + c\right)^{4} + 4 \, {\left(5 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right)^{2} + 6 \, {\left(\cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) + 16 \, {\left(3 \, \cosh\left(d x + c\right)^{6} + 18 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, \sinh\left(d x + c\right)^{6} + {\left(45 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, \cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 3\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{20 \, {\left(b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{4} d \sinh\left(d x + c\right)^{6} + 3 \, b^{4} d \cosh\left(d x + c\right)^{4} + 3 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d + 3 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{4} d \cosh\left(d x + c\right)^{4} + 6 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b^{4} d \cosh\left(d x + c\right)^{5} + 2 \, b^{4} d \cosh\left(d x + c\right)^{3} + b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/20*(10*(cosh(d*x + c)^6 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6 + 3*(5*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 3*cosh(d*x + c)^4 + 4*(5*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 3*cosh(d*x + c)^2 + 6*(cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 5*(cosh(d*x + c)^6 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6 + 3*(5*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 3*cosh(d*x + c)^4 + 4*(5*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 3*cosh(d*x + c)^2 + 6*(cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 16*(3*cosh(d*x + c)^6 + 18*cosh(d*x + c)*sinh(d*x + c)^5 + 3*sinh(d*x + c)^6 + (45*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + cosh(d*x + c)^4 + 4*(15*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c)^3 + (45*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(9*cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) - 3)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^4*d*cosh(d*x + c)^6 + 6*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + b^4*d*sinh(d*x + c)^6 + 3*b^4*d*cosh(d*x + c)^4 + 3*b^4*d*cosh(d*x + c)^2 + b^4*d + 3*(5*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^4 + 4*(5*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^4*d*cosh(d*x + c)^4 + 6*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^2 + 6*(b^4*d*cosh(d*x + c)^5 + 2*b^4*d*cosh(d*x + c)^3 + b^4*d*cosh(d*x + c))*sinh(d*x + c)), -1/20*(10*(cosh(d*x + c)^6 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6 + 3*(5*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 3*cosh(d*x + c)^4 + 4*(5*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 3*cosh(d*x + c)^2 + 6*(cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 5*(cosh(d*x + c)^6 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6 + 3*(5*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 3*cosh(d*x + c)^4 + 4*(5*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 3*cosh(d*x + c)^2 + 6*(cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) + 16*(3*cosh(d*x + c)^6 + 18*cosh(d*x + c)*sinh(d*x + c)^5 + 3*sinh(d*x + c)^6 + (45*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + cosh(d*x + c)^4 + 4*(15*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c)^3 + (45*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(9*cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) - 3)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^4*d*cosh(d*x + c)^6 + 6*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + b^4*d*sinh(d*x + c)^6 + 3*b^4*d*cosh(d*x + c)^4 + 3*b^4*d*cosh(d*x + c)^2 + b^4*d + 3*(5*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^4 + 4*(5*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^4*d*cosh(d*x + c)^4 + 6*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^2 + 6*(b^4*d*cosh(d*x + c)^5 + 2*b^4*d*cosh(d*x + c)^3 + b^4*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
9,1,292,0,0.437095," ","integrate((b*coth(d*x+c))^(4/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} b + 2 \, \sqrt{3} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) - 2 \, \sqrt{3} b^{\frac{4}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + \left(-b\right)^{\frac{1}{3}} b \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + b^{\frac{4}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, \left(-b\right)^{\frac{1}{3}} b \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, b^{\frac{4}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 12 \, b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(3)*(-b)^(1/3)*b*arctan(1/3*(sqrt(3)*b + 2*sqrt(3)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) - 2*sqrt(3)*b^(4/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + (-b)^(1/3)*b*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + b^(4/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(-b)^(1/3)*b*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*b^(4/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 12*b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/d","A",0
10,1,310,0,0.430505," ","integrate((b*coth(d*x+c))^(2/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + 2 \, \sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + \left(-b^{2}\right)^{\frac{1}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - \left(-b^{2}\right)^{\frac{1}{3}} b + \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + {\left(b^{2}\right)}^{\frac{1}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\left(b^{2}\right)}^{\frac{1}{3}} b - {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, \left(-b^{2}\right)^{\frac{1}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \left(-b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2}\right)}^{\frac{1}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + {\left(b^{2}\right)}^{\frac{2}{3}}\right)}{4 \, d}"," ",0,"-1/4*(2*sqrt(3)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*(-b^2)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + 2*sqrt(3)*(b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*(b^2)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + (-b^2)^(1/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (-b^2)^(1/3)*b + (-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + (b^2)^(1/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b^2)^(1/3)*b - (b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(-b^2)^(1/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - (-b^2)^(2/3)) - 2*(b^2)^(1/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b^2)^(2/3)))/d","A",0
11,1,291,0,0.405609," ","integrate((b*coth(d*x+c))^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{3 \, b}\right) - 2 \, \left(-b\right)^{\frac{1}{3}} \log\left(-\left(-b\right)^{\frac{2}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + \left(-b\right)^{\frac{1}{3}} \log\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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - {\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)} \left(-b\right)^{\frac{1}{3}} + {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{\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)}{4 \, d}"," ",0,"-1/4*(2*sqrt(3)*(-b)^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*(-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/b) - 2*(-b)^(1/3)*log(-(-b)^(2/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (-b)^(1/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)))/d","B",0
12,1,1598,0,0.447680," ","integrate(1/(b*coth(d*x+c))^(1/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{3 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 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)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - \sqrt{3} {\left({\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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} - 2 \, {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 4 \, {\left(3 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, b}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(-\left(-b\right)^{\frac{2}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - {\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)} \left(-b\right)^{\frac{1}{3}} + {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}, \frac{2 \, \sqrt{3} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{2 \, \sqrt{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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} - 4 \, \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{9 \, b \cosh\left(d x + c\right)^{4} + 36 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 9 \, b \sinh\left(d x + c\right)^{4} + 14 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(27 \, b \cosh\left(d x + c\right)^{2} + 7 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(9 \, b \cosh\left(d x + c\right)^{3} + 7 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 9 \, b}\right) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(-\left(-b\right)^{\frac{2}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - {\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)} \left(-b\right)^{\frac{1}{3}} + {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}\right]"," ",0,"[1/4*(sqrt(3)*b*sqrt((-b)^(1/3)/b)*log((3*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(9*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 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)*(-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - sqrt(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)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3) - 2*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))*sqrt((-b)^(1/3)/b) + 4*(3*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + 3*b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(-b)^(2/3)*log(-(-b)^(2/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)))/(b*d), 1/4*(2*sqrt(3)*b*sqrt(-(-b)^(1/3)/b)*arctan((2*sqrt(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)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3)*sqrt(-(-b)^(1/3)/b) + sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) - 4*sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b)^(1/3)/b))/(9*b*cosh(d*x + c)^4 + 36*b*cosh(d*x + c)*sinh(d*x + c)^3 + 9*b*sinh(d*x + c)^4 + 14*b*cosh(d*x + c)^2 + 2*(27*b*cosh(d*x + c)^2 + 7*b)*sinh(d*x + c)^2 + 4*(9*b*cosh(d*x + c)^3 + 7*b*cosh(d*x + c))*sinh(d*x + c) + 9*b)) - 2*(-b)^(2/3)*log(-(-b)^(2/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)))/(b*d)]","B",0
13,1,356,0,0.457835," ","integrate(1/(b*coth(d*x+c))^(2/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} - 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2}}\right) + 2 \, \sqrt{3} {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(-\frac{\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{6}} {\left({\left(b^{2}\right)}^{\frac{1}{3}} b - 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{2}}\right) + \left(-b^{2}\right)^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - \left(-b^{2}\right)^{\frac{1}{3}} b + \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\left(b^{2}\right)}^{\frac{1}{3}} b - {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, \left(-b^{2}\right)^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \left(-b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + {\left(b^{2}\right)}^{\frac{2}{3}}\right)}{4 \, b^{2} d}"," ",0,"1/4*(2*sqrt(3)*b*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*sqrt(-(-b^2)^(1/3)) - 2*sqrt(3)*(-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b^2)^(1/3)))/b^2) + 2*sqrt(3)*(b^2)^(1/6)*b*arctan(-1/3*sqrt(3)*(b^2)^(1/6)*((b^2)^(1/3)*b - 2*(b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^2) + (-b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (-b^2)^(1/3)*b + (-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - (b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b^2)^(1/3)*b - (b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(-b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - (-b^2)^(2/3)) + 2*(b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b^2)^(2/3)))/(b^2*d)","B",0
14,1,3348,0,0.513859," ","integrate(1/(b*coth(d*x+c))^(4/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b \cosh\left(d x + c\right)^{2} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 3 \, b \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \sqrt{3} {\left(2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\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)} \left(-b\right)^{\frac{1}{3}} - {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + b\right) + \sqrt{3} {\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{1}{b^{\frac{2}{3}}}} \log\left(-\frac{2 \, \sqrt{3} {\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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 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} - \sqrt{3} {\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)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + {\left(\sqrt{3} {\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{1}{b^{\frac{2}{3}}}} + 3 \, {\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)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - 3 \, b}{\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) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}, -\frac{2 \, \sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{1}{3} \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + \frac{2}{3} \, \sqrt{3} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}\right) - \sqrt{3} {\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{1}{b^{\frac{2}{3}}}} \log\left(-\frac{2 \, \sqrt{3} {\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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 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} - \sqrt{3} {\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)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + {\left(\sqrt{3} {\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{1}{b^{\frac{2}{3}}}} + 3 \, {\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)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - 3 \, b}{\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) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}, \frac{\sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b \cosh\left(d x + c\right)^{2} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 3 \, b \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \sqrt{3} {\left(2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\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)} \left(-b\right)^{\frac{1}{3}} - {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + b\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - \frac{2 \, \sqrt{3} {\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)} \arctan\left(-\frac{\sqrt{3} {\left(b^{\frac{1}{3}} - 2 \, \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}, -\frac{2 \, \sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{1}{3} \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + \frac{2}{3} \, \sqrt{3} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + \frac{2 \, \sqrt{3} {\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)} \arctan\left(-\frac{\sqrt{3} {\left(b^{\frac{1}{3}} - 2 \, \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}\right]"," ",0,"[1/4*(sqrt(3)*(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)^(1/3)/b)*log(3*b*cosh(d*x + c)^2 + 6*b*cosh(d*x + c)*sinh(d*x + c) + 3*b*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - sqrt(3)*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))*sqrt((-b)^(1/3)/b) + b) + sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(-1/b^(2/3))*log(-(2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3)*sqrt(-1/b^(2/3)) - b*cosh(d*x + c)^2 - 2*b*cosh(d*x + c)*sinh(d*x + c) - b*sinh(d*x + c)^2 - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*sqrt(-1/b^(2/3)) + (sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3))*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - 3*b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d), -1/4*(2*sqrt(3)*(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)^(1/3)/b)*arctan(-1/3*sqrt(3)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) + 2/3*sqrt(3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b)^(1/3)/b)) - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(-1/b^(2/3))*log(-(2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3)*sqrt(-1/b^(2/3)) - b*cosh(d*x + c)^2 - 2*b*cosh(d*x + c)*sinh(d*x + c) - b*sinh(d*x + c)^2 - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*sqrt(-1/b^(2/3)) + (sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3))*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - 3*b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d), 1/4*(sqrt(3)*(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)^(1/3)/b)*log(3*b*cosh(d*x + c)^2 + 6*b*cosh(d*x + c)*sinh(d*x + c) + 3*b*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - sqrt(3)*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))*sqrt((-b)^(1/3)/b) + b) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*arctan(-1/3*sqrt(3)*(b^(1/3) - 2*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^(1/3))/b^(1/3) - 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d), -1/4*(2*sqrt(3)*(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)^(1/3)/b)*arctan(-1/3*sqrt(3)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) + 2/3*sqrt(3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b)^(1/3)/b)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*arctan(-1/3*sqrt(3)*(b^(1/3) - 2*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^(1/3))/b^(1/3) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d)]","B",0
15,0,0,0,0.416521," ","integrate(coth(b*x+a)^n,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(b x + a\right)^{n}, x\right)"," ",0,"integral(coth(b*x + a)^n, x)","F",0
16,0,0,0,0.434276," ","integrate((b*coth(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \coth\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((b*coth(d*x + c))^n, x)","F",0
17,0,0,0,0.439206," ","integrate((b*coth(d*x+c)^2)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \coth\left(d x + c\right)^{2}\right)^{n}, x\right)"," ",0,"integral((b*coth(d*x + c)^2)^n, x)","F",0
18,1,823,0,0.434958," ","integrate((b*coth(d*x+c)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b d x \cosh\left(d x + c\right)^{4} - {\left(b d x e^{\left(2 \, d x + 2 \, c\right)} - b d x\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(b d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - b d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b d x - 2 \, {\left(b d x - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b d x \cosh\left(d x + c\right)^{2} - b d x - {\left(3 \, b d x \cosh\left(d x + c\right)^{2} - b d x + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + b\right)} \sinh\left(d x + c\right)^{2} - {\left(b d x \cosh\left(d x + c\right)^{4} + b d x - 2 \, {\left(b d x - b\right)} \cosh\left(d x + c\right)^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(b \cosh\left(d x + c\right)^{4} - {\left(b e^{\left(2 \, d x + 2 \, c\right)} - b\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(b \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} e^{\left(2 \, d x + 2 \, c\right)} - b\right)} \sinh\left(d x + c\right)^{2} - {\left(b \cosh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) + b\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(b d x \cosh\left(d x + c\right)^{3} - {\left(b d x - b\right)} \cosh\left(d x + c\right) - {\left(b d x \cosh\left(d x + c\right)^{3} - {\left(b d x - b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(4 \, d x + 4 \, c\right)} - 2 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{d \cosh\left(d x + c\right)^{4} + {\left(d e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} + {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} - d\right)} \sinh\left(d x + c\right)^{2} + {\left(d \cosh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right) + {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) + d}"," ",0,"(b*d*x*cosh(d*x + c)^4 - (b*d*x*e^(2*d*x + 2*c) - b*d*x)*sinh(d*x + c)^4 - 4*(b*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) - b*d*x*cosh(d*x + c))*sinh(d*x + c)^3 + b*d*x - 2*(b*d*x - b)*cosh(d*x + c)^2 + 2*(3*b*d*x*cosh(d*x + c)^2 - b*d*x - (3*b*d*x*cosh(d*x + c)^2 - b*d*x + b)*e^(2*d*x + 2*c) + b)*sinh(d*x + c)^2 - (b*d*x*cosh(d*x + c)^4 + b*d*x - 2*(b*d*x - b)*cosh(d*x + c)^2)*e^(2*d*x + 2*c) - (b*cosh(d*x + c)^4 - (b*e^(2*d*x + 2*c) - b)*sinh(d*x + c)^4 - 4*(b*cosh(d*x + c)*e^(2*d*x + 2*c) - b*cosh(d*x + c))*sinh(d*x + c)^3 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - (3*b*cosh(d*x + c)^2 - b)*e^(2*d*x + 2*c) - b)*sinh(d*x + c)^2 - (b*cosh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + b)*e^(2*d*x + 2*c) + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c) - (b*cosh(d*x + c)^3 - b*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) + b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(b*d*x*cosh(d*x + c)^3 - (b*d*x - b)*cosh(d*x + c) - (b*d*x*cosh(d*x + c)^3 - (b*d*x - b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c))*sqrt((b*e^(4*d*x + 4*c) + 2*b*e^(2*d*x + 2*c) + b)/(e^(4*d*x + 4*c) - 2*e^(2*d*x + 2*c) + 1))/(d*cosh(d*x + c)^4 + (d*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^4 + 4*(d*cosh(d*x + c)*e^(2*d*x + 2*c) + d*cosh(d*x + c))*sinh(d*x + c)^3 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 + (3*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) - d)*sinh(d*x + c)^2 + (d*cosh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + d)*e^(2*d*x + 2*c) + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c) + (d*cosh(d*x + c)^3 - d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) + d)","B",0
19,1,125,0,0.423435," ","integrate((b*coth(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(d x e^{\left(2 \, d x + 2 \, c\right)} - d x - {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)\right)} \sqrt{\frac{b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(4 \, d x + 4 \, c\right)} - 2 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{d e^{\left(2 \, d x + 2 \, c\right)} + d}"," ",0,"-(d*x*e^(2*d*x + 2*c) - d*x - (e^(2*d*x + 2*c) - 1)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))*sqrt((b*e^(4*d*x + 4*c) + 2*b*e^(2*d*x + 2*c) + b)/(e^(4*d*x + 4*c) - 2*e^(2*d*x + 2*c) + 1))/(d*e^(2*d*x + 2*c) + d)","B",0
20,1,128,0,0.414518," ","integrate(1/(b*coth(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(d x e^{\left(2 \, d x + 2 \, c\right)} - d x - {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)\right)} \sqrt{\frac{b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(4 \, d x + 4 \, c\right)} - 2 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{b d e^{\left(2 \, d x + 2 \, c\right)} + b d}"," ",0,"-(d*x*e^(2*d*x + 2*c) - d*x - (e^(2*d*x + 2*c) - 1)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))*sqrt((b*e^(4*d*x + 4*c) + 2*b*e^(2*d*x + 2*c) + b)/(e^(4*d*x + 4*c) - 2*e^(2*d*x + 2*c) + 1))/(b*d*e^(2*d*x + 2*c) + b*d)","B",0
21,1,817,0,0.453540," ","integrate(1/(b*coth(d*x+c)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(d x \cosh\left(d x + c\right)^{4} - {\left(d x e^{\left(2 \, d x + 2 \, c\right)} - d x\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(d x - 1\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d x \cosh\left(d x + c\right)^{2} + d x - {\left(3 \, d x \cosh\left(d x + c\right)^{2} + d x - 1\right)} e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} \sinh\left(d x + c\right)^{2} + d x - {\left(d x \cosh\left(d x + c\right)^{4} + 2 \, {\left(d x - 1\right)} \cosh\left(d x + c\right)^{2} + d x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left({\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} \sinh\left(d x + c\right)^{4} - \cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} e^{\left(2 \, d x + 2 \, c\right)} + 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{4} + 2 \, \cosh\left(d x + c\right)^{2} + 1\right)} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, {\left(\cosh\left(d x + c\right)^{3} - {\left(\cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 1\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(d x \cosh\left(d x + c\right)^{3} + {\left(d x - 1\right)} \cosh\left(d x + c\right) - {\left(d x \cosh\left(d x + c\right)^{3} + {\left(d x - 1\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(4 \, d x + 4 \, c\right)} - 2 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{b^{2} d \cosh\left(d x + c\right)^{4} + 2 \, b^{2} d \cosh\left(d x + c\right)^{2} + {\left(b^{2} d e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} d + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{2} + {\left(b^{2} d \cosh\left(d x + c\right)^{4} + 2 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right) + {\left(b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)}"," ",0,"(d*x*cosh(d*x + c)^4 - (d*x*e^(2*d*x + 2*c) - d*x)*sinh(d*x + c)^4 - 4*(d*x*cosh(d*x + c)*e^(2*d*x + 2*c) - d*x*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(d*x - 1)*cosh(d*x + c)^2 + 2*(3*d*x*cosh(d*x + c)^2 + d*x - (3*d*x*cosh(d*x + c)^2 + d*x - 1)*e^(2*d*x + 2*c) - 1)*sinh(d*x + c)^2 + d*x - (d*x*cosh(d*x + c)^4 + 2*(d*x - 1)*cosh(d*x + c)^2 + d*x)*e^(2*d*x + 2*c) + ((e^(2*d*x + 2*c) - 1)*sinh(d*x + c)^4 - cosh(d*x + c)^4 + 4*(cosh(d*x + c)*e^(2*d*x + 2*c) - cosh(d*x + c))*sinh(d*x + c)^3 - 2*(3*cosh(d*x + c)^2 - (3*cosh(d*x + c)^2 + 1)*e^(2*d*x + 2*c) + 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + (cosh(d*x + c)^4 + 2*cosh(d*x + c)^2 + 1)*e^(2*d*x + 2*c) - 4*(cosh(d*x + c)^3 - (cosh(d*x + c)^3 + cosh(d*x + c))*e^(2*d*x + 2*c) + cosh(d*x + c))*sinh(d*x + c) - 1)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(d*x*cosh(d*x + c)^3 + (d*x - 1)*cosh(d*x + c) - (d*x*cosh(d*x + c)^3 + (d*x - 1)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c))*sqrt((b*e^(4*d*x + 4*c) + 2*b*e^(2*d*x + 2*c) + b)/(e^(4*d*x + 4*c) - 2*e^(2*d*x + 2*c) + 1))/(b^2*d*cosh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + (b^2*d*e^(2*d*x + 2*c) + b^2*d)*sinh(d*x + c)^4 + 4*(b^2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + b^2*d*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*d + 2*(3*b^2*d*cosh(d*x + c)^2 + b^2*d + (3*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^2 + (b^2*d*cosh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c) + 4*(b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c) + (b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c))","B",0
22,1,1994,0,0.462992," ","integrate((b*coth(d*x+c)^2)^(4/3),x, algorithm=""fricas"")","-\frac{10 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} + 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) - 10 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - \sqrt{3} b\right)} b^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) + 5 \, {\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)} \left(-b\right)^{\frac{1}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + 5 \, {\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)} b^{\frac{1}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - 10 \, {\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)} \left(-b\right)^{\frac{1}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 10 \, {\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)} b^{\frac{1}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) + 12 \, {\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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{20 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/20*(10*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - sqrt(3)*b)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 + 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 10*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - sqrt(3)*b)*b^(1/3)*arctan(-1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*b^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 5*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + 5*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - 10*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 10*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 12*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(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
23,1,2037,0,0.466341," ","integrate((b*coth(d*x+c)^2)^(2/3),x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} + \sqrt{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) + 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} + \sqrt{3}\right)} {\left(b^{2}\right)}^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} {\left(b^{2}\right)}^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) + \left(-b^{2}\right)^{\frac{1}{3}} {\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)} \log\left(\frac{{\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b^{2}\right)^{\frac{1}{3}}}{\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) + {\left(b^{2}\right)}^{\frac{1}{3}} {\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)} \log\left(-\frac{{\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} {\left(b^{2}\right)}^{\frac{1}{3}}}{\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) - 2 \, \left(-b^{2}\right)^{\frac{1}{3}} {\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)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} - {\left(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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 2 \, {\left(b^{2}\right)}^{\frac{1}{3}} {\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)} \log\left(\frac{{\left(b^{2}\right)}^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} + {\left(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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{4 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/4*(2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 + sqrt(3))*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(-b^2)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 + sqrt(3))*(b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(b^2)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + (-b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(((cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b^2)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b^2)^(1/3))/(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)) + (b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(-((cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(b^2)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(b^2)^(1/3))/(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)) - 2*(-b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(-((-b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*(b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(((b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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
24,1,1618,0,0.492529," ","integrate((b*coth(d*x+c)^2)^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} + 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) - 2 \, \sqrt{3} b^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - 2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, {\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)}}\right) + \left(-b\right)^{\frac{1}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + b^{\frac{1}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - 2 \, \left(-b\right)^{\frac{1}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 2 \, b^{\frac{1}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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)}{4 \, d}"," ",0,"-1/4*(2*sqrt(3)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 + 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 2*sqrt(3)*b^(1/3)*arctan(-1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - 2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*b^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + sqrt(3)*b)/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + (-b)^(1/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + b^(1/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - 2*(-b)^(1/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*b^(1/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/d","B",0
25,1,8338,0,0.616262," ","integrate(1/(b*coth(d*x+c)^2)^(1/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, \sqrt{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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(\sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 3 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - 3 \, b}{\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} + {\left(6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + \sqrt{3} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(-\frac{3 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - \sqrt{3} {\left(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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 4 \, {\left(3 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1}\right) + \left(-b\right)^{\frac{2}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - b^{\frac{2}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) + 2 \, b^{\frac{2}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}, -\frac{2 \, \sqrt{3} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{3} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} - 2 \, \sqrt{3} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{3 \, {\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)}}\right) - \sqrt{3} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, \sqrt{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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(\sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 3 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - 3 \, b}{\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} + {\left(6 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) - \left(-b\right)^{\frac{2}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + b^{\frac{2}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + 2 \, \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 2 \, b^{\frac{2}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}, \frac{\sqrt{3} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(-\frac{3 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - \sqrt{3} {\left(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)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 4 \, {\left(3 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b}{\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) - 2 \, \sqrt{3} b^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} {\left({\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)} b^{\frac{1}{3}} - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}\right)}}{3 \, {\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)} b^{\frac{1}{3}}}\right) + \left(-b\right)^{\frac{2}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - b^{\frac{2}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) + 2 \, b^{\frac{2}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}, -\frac{2 \, \sqrt{3} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{3} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} - 2 \, \sqrt{3} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{3 \, {\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)}}\right) + 2 \, \sqrt{3} b^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} {\left({\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)} b^{\frac{1}{3}} - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}\right)}}{3 \, {\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)} b^{\frac{1}{3}}}\right) - \left(-b\right)^{\frac{2}{3}} \log\left(\frac{{\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)} \left(-b\right)^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + b^{\frac{2}{3}} \log\left(\frac{{\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)} b^{\frac{2}{3}} - {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}}}{\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) + 2 \, \left(-b\right)^{\frac{2}{3}} \log\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)} \left(-b\right)^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 2 \, b^{\frac{2}{3}} \log\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)} b^{\frac{1}{3}} + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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)}{4 \, b d}\right]"," ",0,"[1/4*(sqrt(3)*b*sqrt(-1/b^(2/3))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*sqrt(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)*b^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3)*sqrt(-1/b^(2/3)) - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*b^(1/3)*sqrt(-1/b^(2/3)) + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) - (sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(2/3))*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - 3*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c))) + sqrt(3)*b*sqrt((-b)^(1/3)/b)*log(-(3*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(9*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - sqrt(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)*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))*sqrt((-b)^(1/3)/b) + 4*(3*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + (-b)^(2/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - b^(2/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - 2*(-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 2*b^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(b*d), -1/4*(2*sqrt(3)*b*sqrt(-(-b)^(1/3)/b)*arctan(-1/3*(sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) - 2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3)*sqrt(-(-b)^(1/3)/b))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - sqrt(3)*b*sqrt(-1/b^(2/3))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*sqrt(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)*b^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3)*sqrt(-1/b^(2/3)) - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*b^(1/3)*sqrt(-1/b^(2/3)) + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) - (sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(2/3))*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - 3*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c))) - (-b)^(2/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + b^(2/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + 2*(-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*b^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(b*d), 1/4*(sqrt(3)*b*sqrt((-b)^(1/3)/b)*log(-(3*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(9*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - sqrt(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)*(-b)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))*sqrt((-b)^(1/3)/b) + 4*(3*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*sqrt(3)*b^(2/3)*arctan(-1/3*sqrt(3)*((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3))) + (-b)^(2/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - b^(2/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) - 2*(-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 2*b^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(b*d), -1/4*(2*sqrt(3)*b*sqrt(-(-b)^(1/3)/b)*arctan(-1/3*(sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) - 2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3)*sqrt(-(-b)^(1/3)/b))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 2*sqrt(3)*b^(2/3)*arctan(-1/3*sqrt(3)*((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3))) - (-b)^(2/3)*log(((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)*(-b)^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b)^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + b^(2/3)*log(((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)*b^(2/3) - (cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*b^(1/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (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)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3))/(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)) + 2*(-b)^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*b^(2/3)*log(((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(1/3) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(b*d)]","B",0
26,1,2066,0,0.454553," ","integrate(1/(b*coth(d*x+c)^2)^(2/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\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{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(\frac{2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{2}{3}} {\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{-\left(-b^{2}\right)^{\frac{1}{3}}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - \sqrt{3} {\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)} \left(-b^{2}\right)^{\frac{1}{3}} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2}\right)}}\right) + 2 \, \sqrt{3} {\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)} {\left(b^{2}\right)}^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{6}} {\left(2 \, {\left(b^{2}\right)}^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - {\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)} {\left(b^{2}\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2}\right)}}\right) + \left(-b^{2}\right)^{\frac{2}{3}} {\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)} \log\left(\frac{{\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b^{2}\right)^{\frac{1}{3}}}{\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) - {\left(b^{2}\right)}^{\frac{2}{3}} {\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)} \log\left(-\frac{{\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 1\right)} {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{2}{3}} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} {\left(b^{2}\right)}^{\frac{1}{3}}}{\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) - 2 \, \left(-b^{2}\right)^{\frac{2}{3}} {\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)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} - {\left(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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) + 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} {\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)} \log\left(\frac{{\left(b^{2}\right)}^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} + {\left(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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{\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) - 12 \, {\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)} \left(\frac{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + b}{\cosh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{2} - 1}\right)^{\frac{1}{3}}}{4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2} + b^{2} d\right)}}"," ",0,"1/4*(2*sqrt(3)*(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^2)^(1/3))*arctan(1/3*(2*sqrt(3)*(-b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-(-b^2)^(1/3))*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(-b^2)^(1/3)*sqrt(-(-b^2)^(1/3)))/(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2)) + 2*sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(b^2)^(1/6)*arctan(1/3*sqrt(3)*(b^2)^(1/6)*(2*(b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*(b^2)^(1/3))/(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2)) + (-b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(((cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(-b^2)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b^2)^(1/3))/(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)) - (b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(-((cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 1)*(b^2)^(2/3)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(2/3) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(b^2)^(1/3))/(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)) - 2*(-b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(-((-b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 2*(b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*log(((b^2)^(2/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 12*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*((b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + b)/(cosh(d*x + c)^2 + sinh(d*x + c)^2 - 1))^(1/3))/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2 + b^2*d)","B",0
27,-1,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^2)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,0,0,0,0.666285," ","integrate((b*coth(d*x+c)^3)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \coth\left(d x + c\right)^{3}\right)^{n}, x\right)"," ",0,"integral((b*coth(d*x + c)^3)^n, x)","F",0
29,1,2152,0,1.815325," ","integrate((b*coth(d*x+c)^3)^(3/2),x, algorithm=""fricas"")","\left[-\frac{42 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 21 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \sqrt{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 16 \, {\left(5 \, b \cosh\left(d x + c\right)^{6} + 30 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 5 \, b \sinh\left(d x + c\right)^{6} + b \cosh\left(d x + c\right)^{4} + {\left(75 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(25 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)^{2} + {\left(75 \, b \cosh\left(d x + c\right)^{4} + 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(15 \, b \cosh\left(d x + c\right)^{5} + 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5 \, b\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{84 \, {\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)}}, -\frac{42 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - 21 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \sqrt{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) + 16 \, {\left(5 \, b \cosh\left(d x + c\right)^{6} + 30 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 5 \, b \sinh\left(d x + c\right)^{6} + b \cosh\left(d x + c\right)^{4} + {\left(75 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(25 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)^{2} + {\left(75 \, b \cosh\left(d x + c\right)^{4} + 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(15 \, b \cosh\left(d x + c\right)^{5} + 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5 \, b\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{84 \, {\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)}}\right]"," ",0,"[-1/84*(42*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 21*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 16*(5*b*cosh(d*x + c)^6 + 30*b*cosh(d*x + c)*sinh(d*x + c)^5 + 5*b*sinh(d*x + c)^6 + b*cosh(d*x + c)^4 + (75*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^4 + 4*(25*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c)^3 + b*cosh(d*x + c)^2 + (75*b*cosh(d*x + c)^4 + 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 2*(15*b*cosh(d*x + c)^5 + 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + 5*b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 - 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), -1/84*(42*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - 21*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) + 16*(5*b*cosh(d*x + c)^6 + 30*b*cosh(d*x + c)*sinh(d*x + c)^5 + 5*b*sinh(d*x + c)^6 + b*cosh(d*x + c)^4 + (75*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^4 + 4*(25*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c)^3 + b*cosh(d*x + c)^2 + (75*b*cosh(d*x + c)^4 + 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 2*(15*b*cosh(d*x + c)^5 + 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + 5*b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 - 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
30,1,633,0,1.586909," ","integrate((b*coth(d*x+c)^3)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, d}, \frac{2 \, \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) - 8 \, \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, d}\right]"," ",0,"[-1/4*(2*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/d, 1/4*(2*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(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)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) - 8*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/d]","B",0
31,1,907,0,1.211486," ","integrate(1/(b*coth(d*x+c)^3)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + {\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{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 8 \, {\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 \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}, -\frac{2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) - {\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{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) + 8 \, {\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 \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}\right]"," ",0,"[-1/4*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 8*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d), -1/4*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) + 8*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d)]","B",0
32,1,3022,0,1.583392," ","integrate(1/(b*coth(d*x+c)^3)^(3/2),x, algorithm=""fricas"")","\left[-\frac{42 \, {\left(\cosh\left(d x + c\right)^{8} + 8 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sinh\left(d x + c\right)^{8} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{6} + 4 \, \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, \cosh\left(d x + c\right)^{4} + 30 \, \cosh\left(d x + c\right)^{2} + 3\right)} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{5} + 10 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{6} + 15 \, \cosh\left(d x + c\right)^{4} + 9 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right)^{2} + 8 \, {\left(\cosh\left(d x + c\right)^{7} + 3 \, \cosh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{-b} \arctan\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}\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 21 \, {\left(\cosh\left(d x + c\right)^{8} + 8 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sinh\left(d x + c\right)^{8} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{6} + 4 \, \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, \cosh\left(d x + c\right)^{4} + 30 \, \cosh\left(d x + c\right)^{2} + 3\right)} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{5} + 10 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{6} + 15 \, \cosh\left(d x + c\right)^{4} + 9 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right)^{2} + 8 \, {\left(\cosh\left(d x + c\right)^{7} + 3 \, \cosh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{-b} \log\left(-\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(\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{-b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - 2 \, b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right) + 16 \, {\left(5 \, \cosh\left(d x + c\right)^{8} + 40 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 5 \, \sinh\left(d x + c\right)^{8} + 2 \, {\left(70 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{6} - 6 \, \cosh\left(d x + c\right)^{6} + 4 \, {\left(70 \, \cosh\left(d x + c\right)^{3} - 9 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(175 \, \cosh\left(d x + c\right)^{4} - 45 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 2 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(35 \, \cosh\left(d x + c\right)^{5} - 15 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(70 \, \cosh\left(d x + c\right)^{6} - 45 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{2} - 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(10 \, \cosh\left(d x + c\right)^{7} - 9 \, \cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{84 \, {\left(b^{2} d \cosh\left(d x + c\right)^{8} + 8 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} d \sinh\left(d x + c\right)^{8} + 4 \, b^{2} d \cosh\left(d x + c\right)^{6} + 6 \, b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(35 \, b^{2} d \cosh\left(d x + c\right)^{4} + 30 \, b^{2} d \cosh\left(d x + c\right)^{2} + 3 \, b^{2} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{5} + 10 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} d + 4 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{6} + 15 \, b^{2} d \cosh\left(d x + c\right)^{4} + 9 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{7} + 3 \, b^{2} d \cosh\left(d x + c\right)^{5} + 3 \, 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{42 \, {\left(\cosh\left(d x + c\right)^{8} + 8 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sinh\left(d x + c\right)^{8} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{6} + 4 \, \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, \cosh\left(d x + c\right)^{4} + 30 \, \cosh\left(d x + c\right)^{2} + 3\right)} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{5} + 10 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{6} + 15 \, \cosh\left(d x + c\right)^{4} + 9 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right)^{2} + 8 \, {\left(\cosh\left(d x + c\right)^{7} + 3 \, \cosh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{b} \arctan\left(\frac{\sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{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) + 21 \, {\left(\cosh\left(d x + c\right)^{8} + 8 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sinh\left(d x + c\right)^{8} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{6} + 4 \, \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, \cosh\left(d x + c\right)^{4} + 30 \, \cosh\left(d x + c\right)^{2} + 3\right)} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{5} + 10 \, \cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, \cosh\left(d x + c\right)^{6} + 15 \, \cosh\left(d x + c\right)^{4} + 9 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right)^{2} + 8 \, {\left(\cosh\left(d x + c\right)^{7} + 3 \, \cosh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \sqrt{b} \log\left(2 \, b \cosh\left(d x + c\right)^{4} + 8 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 12 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b \sinh\left(d x + c\right)^{4} + 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} + {\left(6 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}} - b\right) - 16 \, {\left(5 \, \cosh\left(d x + c\right)^{8} + 40 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 5 \, \sinh\left(d x + c\right)^{8} + 2 \, {\left(70 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{6} - 6 \, \cosh\left(d x + c\right)^{6} + 4 \, {\left(70 \, \cosh\left(d x + c\right)^{3} - 9 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(175 \, \cosh\left(d x + c\right)^{4} - 45 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right)^{4} + 2 \, \cosh\left(d x + c\right)^{4} + 8 \, {\left(35 \, \cosh\left(d x + c\right)^{5} - 15 \, \cosh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(70 \, \cosh\left(d x + c\right)^{6} - 45 \, \cosh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{2} - 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(10 \, \cosh\left(d x + c\right)^{7} - 9 \, \cosh\left(d x + c\right)^{5} + 2 \, \cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5\right)} \sqrt{\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{84 \, {\left(b^{2} d \cosh\left(d x + c\right)^{8} + 8 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} d \sinh\left(d x + c\right)^{8} + 4 \, b^{2} d \cosh\left(d x + c\right)^{6} + 6 \, b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(35 \, b^{2} d \cosh\left(d x + c\right)^{4} + 30 \, b^{2} d \cosh\left(d x + c\right)^{2} + 3 \, b^{2} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{5} + 10 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} d + 4 \, {\left(7 \, b^{2} d \cosh\left(d x + c\right)^{6} + 15 \, b^{2} d \cosh\left(d x + c\right)^{4} + 9 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{7} + 3 \, b^{2} d \cosh\left(d x + c\right)^{5} + 3 \, 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)}}\right]"," ",0,"[-1/84*(42*(cosh(d*x + c)^8 + 8*cosh(d*x + c)*sinh(d*x + c)^7 + sinh(d*x + c)^8 + 4*(7*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^6 + 4*cosh(d*x + c)^6 + 8*(7*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*cosh(d*x + c)^4 + 30*cosh(d*x + c)^2 + 3)*sinh(d*x + c)^4 + 6*cosh(d*x + c)^4 + 8*(7*cosh(d*x + c)^5 + 10*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*cosh(d*x + c)^6 + 15*cosh(d*x + c)^4 + 9*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 4*cosh(d*x + c)^2 + 8*(cosh(d*x + c)^7 + 3*cosh(d*x + c)^5 + 3*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(-b)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 21*(cosh(d*x + c)^8 + 8*cosh(d*x + c)*sinh(d*x + c)^7 + sinh(d*x + c)^8 + 4*(7*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^6 + 4*cosh(d*x + c)^6 + 8*(7*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*cosh(d*x + c)^4 + 30*cosh(d*x + c)^2 + 3)*sinh(d*x + c)^4 + 6*cosh(d*x + c)^4 + 8*(7*cosh(d*x + c)^5 + 10*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*cosh(d*x + c)^6 + 15*cosh(d*x + c)^4 + 9*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 4*cosh(d*x + c)^2 + 8*(cosh(d*x + c)^7 + 3*cosh(d*x + c)^5 + 3*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(-b)*log(-(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)^3*sinh(d*x + c) + 6*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - 2*b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)) + 16*(5*cosh(d*x + c)^8 + 40*cosh(d*x + c)*sinh(d*x + c)^7 + 5*sinh(d*x + c)^8 + 2*(70*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^6 - 6*cosh(d*x + c)^6 + 4*(70*cosh(d*x + c)^3 - 9*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(175*cosh(d*x + c)^4 - 45*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 2*cosh(d*x + c)^4 + 8*(35*cosh(d*x + c)^5 - 15*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c)^3 + 2*(70*cosh(d*x + c)^6 - 45*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^2 - 6*cosh(d*x + c)^2 + 4*(10*cosh(d*x + c)^7 - 9*cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 - 3*cosh(d*x + c))*sinh(d*x + c) + 5)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^2*d*cosh(d*x + c)^8 + 8*b^2*d*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*d*sinh(d*x + c)^8 + 4*b^2*d*cosh(d*x + c)^6 + 6*b^2*d*cosh(d*x + c)^4 + 4*(7*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^6 + 8*(7*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*sinh(d*x + c)^5 + 4*b^2*d*cosh(d*x + c)^2 + 2*(35*b^2*d*cosh(d*x + c)^4 + 30*b^2*d*cosh(d*x + c)^2 + 3*b^2*d)*sinh(d*x + c)^4 + 8*(7*b^2*d*cosh(d*x + c)^5 + 10*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*d + 4*(7*b^2*d*cosh(d*x + c)^6 + 15*b^2*d*cosh(d*x + c)^4 + 9*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 8*(b^2*d*cosh(d*x + c)^7 + 3*b^2*d*cosh(d*x + c)^5 + 3*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c)), 1/84*(42*(cosh(d*x + c)^8 + 8*cosh(d*x + c)*sinh(d*x + c)^7 + sinh(d*x + c)^8 + 4*(7*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^6 + 4*cosh(d*x + c)^6 + 8*(7*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*cosh(d*x + c)^4 + 30*cosh(d*x + c)^2 + 3)*sinh(d*x + c)^4 + 6*cosh(d*x + c)^4 + 8*(7*cosh(d*x + c)^5 + 10*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*cosh(d*x + c)^6 + 15*cosh(d*x + c)^4 + 9*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 4*cosh(d*x + c)^2 + 8*(cosh(d*x + c)^7 + 3*cosh(d*x + c)^5 + 3*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(b)*arctan(sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c))/(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)) + 21*(cosh(d*x + c)^8 + 8*cosh(d*x + c)*sinh(d*x + c)^7 + sinh(d*x + c)^8 + 4*(7*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^6 + 4*cosh(d*x + c)^6 + 8*(7*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*cosh(d*x + c)^4 + 30*cosh(d*x + c)^2 + 3)*sinh(d*x + c)^4 + 6*cosh(d*x + c)^4 + 8*(7*cosh(d*x + c)^5 + 10*cosh(d*x + c)^3 + 3*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*cosh(d*x + c)^6 + 15*cosh(d*x + c)^4 + 9*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^2 + 4*cosh(d*x + c)^2 + 8*(cosh(d*x + c)^7 + 3*cosh(d*x + c)^5 + 3*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c) + 1)*sqrt(b)*log(2*b*cosh(d*x + c)^4 + 8*b*cosh(d*x + c)^3*sinh(d*x + c) + 12*b*cosh(d*x + c)^2*sinh(d*x + c)^2 + 8*b*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b*sinh(d*x + c)^4 + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + (6*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - cosh(d*x + c)^2 + 2*(2*cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c))*sqrt(b)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)) - b) - 16*(5*cosh(d*x + c)^8 + 40*cosh(d*x + c)*sinh(d*x + c)^7 + 5*sinh(d*x + c)^8 + 2*(70*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^6 - 6*cosh(d*x + c)^6 + 4*(70*cosh(d*x + c)^3 - 9*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(175*cosh(d*x + c)^4 - 45*cosh(d*x + c)^2 + 1)*sinh(d*x + c)^4 + 2*cosh(d*x + c)^4 + 8*(35*cosh(d*x + c)^5 - 15*cosh(d*x + c)^3 + cosh(d*x + c))*sinh(d*x + c)^3 + 2*(70*cosh(d*x + c)^6 - 45*cosh(d*x + c)^4 + 6*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^2 - 6*cosh(d*x + c)^2 + 4*(10*cosh(d*x + c)^7 - 9*cosh(d*x + c)^5 + 2*cosh(d*x + c)^3 - 3*cosh(d*x + c))*sinh(d*x + c) + 5)*sqrt(b*cosh(d*x + c)/sinh(d*x + c)))/(b^2*d*cosh(d*x + c)^8 + 8*b^2*d*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*d*sinh(d*x + c)^8 + 4*b^2*d*cosh(d*x + c)^6 + 6*b^2*d*cosh(d*x + c)^4 + 4*(7*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^6 + 8*(7*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*sinh(d*x + c)^5 + 4*b^2*d*cosh(d*x + c)^2 + 2*(35*b^2*d*cosh(d*x + c)^4 + 30*b^2*d*cosh(d*x + c)^2 + 3*b^2*d)*sinh(d*x + c)^4 + 8*(7*b^2*d*cosh(d*x + c)^5 + 10*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*d + 4*(7*b^2*d*cosh(d*x + c)^6 + 15*b^2*d*cosh(d*x + c)^4 + 9*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 8*(b^2*d*cosh(d*x + c)^7 + 3*b^2*d*cosh(d*x + c)^5 + 3*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
33,1,1046,0,1.448246," ","integrate((b*coth(d*x+c)^3)^(4/3),x, algorithm=""fricas"")","-\frac{{\left(3 \, b d x \cosh\left(d x + c\right)^{6} - 3 \, {\left(b d x e^{\left(2 \, d x + 2 \, c\right)} - b d x\right)} \sinh\left(d x + c\right)^{6} - 18 \, {\left(b d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - b d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 3 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{2} - 3 \, b d x - {\left(15 \, b d x \cosh\left(d x + c\right)^{2} - 3 \, b d x - 4 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, b\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(5 \, b d x \cosh\left(d x + c\right)^{3} - {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right) - {\left(5 \, b d x \cosh\left(d x + c\right)^{3} - {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} - 3 \, b d x + 3 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{4} + 3 \, b d x - 6 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{2} - {\left(15 \, b d x \cosh\left(d x + c\right)^{4} + 3 \, b d x - 6 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, b\right)} \sinh\left(d x + c\right)^{2} - {\left(3 \, b d x \cosh\left(d x + c\right)^{6} - 3 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{4} - 3 \, b d x + 3 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{2} - 8 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(3 \, b d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right) - {\left(3 \, b d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, b d x + 4 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) - 8 \, b\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{1}{3}}}{3 \, {\left(d \cosh\left(d x + c\right)^{6} + {\left(d e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 3 \, d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} + {\left(5 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} - 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) + {\left(5 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, 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} + {\left(5 \, d \cosh\left(d x + c\right)^{4} - 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{2} + {\left(d \cosh\left(d x + c\right)^{6} - 3 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 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) + {\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)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) - d\right)}}"," ",0,"-1/3*(3*b*d*x*cosh(d*x + c)^6 - 3*(b*d*x*e^(2*d*x + 2*c) - b*d*x)*sinh(d*x + c)^6 - 18*(b*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) - b*d*x*cosh(d*x + c))*sinh(d*x + c)^5 - 3*(3*b*d*x + 4*b)*cosh(d*x + c)^4 + 3*(15*b*d*x*cosh(d*x + c)^2 - 3*b*d*x - (15*b*d*x*cosh(d*x + c)^2 - 3*b*d*x - 4*b)*e^(2*d*x + 2*c) - 4*b)*sinh(d*x + c)^4 + 12*(5*b*d*x*cosh(d*x + c)^3 - (3*b*d*x + 4*b)*cosh(d*x + c) - (5*b*d*x*cosh(d*x + c)^3 - (3*b*d*x + 4*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 - 3*b*d*x + 3*(3*b*d*x + 4*b)*cosh(d*x + c)^2 + 3*(15*b*d*x*cosh(d*x + c)^4 + 3*b*d*x - 6*(3*b*d*x + 4*b)*cosh(d*x + c)^2 - (15*b*d*x*cosh(d*x + c)^4 + 3*b*d*x - 6*(3*b*d*x + 4*b)*cosh(d*x + c)^2 + 4*b)*e^(2*d*x + 2*c) + 4*b)*sinh(d*x + c)^2 - (3*b*d*x*cosh(d*x + c)^6 - 3*(3*b*d*x + 4*b)*cosh(d*x + c)^4 - 3*b*d*x + 3*(3*b*d*x + 4*b)*cosh(d*x + c)^2 - 8*b)*e^(2*d*x + 2*c) + 6*(3*b*d*x*cosh(d*x + c)^5 - 2*(3*b*d*x + 4*b)*cosh(d*x + c)^3 + (3*b*d*x + 4*b)*cosh(d*x + c) - (3*b*d*x*cosh(d*x + c)^5 - 2*(3*b*d*x + 4*b)*cosh(d*x + c)^3 + (3*b*d*x + 4*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) - 8*b)*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(1/3)/(d*cosh(d*x + c)^6 + (d*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^6 + 6*(d*cosh(d*x + c)*e^(2*d*x + 2*c) + d*cosh(d*x + c))*sinh(d*x + c)^5 - 3*d*cosh(d*x + c)^4 + 3*(5*d*cosh(d*x + c)^2 + (5*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) - d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c) + (5*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*e^(2*d*x + 2*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 + (5*d*cosh(d*x + c)^4 - 6*d*cosh(d*x + c)^2 + d)*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^2 + (d*cosh(d*x + c)^6 - 3*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) + 6*(d*cosh(d*x + c)^5 - 2*d*cosh(d*x + c)^3 + d*cosh(d*x + c) + (d*cosh(d*x + c)^5 - 2*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) - d)","B",0
34,1,392,0,0.656587," ","integrate((b*coth(d*x+c)^3)^(2/3),x, algorithm=""fricas"")","\frac{{\left(d x \cosh\left(d x + c\right)^{2} + {\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x\right)} \sinh\left(d x + c\right)^{2} - d x + {\left(d x \cosh\left(d x + c\right)^{2} - d x - 2\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(d x \cosh\left(d x + c\right)^{2} - d x - 2\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 2\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{2}{3}}}{d \cosh\left(d x + c\right)^{2} + {\left(d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{2} + {\left(d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - d}"," ",0,"(d*x*cosh(d*x + c)^2 + (d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x)*sinh(d*x + c)^2 - d*x + (d*x*cosh(d*x + c)^2 - d*x - 2)*e^(4*d*x + 4*c) - 2*(d*x*cosh(d*x + c)^2 - d*x - 2)*e^(2*d*x + 2*c) + 2*(d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + d*x*cosh(d*x + c))*sinh(d*x + c) - 2)*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(2/3)/(d*cosh(d*x + c)^2 + (d*e^(4*d*x + 4*c) + 2*d*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^2 + (d*cosh(d*x + c)^2 - d)*e^(4*d*x + 4*c) + 2*(d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) + 2*(d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
35,1,148,0,0.567839," ","integrate((b*coth(d*x+c)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(d x e^{\left(2 \, d x + 2 \, c\right)} - d x - {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{1}{3}}}{d e^{\left(2 \, d x + 2 \, c\right)} + d}"," ",0,"-(d*x*e^(2*d*x + 2*c) - d*x - (e^(2*d*x + 2*c) - 1)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(1/3)/(d*e^(2*d*x + 2*c) + d)","B",0
36,1,187,0,1.534388," ","integrate(1/(b*coth(d*x+c)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x - {\left(e^{\left(4 \, d x + 4 \, c\right)} - 2 \, e^{\left(2 \, d x + 2 \, c\right)} + 1\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{2}{3}}}{b d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b d e^{\left(2 \, d x + 2 \, c\right)} + b d}"," ",0,"-(d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x - (e^(4*d*x + 4*c) - 2*e^(2*d*x + 2*c) + 1)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(2/3)/(b*d*e^(4*d*x + 4*c) + 2*b*d*e^(2*d*x + 2*c) + b*d)","B",0
37,1,287,0,0.596281," ","integrate(1/(b*coth(d*x+c)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(d x \cosh\left(d x + c\right)^{2} - {\left(d x e^{\left(2 \, d x + 2 \, c\right)} - d x\right)} \sinh\left(d x + c\right)^{2} + d x - {\left(d x \cosh\left(d x + c\right)^{2} + d x + 2\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} - d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 2\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{1}{3}}}{b d \cosh\left(d x + c\right)^{2} + {\left(b d e^{\left(2 \, d x + 2 \, c\right)} + b d\right)} \sinh\left(d x + c\right)^{2} + b d + {\left(b d \cosh\left(d x + c\right)^{2} + b d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(b d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-(d*x*cosh(d*x + c)^2 - (d*x*e^(2*d*x + 2*c) - d*x)*sinh(d*x + c)^2 + d*x - (d*x*cosh(d*x + c)^2 + d*x + 2)*e^(2*d*x + 2*c) - 2*(d*x*cosh(d*x + c)*e^(2*d*x + 2*c) - d*x*cosh(d*x + c))*sinh(d*x + c) + 2)*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(1/3)/(b*d*cosh(d*x + c)^2 + (b*d*e^(2*d*x + 2*c) + b*d)*sinh(d*x + c)^2 + b*d + (b*d*cosh(d*x + c)^2 + b*d)*e^(2*d*x + 2*c) + 2*(b*d*cosh(d*x + c)*e^(2*d*x + 2*c) + b*d*cosh(d*x + c))*sinh(d*x + c))","B",0
38,1,1579,0,0.557261," ","integrate(1/(b*coth(d*x+c)^3)^(4/3),x, algorithm=""fricas"")","\frac{{\left(3 \, d x \cosh\left(d x + c\right)^{6} + 3 \, {\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x\right)} \sinh\left(d x + c\right)^{6} + 18 \, {\left(d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, d x \cosh\left(d x + c\right)^{2} + 3 \, d x + {\left(15 \, d x \cosh\left(d x + c\right)^{2} + 3 \, d x + 4\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, d x \cosh\left(d x + c\right)^{2} + 3 \, d x + 4\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(5 \, d x \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right) + {\left(5 \, d x \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(5 \, d x \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, d x \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, d x + {\left(15 \, d x \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, d x + 4\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, d x \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, d x + 4\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4\right)} \sinh\left(d x + c\right)^{2} + 3 \, d x + {\left(3 \, d x \cosh\left(d x + c\right)^{6} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, d x + 8\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(3 \, d x \cosh\left(d x + c\right)^{6} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{2} + 3 \, d x + 8\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(3 \, d x \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right) + {\left(3 \, d x \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(3 \, d x \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, d x + 4\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) + 8\right)} \left(\frac{b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(6 \, d x + 6 \, c\right)} - 3 \, e^{\left(4 \, d x + 4 \, c\right)} + 3 \, e^{\left(2 \, d x + 2 \, c\right)} - 1}\right)^{\frac{2}{3}}}{3 \, {\left(b^{2} d \cosh\left(d x + c\right)^{6} + 3 \, b^{2} d \cosh\left(d x + c\right)^{4} + {\left(b^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b^{2} d e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(b^{2} d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b^{2} d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, b^{2} d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right) + {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{3} + 3 \, b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} + b^{2} d + 3 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{4} + 6 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{4} + 6 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(5 \, b^{2} d \cosh\left(d x + c\right)^{4} + 6 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{2} + {\left(b^{2} d \cosh\left(d x + c\right)^{6} + 3 \, b^{2} d \cosh\left(d x + c\right)^{4} + 3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(b^{2} d \cosh\left(d x + c\right)^{6} + 3 \, b^{2} d \cosh\left(d x + c\right)^{4} + 3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(b^{2} d \cosh\left(d x + c\right)^{5} + 2 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right) + {\left(b^{2} d \cosh\left(d x + c\right)^{5} + 2 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(b^{2} d \cosh\left(d x + c\right)^{5} + 2 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/3*(3*d*x*cosh(d*x + c)^6 + 3*(d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x)*sinh(d*x + c)^6 + 18*(d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + d*x*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(3*d*x + 4)*cosh(d*x + c)^4 + 3*(15*d*x*cosh(d*x + c)^2 + 3*d*x + (15*d*x*cosh(d*x + c)^2 + 3*d*x + 4)*e^(4*d*x + 4*c) - 2*(15*d*x*cosh(d*x + c)^2 + 3*d*x + 4)*e^(2*d*x + 2*c) + 4)*sinh(d*x + c)^4 + 12*(5*d*x*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c) + (5*d*x*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(5*d*x*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 + 3*(3*d*x + 4)*cosh(d*x + c)^2 + 3*(15*d*x*cosh(d*x + c)^4 + 6*(3*d*x + 4)*cosh(d*x + c)^2 + 3*d*x + (15*d*x*cosh(d*x + c)^4 + 6*(3*d*x + 4)*cosh(d*x + c)^2 + 3*d*x + 4)*e^(4*d*x + 4*c) - 2*(15*d*x*cosh(d*x + c)^4 + 6*(3*d*x + 4)*cosh(d*x + c)^2 + 3*d*x + 4)*e^(2*d*x + 2*c) + 4)*sinh(d*x + c)^2 + 3*d*x + (3*d*x*cosh(d*x + c)^6 + 3*(3*d*x + 4)*cosh(d*x + c)^4 + 3*(3*d*x + 4)*cosh(d*x + c)^2 + 3*d*x + 8)*e^(4*d*x + 4*c) - 2*(3*d*x*cosh(d*x + c)^6 + 3*(3*d*x + 4)*cosh(d*x + c)^4 + 3*(3*d*x + 4)*cosh(d*x + c)^2 + 3*d*x + 8)*e^(2*d*x + 2*c) + 6*(3*d*x*cosh(d*x + c)^5 + 2*(3*d*x + 4)*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c) + (3*d*x*cosh(d*x + c)^5 + 2*(3*d*x + 4)*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(3*d*x*cosh(d*x + c)^5 + 2*(3*d*x + 4)*cosh(d*x + c)^3 + (3*d*x + 4)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) + 8)*((b*e^(6*d*x + 6*c) + 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) + b)/(e^(6*d*x + 6*c) - 3*e^(4*d*x + 4*c) + 3*e^(2*d*x + 2*c) - 1))^(2/3)/(b^2*d*cosh(d*x + c)^6 + 3*b^2*d*cosh(d*x + c)^4 + (b^2*d*e^(4*d*x + 4*c) + 2*b^2*d*e^(2*d*x + 2*c) + b^2*d)*sinh(d*x + c)^6 + 6*(b^2*d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*b^2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + b^2*d*cosh(d*x + c))*sinh(d*x + c)^5 + 3*b^2*d*cosh(d*x + c)^2 + 3*(5*b^2*d*cosh(d*x + c)^2 + b^2*d + (5*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(5*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^4 + 4*(5*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c) + (5*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(5*b^2*d*cosh(d*x + c)^3 + 3*b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 + b^2*d + 3*(5*b^2*d*cosh(d*x + c)^4 + 6*b^2*d*cosh(d*x + c)^2 + b^2*d + (5*b^2*d*cosh(d*x + c)^4 + 6*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(5*b^2*d*cosh(d*x + c)^4 + 6*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^2 + (b^2*d*cosh(d*x + c)^6 + 3*b^2*d*cosh(d*x + c)^4 + 3*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(b^2*d*cosh(d*x + c)^6 + 3*b^2*d*cosh(d*x + c)^4 + 3*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c) + 6*(b^2*d*cosh(d*x + c)^5 + 2*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c) + (b^2*d*cosh(d*x + c)^5 + 2*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(b^2*d*cosh(d*x + c)^5 + 2*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c))","B",0
39,0,0,0,0.608680," ","integrate((b*coth(d*x+c)^4)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \coth\left(d x + c\right)^{4}\right)^{n}, x\right)"," ",0,"integral((b*coth(d*x + c)^4)^n, x)","F",0
40,1,3421,0,0.908211," ","integrate((b*coth(d*x+c)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b d x \cosh\left(d x + c\right)^{10} + 15 \, {\left(b d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, b d x e^{\left(2 \, d x + 2 \, c\right)} + b d x\right)} \sinh\left(d x + c\right)^{10} + 150 \, {\left(b d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, b d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(45 \, b d x \cosh\left(d x + c\right)^{2} - 5 \, b d x + {\left(45 \, b d x \cosh\left(d x + c\right)^{2} - 5 \, b d x - 6 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(45 \, b d x \cosh\left(d x + c\right)^{2} - 5 \, b d x - 6 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b\right)} \sinh\left(d x + c\right)^{8} + 120 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{3} - {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right) + {\left(15 \, b d x \cosh\left(d x + c\right)^{3} - {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{3} - {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(105 \, b d x \cosh\left(d x + c\right)^{4} + 5 \, b d x - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(105 \, b d x \cosh\left(d x + c\right)^{4} + 5 \, b d x - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(105 \, b d x \cosh\left(d x + c\right)^{4} + 5 \, b d x - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b\right)} \sinh\left(d x + c\right)^{6} + 60 \, {\left(63 \, b d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right) + {\left(63 \, b d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(63 \, b d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{5} - 10 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(315 \, b d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, b d x + 45 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(315 \, b d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, b d x + 45 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} - 28 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(315 \, b d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, b d x + 45 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{2} - 28 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} - 28 \, b\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(45 \, b d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right) + {\left(45 \, b d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(45 \, b d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} - 15 \, b d x + 5 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(135 \, b d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, b d x - 12 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(135 \, b d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, b d x - 12 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} + 28 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(135 \, b d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, b d x - 12 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} + 28 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 28 \, b\right)} \sinh\left(d x + c\right)^{2} + {\left(15 \, b d x \cosh\left(d x + c\right)^{10} - 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{8} + 30 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, b d x + 5 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} - 46 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{10} - 15 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{8} + 30 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, b d x + 5 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{2} - 46 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 10 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right) + {\left(15 \, b d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, b d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, b d x + 6 \, b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, b d x + 28 \, b\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) - 46 \, b\right)} \sqrt{\frac{b e^{\left(8 \, d x + 8 \, c\right)} + 4 \, b e^{\left(6 \, d x + 6 \, c\right)} + 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(8 \, d x + 8 \, c\right)} - 4 \, e^{\left(6 \, d x + 6 \, c\right)} + 6 \, e^{\left(4 \, d x + 4 \, c\right)} - 4 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{15 \, {\left(d \cosh\left(d x + c\right)^{10} + {\left(d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{10} + 10 \, {\left(d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, d \cosh\left(d x + c\right)^{2} + {\left(9 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(9 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} - 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) + {\left(3 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, 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} + {\left(21 \, d \cosh\left(d x + c\right)^{4} - 14 \, d \cosh\left(d x + c\right)^{2} + d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(21 \, d \cosh\left(d x + c\right)^{4} - 14 \, d \cosh\left(d x + c\right)^{2} + d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 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) + {\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)} e^{\left(4 \, d x + 4 \, c\right)} + 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)} e^{\left(2 \, d x + 2 \, 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} + {\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)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\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)} e^{\left(2 \, d x + 2 \, c\right)} - 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) + {\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)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\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)} e^{\left(2 \, d x + 2 \, 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} + {\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)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\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)} e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{2} + {\left(d \cosh\left(d x + c\right)^{10} - 5 \, d \cosh\left(d x + c\right)^{8} + 10 \, d \cosh\left(d x + c\right)^{6} - 10 \, d \cosh\left(d x + c\right)^{4} + 5 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(d \cosh\left(d x + c\right)^{10} - 5 \, d \cosh\left(d x + c\right)^{8} + 10 \, d \cosh\left(d x + c\right)^{6} - 10 \, d \cosh\left(d x + c\right)^{4} + 5 \, d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 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) + {\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)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\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)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) - d\right)}}"," ",0,"1/15*(15*b*d*x*cosh(d*x + c)^10 + 15*(b*d*x*e^(4*d*x + 4*c) - 2*b*d*x*e^(2*d*x + 2*c) + b*d*x)*sinh(d*x + c)^10 + 150*(b*d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*b*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + b*d*x*cosh(d*x + c))*sinh(d*x + c)^9 - 15*(5*b*d*x + 6*b)*cosh(d*x + c)^8 + 15*(45*b*d*x*cosh(d*x + c)^2 - 5*b*d*x + (45*b*d*x*cosh(d*x + c)^2 - 5*b*d*x - 6*b)*e^(4*d*x + 4*c) - 2*(45*b*d*x*cosh(d*x + c)^2 - 5*b*d*x - 6*b)*e^(2*d*x + 2*c) - 6*b)*sinh(d*x + c)^8 + 120*(15*b*d*x*cosh(d*x + c)^3 - (5*b*d*x + 6*b)*cosh(d*x + c) + (15*b*d*x*cosh(d*x + c)^3 - (5*b*d*x + 6*b)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(15*b*d*x*cosh(d*x + c)^3 - (5*b*d*x + 6*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^7 + 30*(5*b*d*x + 6*b)*cosh(d*x + c)^6 + 30*(105*b*d*x*cosh(d*x + c)^4 + 5*b*d*x - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^2 + (105*b*d*x*cosh(d*x + c)^4 + 5*b*d*x - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^2 + 6*b)*e^(4*d*x + 4*c) - 2*(105*b*d*x*cosh(d*x + c)^4 + 5*b*d*x - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^2 + 6*b)*e^(2*d*x + 2*c) + 6*b)*sinh(d*x + c)^6 + 60*(63*b*d*x*cosh(d*x + c)^5 - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^3 + 3*(5*b*d*x + 6*b)*cosh(d*x + c) + (63*b*d*x*cosh(d*x + c)^5 - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^3 + 3*(5*b*d*x + 6*b)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(63*b*d*x*cosh(d*x + c)^5 - 14*(5*b*d*x + 6*b)*cosh(d*x + c)^3 + 3*(5*b*d*x + 6*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^5 - 10*(15*b*d*x + 28*b)*cosh(d*x + c)^4 + 10*(315*b*d*x*cosh(d*x + c)^6 - 105*(5*b*d*x + 6*b)*cosh(d*x + c)^4 - 15*b*d*x + 45*(5*b*d*x + 6*b)*cosh(d*x + c)^2 + (315*b*d*x*cosh(d*x + c)^6 - 105*(5*b*d*x + 6*b)*cosh(d*x + c)^4 - 15*b*d*x + 45*(5*b*d*x + 6*b)*cosh(d*x + c)^2 - 28*b)*e^(4*d*x + 4*c) - 2*(315*b*d*x*cosh(d*x + c)^6 - 105*(5*b*d*x + 6*b)*cosh(d*x + c)^4 - 15*b*d*x + 45*(5*b*d*x + 6*b)*cosh(d*x + c)^2 - 28*b)*e^(2*d*x + 2*c) - 28*b)*sinh(d*x + c)^4 + 40*(45*b*d*x*cosh(d*x + c)^7 - 21*(5*b*d*x + 6*b)*cosh(d*x + c)^5 + 15*(5*b*d*x + 6*b)*cosh(d*x + c)^3 - (15*b*d*x + 28*b)*cosh(d*x + c) + (45*b*d*x*cosh(d*x + c)^7 - 21*(5*b*d*x + 6*b)*cosh(d*x + c)^5 + 15*(5*b*d*x + 6*b)*cosh(d*x + c)^3 - (15*b*d*x + 28*b)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(45*b*d*x*cosh(d*x + c)^7 - 21*(5*b*d*x + 6*b)*cosh(d*x + c)^5 + 15*(5*b*d*x + 6*b)*cosh(d*x + c)^3 - (15*b*d*x + 28*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 - 15*b*d*x + 5*(15*b*d*x + 28*b)*cosh(d*x + c)^2 + 5*(135*b*d*x*cosh(d*x + c)^8 - 84*(5*b*d*x + 6*b)*cosh(d*x + c)^6 + 90*(5*b*d*x + 6*b)*cosh(d*x + c)^4 + 15*b*d*x - 12*(15*b*d*x + 28*b)*cosh(d*x + c)^2 + (135*b*d*x*cosh(d*x + c)^8 - 84*(5*b*d*x + 6*b)*cosh(d*x + c)^6 + 90*(5*b*d*x + 6*b)*cosh(d*x + c)^4 + 15*b*d*x - 12*(15*b*d*x + 28*b)*cosh(d*x + c)^2 + 28*b)*e^(4*d*x + 4*c) - 2*(135*b*d*x*cosh(d*x + c)^8 - 84*(5*b*d*x + 6*b)*cosh(d*x + c)^6 + 90*(5*b*d*x + 6*b)*cosh(d*x + c)^4 + 15*b*d*x - 12*(15*b*d*x + 28*b)*cosh(d*x + c)^2 + 28*b)*e^(2*d*x + 2*c) + 28*b)*sinh(d*x + c)^2 + (15*b*d*x*cosh(d*x + c)^10 - 15*(5*b*d*x + 6*b)*cosh(d*x + c)^8 + 30*(5*b*d*x + 6*b)*cosh(d*x + c)^6 - 10*(15*b*d*x + 28*b)*cosh(d*x + c)^4 - 15*b*d*x + 5*(15*b*d*x + 28*b)*cosh(d*x + c)^2 - 46*b)*e^(4*d*x + 4*c) - 2*(15*b*d*x*cosh(d*x + c)^10 - 15*(5*b*d*x + 6*b)*cosh(d*x + c)^8 + 30*(5*b*d*x + 6*b)*cosh(d*x + c)^6 - 10*(15*b*d*x + 28*b)*cosh(d*x + c)^4 - 15*b*d*x + 5*(15*b*d*x + 28*b)*cosh(d*x + c)^2 - 46*b)*e^(2*d*x + 2*c) + 10*(15*b*d*x*cosh(d*x + c)^9 - 12*(5*b*d*x + 6*b)*cosh(d*x + c)^7 + 18*(5*b*d*x + 6*b)*cosh(d*x + c)^5 - 4*(15*b*d*x + 28*b)*cosh(d*x + c)^3 + (15*b*d*x + 28*b)*cosh(d*x + c) + (15*b*d*x*cosh(d*x + c)^9 - 12*(5*b*d*x + 6*b)*cosh(d*x + c)^7 + 18*(5*b*d*x + 6*b)*cosh(d*x + c)^5 - 4*(15*b*d*x + 28*b)*cosh(d*x + c)^3 + (15*b*d*x + 28*b)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(15*b*d*x*cosh(d*x + c)^9 - 12*(5*b*d*x + 6*b)*cosh(d*x + c)^7 + 18*(5*b*d*x + 6*b)*cosh(d*x + c)^5 - 4*(15*b*d*x + 28*b)*cosh(d*x + c)^3 + (15*b*d*x + 28*b)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) - 46*b)*sqrt((b*e^(8*d*x + 8*c) + 4*b*e^(6*d*x + 6*c) + 6*b*e^(4*d*x + 4*c) + 4*b*e^(2*d*x + 2*c) + b)/(e^(8*d*x + 8*c) - 4*e^(6*d*x + 6*c) + 6*e^(4*d*x + 4*c) - 4*e^(2*d*x + 2*c) + 1))/(d*cosh(d*x + c)^10 + (d*e^(4*d*x + 4*c) + 2*d*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^10 + 10*(d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + d*cosh(d*x + c))*sinh(d*x + c)^9 - 5*d*cosh(d*x + c)^8 + 5*(9*d*cosh(d*x + c)^2 + (9*d*cosh(d*x + c)^2 - d)*e^(4*d*x + 4*c) + 2*(9*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) - d)*sinh(d*x + c)^8 + 40*(3*d*cosh(d*x + c)^3 - d*cosh(d*x + c) + (3*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(3*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*e^(2*d*x + 2*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 + (21*d*cosh(d*x + c)^4 - 14*d*cosh(d*x + c)^2 + d)*e^(4*d*x + 4*c) + 2*(21*d*cosh(d*x + c)^4 - 14*d*cosh(d*x + c)^2 + d)*e^(2*d*x + 2*c) + 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) + (63*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(63*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*e^(2*d*x + 2*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 + (21*d*cosh(d*x + c)^6 - 35*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*e^(4*d*x + 4*c) + 2*(21*d*cosh(d*x + c)^6 - 35*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) - 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) + (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))*e^(4*d*x + 4*c) + 2*(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))*e^(2*d*x + 2*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 + (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)*e^(4*d*x + 4*c) + 2*(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)*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^2 + (d*cosh(d*x + c)^10 - 5*d*cosh(d*x + c)^8 + 10*d*cosh(d*x + c)^6 - 10*d*cosh(d*x + c)^4 + 5*d*cosh(d*x + c)^2 - d)*e^(4*d*x + 4*c) + 2*(d*cosh(d*x + c)^10 - 5*d*cosh(d*x + c)^8 + 10*d*cosh(d*x + c)^6 - 10*d*cosh(d*x + c)^4 + 5*d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) + 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) + (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))*e^(4*d*x + 4*c) + 2*(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))*e^(2*d*x + 2*c))*sinh(d*x + c) - d)","B",0
41,1,415,0,1.097185," ","integrate((b*coth(d*x+c)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left(d x \cosh\left(d x + c\right)^{2} + {\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x\right)} \sinh\left(d x + c\right)^{2} - d x + {\left(d x \cosh\left(d x + c\right)^{2} - d x - 2\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(d x \cosh\left(d x + c\right)^{2} - d x - 2\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 2\right)} \sqrt{\frac{b e^{\left(8 \, d x + 8 \, c\right)} + 4 \, b e^{\left(6 \, d x + 6 \, c\right)} + 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(8 \, d x + 8 \, c\right)} - 4 \, e^{\left(6 \, d x + 6 \, c\right)} + 6 \, e^{\left(4 \, d x + 4 \, c\right)} - 4 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{d \cosh\left(d x + c\right)^{2} + {\left(d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d e^{\left(2 \, d x + 2 \, c\right)} + d\right)} \sinh\left(d x + c\right)^{2} + {\left(d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - d}"," ",0,"(d*x*cosh(d*x + c)^2 + (d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x)*sinh(d*x + c)^2 - d*x + (d*x*cosh(d*x + c)^2 - d*x - 2)*e^(4*d*x + 4*c) - 2*(d*x*cosh(d*x + c)^2 - d*x - 2)*e^(2*d*x + 2*c) + 2*(d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + d*x*cosh(d*x + c))*sinh(d*x + c) - 2)*sqrt((b*e^(8*d*x + 8*c) + 4*b*e^(6*d*x + 6*c) + 6*b*e^(4*d*x + 4*c) + 4*b*e^(2*d*x + 2*c) + b)/(e^(8*d*x + 8*c) - 4*e^(6*d*x + 6*c) + 6*e^(4*d*x + 4*c) - 4*e^(2*d*x + 2*c) + 1))/(d*cosh(d*x + c)^2 + (d*e^(4*d*x + 4*c) + 2*d*e^(2*d*x + 2*c) + d)*sinh(d*x + c)^2 + (d*cosh(d*x + c)^2 - d)*e^(4*d*x + 4*c) + 2*(d*cosh(d*x + c)^2 - d)*e^(2*d*x + 2*c) + 2*(d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
42,1,422,0,1.301148," ","integrate(1/(b*coth(d*x+c)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left(d x \cosh\left(d x + c\right)^{2} + {\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x\right)} \sinh\left(d x + c\right)^{2} + d x + {\left(d x \cosh\left(d x + c\right)^{2} + d x + 2\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(d x \cosh\left(d x + c\right)^{2} + d x + 2\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 2\right)} \sqrt{\frac{b e^{\left(8 \, d x + 8 \, c\right)} + 4 \, b e^{\left(6 \, d x + 6 \, c\right)} + 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(8 \, d x + 8 \, c\right)} - 4 \, e^{\left(6 \, d x + 6 \, c\right)} + 6 \, e^{\left(4 \, d x + 4 \, c\right)} - 4 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{b d \cosh\left(d x + c\right)^{2} + {\left(b d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b d e^{\left(2 \, d x + 2 \, c\right)} + b d\right)} \sinh\left(d x + c\right)^{2} + b d + {\left(b d \cosh\left(d x + c\right)^{2} + b d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(b d \cosh\left(d x + c\right)^{2} + b d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(b d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(d*x*cosh(d*x + c)^2 + (d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x)*sinh(d*x + c)^2 + d*x + (d*x*cosh(d*x + c)^2 + d*x + 2)*e^(4*d*x + 4*c) - 2*(d*x*cosh(d*x + c)^2 + d*x + 2)*e^(2*d*x + 2*c) + 2*(d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + d*x*cosh(d*x + c))*sinh(d*x + c) + 2)*sqrt((b*e^(8*d*x + 8*c) + 4*b*e^(6*d*x + 6*c) + 6*b*e^(4*d*x + 4*c) + 4*b*e^(2*d*x + 2*c) + b)/(e^(8*d*x + 8*c) - 4*e^(6*d*x + 6*c) + 6*e^(4*d*x + 4*c) - 4*e^(2*d*x + 2*c) + 1))/(b*d*cosh(d*x + c)^2 + (b*d*e^(4*d*x + 4*c) + 2*b*d*e^(2*d*x + 2*c) + b*d)*sinh(d*x + c)^2 + b*d + (b*d*cosh(d*x + c)^2 + b*d)*e^(4*d*x + 4*c) + 2*(b*d*cosh(d*x + c)^2 + b*d)*e^(2*d*x + 2*c) + 2*(b*d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*b*d*cosh(d*x + c)*e^(2*d*x + 2*c) + b*d*cosh(d*x + c))*sinh(d*x + c))","B",0
43,1,3473,0,0.556259," ","integrate(1/(b*coth(d*x+c)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 \, d x \cosh\left(d x + c\right)^{10} + 15 \, {\left(d x e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x e^{\left(2 \, d x + 2 \, c\right)} + d x\right)} \sinh\left(d x + c\right)^{10} + 150 \, {\left(d x \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} - 2 \, d x \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(45 \, d x \cosh\left(d x + c\right)^{2} + 5 \, d x + {\left(45 \, d x \cosh\left(d x + c\right)^{2} + 5 \, d x + 6\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(45 \, d x \cosh\left(d x + c\right)^{2} + 5 \, d x + 6\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6\right)} \sinh\left(d x + c\right)^{8} + 120 \, {\left(15 \, d x \cosh\left(d x + c\right)^{3} + {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right) + {\left(15 \, d x \cosh\left(d x + c\right)^{3} + {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, d x \cosh\left(d x + c\right)^{3} + {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(105 \, d x \cosh\left(d x + c\right)^{4} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 5 \, d x + {\left(105 \, d x \cosh\left(d x + c\right)^{4} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 5 \, d x + 6\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(105 \, d x \cosh\left(d x + c\right)^{4} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 5 \, d x + 6\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6\right)} \sinh\left(d x + c\right)^{6} + 60 \, {\left(63 \, d x \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right) + {\left(63 \, d x \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(63 \, d x \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(315 \, d x \cosh\left(d x + c\right)^{6} + 105 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + {\left(315 \, d x \cosh\left(d x + c\right)^{6} + 105 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 28\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(315 \, d x \cosh\left(d x + c\right)^{6} + 105 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 28\right)} e^{\left(2 \, d x + 2 \, c\right)} + 28\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(45 \, d x \cosh\left(d x + c\right)^{7} + 21 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right) + {\left(45 \, d x \cosh\left(d x + c\right)^{7} + 21 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(45 \, d x \cosh\left(d x + c\right)^{7} + 21 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(135 \, d x \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + {\left(135 \, d x \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 28\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(135 \, d x \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 28\right)} e^{\left(2 \, d x + 2 \, c\right)} + 28\right)} \sinh\left(d x + c\right)^{2} + 15 \, d x + {\left(15 \, d x \cosh\left(d x + c\right)^{10} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{8} + 30 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 46\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, d x \cosh\left(d x + c\right)^{10} + 15 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{8} + 30 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{2} + 15 \, d x + 46\right)} e^{\left(2 \, d x + 2 \, c\right)} + 10 \, {\left(15 \, d x \cosh\left(d x + c\right)^{9} + 12 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right) + {\left(15 \, d x \cosh\left(d x + c\right)^{9} + 12 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(15 \, d x \cosh\left(d x + c\right)^{9} + 12 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, d x + 6\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, d x + 28\right)} \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right) + 46\right)} \sqrt{\frac{b e^{\left(8 \, d x + 8 \, c\right)} + 4 \, b e^{\left(6 \, d x + 6 \, c\right)} + 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + b}{e^{\left(8 \, d x + 8 \, c\right)} - 4 \, e^{\left(6 \, d x + 6 \, c\right)} + 6 \, e^{\left(4 \, d x + 4 \, c\right)} - 4 \, e^{\left(2 \, d x + 2 \, c\right)} + 1}}}{15 \, {\left(b^{2} d \cosh\left(d x + c\right)^{10} + 5 \, b^{2} d \cosh\left(d x + c\right)^{8} + {\left(b^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b^{2} d e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d\right)} \sinh\left(d x + c\right)^{10} + 10 \, {\left(b^{2} d \cosh\left(d x + c\right) e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b^{2} d \cosh\left(d x + c\right) e^{\left(2 \, d x + 2 \, c\right)} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 10 \, b^{2} d \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right) + {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{7} + 10 \, b^{2} d \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{4} + 14 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{4} + 14 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{4} + 14 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{2} d \cosh\left(d x + c\right)^{5} + 70 \, b^{2} d \cosh\left(d x + c\right)^{3} + 15 \, b^{2} d \cosh\left(d x + c\right) + {\left(63 \, b^{2} d \cosh\left(d x + c\right)^{5} + 70 \, b^{2} d \cosh\left(d x + c\right)^{3} + 15 \, b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(63 \, b^{2} d \cosh\left(d x + c\right)^{5} + 70 \, b^{2} d \cosh\left(d x + c\right)^{3} + 15 \, b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{5} + 5 \, b^{2} d \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{6} + 35 \, b^{2} d \cosh\left(d x + c\right)^{4} + 15 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{6} + 35 \, b^{2} d \cosh\left(d x + c\right)^{4} + 15 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(21 \, b^{2} d \cosh\left(d x + c\right)^{6} + 35 \, b^{2} d \cosh\left(d x + c\right)^{4} + 15 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{7} + 7 \, b^{2} d \cosh\left(d x + c\right)^{5} + 5 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right) + {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{7} + 7 \, b^{2} d \cosh\left(d x + c\right)^{5} + 5 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{7} + 7 \, b^{2} d \cosh\left(d x + c\right)^{5} + 5 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{3} + b^{2} d + 5 \, {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{8} + 28 \, b^{2} d \cosh\left(d x + c\right)^{6} + 30 \, b^{2} d \cosh\left(d x + c\right)^{4} + 12 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{8} + 28 \, b^{2} d \cosh\left(d x + c\right)^{6} + 30 \, b^{2} d \cosh\left(d x + c\right)^{4} + 12 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(9 \, b^{2} d \cosh\left(d x + c\right)^{8} + 28 \, b^{2} d \cosh\left(d x + c\right)^{6} + 30 \, b^{2} d \cosh\left(d x + c\right)^{4} + 12 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)^{2} + {\left(b^{2} d \cosh\left(d x + c\right)^{10} + 5 \, b^{2} d \cosh\left(d x + c\right)^{8} + 10 \, b^{2} d \cosh\left(d x + c\right)^{6} + 10 \, b^{2} d \cosh\left(d x + c\right)^{4} + 5 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(b^{2} d \cosh\left(d x + c\right)^{10} + 5 \, b^{2} d \cosh\left(d x + c\right)^{8} + 10 \, b^{2} d \cosh\left(d x + c\right)^{6} + 10 \, b^{2} d \cosh\left(d x + c\right)^{4} + 5 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} e^{\left(2 \, d x + 2 \, c\right)} + 10 \, {\left(b^{2} d \cosh\left(d x + c\right)^{9} + 4 \, b^{2} d \cosh\left(d x + c\right)^{7} + 6 \, b^{2} d \cosh\left(d x + c\right)^{5} + 4 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right) + {\left(b^{2} d \cosh\left(d x + c\right)^{9} + 4 \, b^{2} d \cosh\left(d x + c\right)^{7} + 6 \, b^{2} d \cosh\left(d x + c\right)^{5} + 4 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(b^{2} d \cosh\left(d x + c\right)^{9} + 4 \, b^{2} d \cosh\left(d x + c\right)^{7} + 6 \, b^{2} d \cosh\left(d x + c\right)^{5} + 4 \, b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/15*(15*d*x*cosh(d*x + c)^10 + 15*(d*x*e^(4*d*x + 4*c) - 2*d*x*e^(2*d*x + 2*c) + d*x)*sinh(d*x + c)^10 + 150*(d*x*cosh(d*x + c)*e^(4*d*x + 4*c) - 2*d*x*cosh(d*x + c)*e^(2*d*x + 2*c) + d*x*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*d*x + 6)*cosh(d*x + c)^8 + 15*(45*d*x*cosh(d*x + c)^2 + 5*d*x + (45*d*x*cosh(d*x + c)^2 + 5*d*x + 6)*e^(4*d*x + 4*c) - 2*(45*d*x*cosh(d*x + c)^2 + 5*d*x + 6)*e^(2*d*x + 2*c) + 6)*sinh(d*x + c)^8 + 120*(15*d*x*cosh(d*x + c)^3 + (5*d*x + 6)*cosh(d*x + c) + (15*d*x*cosh(d*x + c)^3 + (5*d*x + 6)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(15*d*x*cosh(d*x + c)^3 + (5*d*x + 6)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^7 + 30*(5*d*x + 6)*cosh(d*x + c)^6 + 30*(105*d*x*cosh(d*x + c)^4 + 14*(5*d*x + 6)*cosh(d*x + c)^2 + 5*d*x + (105*d*x*cosh(d*x + c)^4 + 14*(5*d*x + 6)*cosh(d*x + c)^2 + 5*d*x + 6)*e^(4*d*x + 4*c) - 2*(105*d*x*cosh(d*x + c)^4 + 14*(5*d*x + 6)*cosh(d*x + c)^2 + 5*d*x + 6)*e^(2*d*x + 2*c) + 6)*sinh(d*x + c)^6 + 60*(63*d*x*cosh(d*x + c)^5 + 14*(5*d*x + 6)*cosh(d*x + c)^3 + 3*(5*d*x + 6)*cosh(d*x + c) + (63*d*x*cosh(d*x + c)^5 + 14*(5*d*x + 6)*cosh(d*x + c)^3 + 3*(5*d*x + 6)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(63*d*x*cosh(d*x + c)^5 + 14*(5*d*x + 6)*cosh(d*x + c)^3 + 3*(5*d*x + 6)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^5 + 10*(15*d*x + 28)*cosh(d*x + c)^4 + 10*(315*d*x*cosh(d*x + c)^6 + 105*(5*d*x + 6)*cosh(d*x + c)^4 + 45*(5*d*x + 6)*cosh(d*x + c)^2 + 15*d*x + (315*d*x*cosh(d*x + c)^6 + 105*(5*d*x + 6)*cosh(d*x + c)^4 + 45*(5*d*x + 6)*cosh(d*x + c)^2 + 15*d*x + 28)*e^(4*d*x + 4*c) - 2*(315*d*x*cosh(d*x + c)^6 + 105*(5*d*x + 6)*cosh(d*x + c)^4 + 45*(5*d*x + 6)*cosh(d*x + c)^2 + 15*d*x + 28)*e^(2*d*x + 2*c) + 28)*sinh(d*x + c)^4 + 40*(45*d*x*cosh(d*x + c)^7 + 21*(5*d*x + 6)*cosh(d*x + c)^5 + 15*(5*d*x + 6)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c) + (45*d*x*cosh(d*x + c)^7 + 21*(5*d*x + 6)*cosh(d*x + c)^5 + 15*(5*d*x + 6)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(45*d*x*cosh(d*x + c)^7 + 21*(5*d*x + 6)*cosh(d*x + c)^5 + 15*(5*d*x + 6)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 + 5*(15*d*x + 28)*cosh(d*x + c)^2 + 5*(135*d*x*cosh(d*x + c)^8 + 84*(5*d*x + 6)*cosh(d*x + c)^6 + 90*(5*d*x + 6)*cosh(d*x + c)^4 + 12*(15*d*x + 28)*cosh(d*x + c)^2 + 15*d*x + (135*d*x*cosh(d*x + c)^8 + 84*(5*d*x + 6)*cosh(d*x + c)^6 + 90*(5*d*x + 6)*cosh(d*x + c)^4 + 12*(15*d*x + 28)*cosh(d*x + c)^2 + 15*d*x + 28)*e^(4*d*x + 4*c) - 2*(135*d*x*cosh(d*x + c)^8 + 84*(5*d*x + 6)*cosh(d*x + c)^6 + 90*(5*d*x + 6)*cosh(d*x + c)^4 + 12*(15*d*x + 28)*cosh(d*x + c)^2 + 15*d*x + 28)*e^(2*d*x + 2*c) + 28)*sinh(d*x + c)^2 + 15*d*x + (15*d*x*cosh(d*x + c)^10 + 15*(5*d*x + 6)*cosh(d*x + c)^8 + 30*(5*d*x + 6)*cosh(d*x + c)^6 + 10*(15*d*x + 28)*cosh(d*x + c)^4 + 5*(15*d*x + 28)*cosh(d*x + c)^2 + 15*d*x + 46)*e^(4*d*x + 4*c) - 2*(15*d*x*cosh(d*x + c)^10 + 15*(5*d*x + 6)*cosh(d*x + c)^8 + 30*(5*d*x + 6)*cosh(d*x + c)^6 + 10*(15*d*x + 28)*cosh(d*x + c)^4 + 5*(15*d*x + 28)*cosh(d*x + c)^2 + 15*d*x + 46)*e^(2*d*x + 2*c) + 10*(15*d*x*cosh(d*x + c)^9 + 12*(5*d*x + 6)*cosh(d*x + c)^7 + 18*(5*d*x + 6)*cosh(d*x + c)^5 + 4*(15*d*x + 28)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c) + (15*d*x*cosh(d*x + c)^9 + 12*(5*d*x + 6)*cosh(d*x + c)^7 + 18*(5*d*x + 6)*cosh(d*x + c)^5 + 4*(15*d*x + 28)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c))*e^(4*d*x + 4*c) - 2*(15*d*x*cosh(d*x + c)^9 + 12*(5*d*x + 6)*cosh(d*x + c)^7 + 18*(5*d*x + 6)*cosh(d*x + c)^5 + 4*(15*d*x + 28)*cosh(d*x + c)^3 + (15*d*x + 28)*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c) + 46)*sqrt((b*e^(8*d*x + 8*c) + 4*b*e^(6*d*x + 6*c) + 6*b*e^(4*d*x + 4*c) + 4*b*e^(2*d*x + 2*c) + b)/(e^(8*d*x + 8*c) - 4*e^(6*d*x + 6*c) + 6*e^(4*d*x + 4*c) - 4*e^(2*d*x + 2*c) + 1))/(b^2*d*cosh(d*x + c)^10 + 5*b^2*d*cosh(d*x + c)^8 + (b^2*d*e^(4*d*x + 4*c) + 2*b^2*d*e^(2*d*x + 2*c) + b^2*d)*sinh(d*x + c)^10 + 10*(b^2*d*cosh(d*x + c)*e^(4*d*x + 4*c) + 2*b^2*d*cosh(d*x + c)*e^(2*d*x + 2*c) + b^2*d*cosh(d*x + c))*sinh(d*x + c)^9 + 10*b^2*d*cosh(d*x + c)^6 + 5*(9*b^2*d*cosh(d*x + c)^2 + b^2*d + (9*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(9*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^8 + 40*(3*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c) + (3*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(3*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^7 + 10*b^2*d*cosh(d*x + c)^4 + 10*(21*b^2*d*cosh(d*x + c)^4 + 14*b^2*d*cosh(d*x + c)^2 + b^2*d + (21*b^2*d*cosh(d*x + c)^4 + 14*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(21*b^2*d*cosh(d*x + c)^4 + 14*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^6 + 4*(63*b^2*d*cosh(d*x + c)^5 + 70*b^2*d*cosh(d*x + c)^3 + 15*b^2*d*cosh(d*x + c) + (63*b^2*d*cosh(d*x + c)^5 + 70*b^2*d*cosh(d*x + c)^3 + 15*b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(63*b^2*d*cosh(d*x + c)^5 + 70*b^2*d*cosh(d*x + c)^3 + 15*b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^5 + 5*b^2*d*cosh(d*x + c)^2 + 10*(21*b^2*d*cosh(d*x + c)^6 + 35*b^2*d*cosh(d*x + c)^4 + 15*b^2*d*cosh(d*x + c)^2 + b^2*d + (21*b^2*d*cosh(d*x + c)^6 + 35*b^2*d*cosh(d*x + c)^4 + 15*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(21*b^2*d*cosh(d*x + c)^6 + 35*b^2*d*cosh(d*x + c)^4 + 15*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^4 + 40*(3*b^2*d*cosh(d*x + c)^7 + 7*b^2*d*cosh(d*x + c)^5 + 5*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c) + (3*b^2*d*cosh(d*x + c)^7 + 7*b^2*d*cosh(d*x + c)^5 + 5*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(3*b^2*d*cosh(d*x + c)^7 + 7*b^2*d*cosh(d*x + c)^5 + 5*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c)^3 + b^2*d + 5*(9*b^2*d*cosh(d*x + c)^8 + 28*b^2*d*cosh(d*x + c)^6 + 30*b^2*d*cosh(d*x + c)^4 + 12*b^2*d*cosh(d*x + c)^2 + b^2*d + (9*b^2*d*cosh(d*x + c)^8 + 28*b^2*d*cosh(d*x + c)^6 + 30*b^2*d*cosh(d*x + c)^4 + 12*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(9*b^2*d*cosh(d*x + c)^8 + 28*b^2*d*cosh(d*x + c)^6 + 30*b^2*d*cosh(d*x + c)^4 + 12*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c))*sinh(d*x + c)^2 + (b^2*d*cosh(d*x + c)^10 + 5*b^2*d*cosh(d*x + c)^8 + 10*b^2*d*cosh(d*x + c)^6 + 10*b^2*d*cosh(d*x + c)^4 + 5*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(4*d*x + 4*c) + 2*(b^2*d*cosh(d*x + c)^10 + 5*b^2*d*cosh(d*x + c)^8 + 10*b^2*d*cosh(d*x + c)^6 + 10*b^2*d*cosh(d*x + c)^4 + 5*b^2*d*cosh(d*x + c)^2 + b^2*d)*e^(2*d*x + 2*c) + 10*(b^2*d*cosh(d*x + c)^9 + 4*b^2*d*cosh(d*x + c)^7 + 6*b^2*d*cosh(d*x + c)^5 + 4*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c) + (b^2*d*cosh(d*x + c)^9 + 4*b^2*d*cosh(d*x + c)^7 + 6*b^2*d*cosh(d*x + c)^5 + 4*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(4*d*x + 4*c) + 2*(b^2*d*cosh(d*x + c)^9 + 4*b^2*d*cosh(d*x + c)^7 + 6*b^2*d*cosh(d*x + c)^5 + 4*b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*e^(2*d*x + 2*c))*sinh(d*x + c))","B",0
44,1,2864,0,1.325197," ","integrate((b*coth(d*x+c)^4)^(4/3),x, algorithm=""fricas"")","-\frac{182 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{8} + 8 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sqrt{3} b \sinh\left(d x + c\right)^{8} - 4 \, \sqrt{3} b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} - 3 \, \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} - 30 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} + 3 \, \sqrt{3} b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{5} - 10 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} + 3 \, \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{6} - 15 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} + 9 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{7} - 3 \, \sqrt{3} b \cosh\left(d x + c\right)^{5} + 3 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} - \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + \sqrt{3} b\right)} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b + 2 \, \sqrt{3} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) - 182 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{8} + 8 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + \sqrt{3} b \sinh\left(d x + c\right)^{8} - 4 \, \sqrt{3} b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} - 3 \, \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} - 30 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} + 3 \, \sqrt{3} b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{5} - 10 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} + 3 \, \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, \sqrt{3} b \cosh\left(d x + c\right)^{6} - 15 \, \sqrt{3} b \cosh\left(d x + c\right)^{4} + 9 \, \sqrt{3} b \cosh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(\sqrt{3} b \cosh\left(d x + c\right)^{7} - 3 \, \sqrt{3} b \cosh\left(d x + c\right)^{5} + 3 \, \sqrt{3} b \cosh\left(d x + c\right)^{3} - \sqrt{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + \sqrt{3} b\right)} b^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + 91 \, {\left(b \cosh\left(d x + c\right)^{8} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} - 4 \, b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 30 \, b \cosh\left(d x + c\right)^{2} + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{5} - 10 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 15 \, b \cosh\left(d x + c\right)^{4} + 9 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b \cosh\left(d x + c\right)^{7} - 3 \, b \cosh\left(d x + c\right)^{5} + 3 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 91 \, {\left(b \cosh\left(d x + c\right)^{8} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} - 4 \, b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 30 \, b \cosh\left(d x + c\right)^{2} + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{5} - 10 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 15 \, b \cosh\left(d x + c\right)^{4} + 9 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b \cosh\left(d x + c\right)^{7} - 3 \, b \cosh\left(d x + c\right)^{5} + 3 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} b^{\frac{1}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 182 \, {\left(b \cosh\left(d x + c\right)^{8} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} - 4 \, b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 30 \, b \cosh\left(d x + c\right)^{2} + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{5} - 10 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 15 \, b \cosh\left(d x + c\right)^{4} + 9 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b \cosh\left(d x + c\right)^{7} - 3 \, b \cosh\left(d x + c\right)^{5} + 3 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(-b\right)^{\frac{1}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 182 \, {\left(b \cosh\left(d x + c\right)^{8} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} - 4 \, b \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 30 \, b \cosh\left(d x + c\right)^{2} + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{5} - 10 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 15 \, b \cosh\left(d x + c\right)^{4} + 9 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b \cosh\left(d x + c\right)^{7} - 3 \, b \cosh\left(d x + c\right)^{5} + 3 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} b^{\frac{1}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 12 \, {\left(111 \, b \cosh\left(d x + c\right)^{8} + 888 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 111 \, b \sinh\left(d x + c\right)^{8} - 336 \, b \cosh\left(d x + c\right)^{6} + 84 \, {\left(37 \, b \cosh\left(d x + c\right)^{2} - 4 \, b\right)} \sinh\left(d x + c\right)^{6} + 168 \, {\left(37 \, b \cosh\left(d x + c\right)^{3} - 12 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 562 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(3885 \, b \cosh\left(d x + c\right)^{4} - 2520 \, b \cosh\left(d x + c\right)^{2} + 281 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(777 \, b \cosh\left(d x + c\right)^{5} - 840 \, b \cosh\left(d x + c\right)^{3} + 281 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 336 \, b \cosh\left(d x + c\right)^{2} + 12 \, {\left(259 \, b \cosh\left(d x + c\right)^{6} - 420 \, b \cosh\left(d x + c\right)^{4} + 281 \, b \cosh\left(d x + c\right)^{2} - 28 \, b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(111 \, b \cosh\left(d x + c\right)^{7} - 252 \, b \cosh\left(d x + c\right)^{5} + 281 \, b \cosh\left(d x + c\right)^{3} - 84 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 111 \, b\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{364 \, {\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,"-1/364*(182*(sqrt(3)*b*cosh(d*x + c)^8 + 8*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c)^7 + sqrt(3)*b*sinh(d*x + c)^8 - 4*sqrt(3)*b*cosh(d*x + c)^6 + 4*(7*sqrt(3)*b*cosh(d*x + c)^2 - sqrt(3)*b)*sinh(d*x + c)^6 + 8*(7*sqrt(3)*b*cosh(d*x + c)^3 - 3*sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*sqrt(3)*b*cosh(d*x + c)^4 + 2*(35*sqrt(3)*b*cosh(d*x + c)^4 - 30*sqrt(3)*b*cosh(d*x + c)^2 + 3*sqrt(3)*b)*sinh(d*x + c)^4 + 8*(7*sqrt(3)*b*cosh(d*x + c)^5 - 10*sqrt(3)*b*cosh(d*x + c)^3 + 3*sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*sqrt(3)*b*cosh(d*x + c)^2 + 4*(7*sqrt(3)*b*cosh(d*x + c)^6 - 15*sqrt(3)*b*cosh(d*x + c)^4 + 9*sqrt(3)*b*cosh(d*x + c)^2 - sqrt(3)*b)*sinh(d*x + c)^2 + 8*(sqrt(3)*b*cosh(d*x + c)^7 - 3*sqrt(3)*b*cosh(d*x + c)^5 + 3*sqrt(3)*b*cosh(d*x + c)^3 - sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c) + sqrt(3)*b)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b + 2*sqrt(3)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) - 182*(sqrt(3)*b*cosh(d*x + c)^8 + 8*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c)^7 + sqrt(3)*b*sinh(d*x + c)^8 - 4*sqrt(3)*b*cosh(d*x + c)^6 + 4*(7*sqrt(3)*b*cosh(d*x + c)^2 - sqrt(3)*b)*sinh(d*x + c)^6 + 8*(7*sqrt(3)*b*cosh(d*x + c)^3 - 3*sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*sqrt(3)*b*cosh(d*x + c)^4 + 2*(35*sqrt(3)*b*cosh(d*x + c)^4 - 30*sqrt(3)*b*cosh(d*x + c)^2 + 3*sqrt(3)*b)*sinh(d*x + c)^4 + 8*(7*sqrt(3)*b*cosh(d*x + c)^5 - 10*sqrt(3)*b*cosh(d*x + c)^3 + 3*sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*sqrt(3)*b*cosh(d*x + c)^2 + 4*(7*sqrt(3)*b*cosh(d*x + c)^6 - 15*sqrt(3)*b*cosh(d*x + c)^4 + 9*sqrt(3)*b*cosh(d*x + c)^2 - sqrt(3)*b)*sinh(d*x + c)^2 + 8*(sqrt(3)*b*cosh(d*x + c)^7 - 3*sqrt(3)*b*cosh(d*x + c)^5 + 3*sqrt(3)*b*cosh(d*x + c)^3 - sqrt(3)*b*cosh(d*x + c))*sinh(d*x + c) + sqrt(3)*b)*b^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + 91*(b*cosh(d*x + c)^8 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 4*b*cosh(d*x + c)^6 + 4*(7*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 8*(7*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*b*cosh(d*x + c)^4 + 2*(35*b*cosh(d*x + c)^4 - 30*b*cosh(d*x + c)^2 + 3*b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - 10*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*b*cosh(d*x + c)^2 + 4*(7*b*cosh(d*x + c)^6 - 15*b*cosh(d*x + c)^4 + 9*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - 3*b*cosh(d*x + c)^5 + 3*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + 91*(b*cosh(d*x + c)^8 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 4*b*cosh(d*x + c)^6 + 4*(7*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 8*(7*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*b*cosh(d*x + c)^4 + 2*(35*b*cosh(d*x + c)^4 - 30*b*cosh(d*x + c)^2 + 3*b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - 10*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*b*cosh(d*x + c)^2 + 4*(7*b*cosh(d*x + c)^6 - 15*b*cosh(d*x + c)^4 + 9*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - 3*b*cosh(d*x + c)^5 + 3*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*b^(1/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 182*(b*cosh(d*x + c)^8 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 4*b*cosh(d*x + c)^6 + 4*(7*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 8*(7*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*b*cosh(d*x + c)^4 + 2*(35*b*cosh(d*x + c)^4 - 30*b*cosh(d*x + c)^2 + 3*b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - 10*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*b*cosh(d*x + c)^2 + 4*(7*b*cosh(d*x + c)^6 - 15*b*cosh(d*x + c)^4 + 9*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - 3*b*cosh(d*x + c)^5 + 3*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*(-b)^(1/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 182*(b*cosh(d*x + c)^8 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 4*b*cosh(d*x + c)^6 + 4*(7*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 8*(7*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 6*b*cosh(d*x + c)^4 + 2*(35*b*cosh(d*x + c)^4 - 30*b*cosh(d*x + c)^2 + 3*b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - 10*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^3 - 4*b*cosh(d*x + c)^2 + 4*(7*b*cosh(d*x + c)^6 - 15*b*cosh(d*x + c)^4 + 9*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - 3*b*cosh(d*x + c)^5 + 3*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*b^(1/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 12*(111*b*cosh(d*x + c)^8 + 888*b*cosh(d*x + c)*sinh(d*x + c)^7 + 111*b*sinh(d*x + c)^8 - 336*b*cosh(d*x + c)^6 + 84*(37*b*cosh(d*x + c)^2 - 4*b)*sinh(d*x + c)^6 + 168*(37*b*cosh(d*x + c)^3 - 12*b*cosh(d*x + c))*sinh(d*x + c)^5 + 562*b*cosh(d*x + c)^4 + 2*(3885*b*cosh(d*x + c)^4 - 2520*b*cosh(d*x + c)^2 + 281*b)*sinh(d*x + c)^4 + 8*(777*b*cosh(d*x + c)^5 - 840*b*cosh(d*x + c)^3 + 281*b*cosh(d*x + c))*sinh(d*x + c)^3 - 336*b*cosh(d*x + c)^2 + 12*(259*b*cosh(d*x + c)^6 - 420*b*cosh(d*x + c)^4 + 281*b*cosh(d*x + c)^2 - 28*b)*sinh(d*x + c)^2 + 8*(111*b*cosh(d*x + c)^7 - 252*b*cosh(d*x + c)^5 + 281*b*cosh(d*x + c)^3 - 84*b*cosh(d*x + c))*sinh(d*x + c) + 111*b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/(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
45,1,618,0,1.792720," ","integrate((b*coth(d*x+c)^4)^(2/3),x, algorithm=""fricas"")","-\frac{10 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + 10 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} {\left(b^{2}\right)}^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + 5 \, \left(-b^{2}\right)^{\frac{1}{3}} {\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)} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - \left(-b^{2}\right)^{\frac{1}{3}} b + \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 5 \, {\left(b^{2}\right)}^{\frac{1}{3}} {\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)} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\left(b^{2}\right)}^{\frac{1}{3}} b - {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 10 \, \left(-b^{2}\right)^{\frac{1}{3}} {\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)} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \left(-b^{2}\right)^{\frac{2}{3}}\right) - 10 \, {\left(b^{2}\right)}^{\frac{1}{3}} {\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)} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + {\left(b^{2}\right)}^{\frac{2}{3}}\right) + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{20 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/20*(10*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*(-b^2)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + 10*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*(b^2)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + 5*(-b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (-b^2)^(1/3)*b + (-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 5*(b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b^2)^(1/3)*b - (b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 10*(-b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - (-b^2)^(2/3)) - 10*(b^2)^(1/3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b^2)^(2/3)) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(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
46,1,288,0,3.084958," ","integrate((b*coth(d*x+c)^4)^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b + 2 \, \sqrt{3} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) - 2 \, \sqrt{3} b^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b - 2 \, \sqrt{3} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{3 \, b}\right) + \left(-b\right)^{\frac{1}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + b^{\frac{1}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, \left(-b\right)^{\frac{1}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, b^{\frac{1}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 12 \, \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(3)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b + 2*sqrt(3)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) - 2*sqrt(3)*b^(1/3)*arctan(-1/3*(sqrt(3)*b - 2*sqrt(3)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b) + (-b)^(1/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + b^(1/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(-b)^(1/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*b^(1/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 12*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/d","A",0
47,1,3316,0,0.830955," ","integrate(1/(b*coth(d*x+c)^4)^(1/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b \cosh\left(d x + c\right)^{2} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 3 \, b \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \sqrt{3} {\left(2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\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)} \left(-b\right)^{\frac{1}{3}} - {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + b\right) + \sqrt{3} {\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{1}{b^{\frac{2}{3}}}} \log\left(-\frac{2 \, \sqrt{3} {\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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 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} - \sqrt{3} {\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)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + {\left(\sqrt{3} {\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{1}{b^{\frac{2}{3}}}} + 3 \, {\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)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - 3 \, b}{\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) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}, -\frac{2 \, \sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{1}{3} \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + \frac{2}{3} \, \sqrt{3} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}\right) - \sqrt{3} {\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{1}{b^{\frac{2}{3}}}} \log\left(-\frac{2 \, \sqrt{3} {\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)} b^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 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} - \sqrt{3} {\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)} b^{\frac{1}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + {\left(\sqrt{3} {\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{1}{b^{\frac{2}{3}}}} + 3 \, {\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)} b^{\frac{2}{3}}\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - 3 \, b}{\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) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}, \frac{\sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b \cosh\left(d x + c\right)^{2} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 3 \, b \sinh\left(d x + c\right)^{2} - 3 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \sqrt{3} {\left(2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(-b\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\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)} \left(-b\right)^{\frac{1}{3}} - {\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)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + b\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - \frac{2 \, \sqrt{3} {\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)} \arctan\left(-\frac{\sqrt{3} {\left(b^{\frac{1}{3}} - 2 \, \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}, -\frac{2 \, \sqrt{3} {\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{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{1}{3} \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + \frac{2}{3} \, \sqrt{3} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}\right) - {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{2}{3}} - b^{\frac{1}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\left(-b\right)^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} b^{\frac{2}{3}} \log\left(b^{\frac{1}{3}} + \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) + \frac{2 \, \sqrt{3} {\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)} \arctan\left(-\frac{\sqrt{3} {\left(b^{\frac{1}{3}} - 2 \, \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} + 12 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}}}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2} + b d\right)}}\right]"," ",0,"[1/4*(sqrt(3)*(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)^(1/3)/b)*log(3*b*cosh(d*x + c)^2 + 6*b*cosh(d*x + c)*sinh(d*x + c) + 3*b*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - sqrt(3)*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))*sqrt((-b)^(1/3)/b) + b) + sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(-1/b^(2/3))*log(-(2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3)*sqrt(-1/b^(2/3)) - b*cosh(d*x + c)^2 - 2*b*cosh(d*x + c)*sinh(d*x + c) - b*sinh(d*x + c)^2 - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*sqrt(-1/b^(2/3)) + (sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3))*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - 3*b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d), -1/4*(2*sqrt(3)*(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)^(1/3)/b)*arctan(-1/3*sqrt(3)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) + 2/3*sqrt(3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b)^(1/3)/b)) - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(-1/b^(2/3))*log(-(2*sqrt(3)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3)*sqrt(-1/b^(2/3)) - b*cosh(d*x + c)^2 - 2*b*cosh(d*x + c)*sinh(d*x + c) - b*sinh(d*x + c)^2 - sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*b^(1/3)*sqrt(-1/b^(2/3)) + (sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-1/b^(2/3)) + 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*b^(2/3))*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - 3*b)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d), 1/4*(sqrt(3)*(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)^(1/3)/b)*log(3*b*cosh(d*x + c)^2 + 6*b*cosh(d*x + c)*sinh(d*x + c) + 3*b*sinh(d*x + c)^2 - 3*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - sqrt(3)*(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(-b)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(-b)^(1/3) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))*sqrt((-b)^(1/3)/b) + b) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*arctan(-1/3*sqrt(3)*(b^(1/3) - 2*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^(1/3))/b^(1/3) - 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d), -1/4*(2*sqrt(3)*(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)^(1/3)/b)*arctan(-1/3*sqrt(3)*(-b)^(1/3)*sqrt(-(-b)^(1/3)/b) + 2/3*sqrt(3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b)^(1/3)/b)) - (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(2/3) - (-b)^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(2/3) - b^(1/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(2/3)) + 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*(-b)^(2/3)*log((-b)^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*b^(2/3)*log(b^(1/3) + (b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) + 2*sqrt(3)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*arctan(-1/3*sqrt(3)*(b^(1/3) - 2*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^(1/3))/b^(1/3) + 12*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3))/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2 + b*d)]","B",0
48,1,1159,0,0.485406," ","integrate(1/(b*coth(d*x+c)^4)^(2/3),x, algorithm=""fricas"")","\frac{10 \, \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} - 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2}}\right) + 10 \, \sqrt{3} {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} {\left(b^{2}\right)}^{\frac{1}{6}} \arctan\left(-\frac{\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{6}} {\left({\left(b^{2}\right)}^{\frac{1}{3}} b - 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right)}}{3 \, b^{2}}\right) + 5 \, {\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)} \left(-b^{2}\right)^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} - \left(-b^{2}\right)^{\frac{1}{3}} b + \left(-b^{2}\right)^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 5 \, {\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)} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{2}{3}} + {\left(b^{2}\right)}^{\frac{1}{3}} b - {\left(b^{2}\right)}^{\frac{2}{3}} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}\right) - 10 \, {\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)} \left(-b^{2}\right)^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} - \left(-b^{2}\right)^{\frac{2}{3}}\right) + 10 \, {\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)} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(b \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}} + {\left(b^{2}\right)}^{\frac{2}{3}}\right) - 12 \, {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \left(\frac{b \cosh\left(d x + c\right)}{\sinh\left(d x + c\right)}\right)^{\frac{1}{3}}}{20 \, {\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)}}"," ",0,"1/20*(10*sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*sqrt(-(-b^2)^(1/3)) - 2*sqrt(3)*(-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)*sqrt(-(-b^2)^(1/3)))/b^2) + 10*sqrt(3)*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*(b^2)^(1/6)*arctan(-1/3*sqrt(3)*(b^2)^(1/6)*((b^2)^(1/3)*b - 2*(b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/b^2) + 5*(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)*(-b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) - (-b^2)^(1/3)*b + (-b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 5*(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)*(b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(2/3) + (b^2)^(1/3)*b - (b^2)^(2/3)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3)) - 10*(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)*(-b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) - (-b^2)^(2/3)) + 10*(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)*(b^2)^(2/3)*log(b*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3) + (b^2)^(2/3)) - 12*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*(b*cosh(d*x + c)/sinh(d*x + c))^(1/3))/(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
49,-1,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^4)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,0,0,0,0.423561," ","integrate((b*coth(d*x+c)^m)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \coth\left(d x + c\right)^{m}\right)^{n}, x\right)"," ",0,"integral((b*coth(d*x + c)^m)^n, x)","F",0
51,-2,0,0,0.000000," ","integrate((b*coth(d*x+c)^m)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
52,-2,0,0,0.000000," ","integrate((b*coth(d*x+c)^m)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
53,-2,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^m)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
54,-2,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^m)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
55,-2,0,0,0.000000," ","integrate((b*coth(d*x+c)^m)^(4/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
56,-2,0,0,0.000000," ","integrate((b*coth(d*x+c)^m)^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
57,-2,0,0,0.000000," ","integrate((b*coth(d*x+c)^m)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
58,-2,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^m)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
59,-2,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^m)^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
60,-2,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)^m)^(4/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
61,1,448,0,0.394673," ","integrate((1+coth(x))^5,x, algorithm=""fricas"")","-\frac{4 \, {\left(48 \, \cosh\left(x\right)^{6} + 288 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + 48 \, \sinh\left(x\right)^{6} + 36 \, {\left(20 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{4} - 108 \, \cosh\left(x\right)^{4} + 48 \, {\left(20 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(90 \, \cosh\left(x\right)^{4} - 81 \, \cosh\left(x\right)^{2} + 11\right)} \sinh\left(x\right)^{2} + 88 \, \cosh\left(x\right)^{2} - 12 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 16 \, {\left(18 \, \cosh\left(x\right)^{5} - 27 \, \cosh\left(x\right)^{3} + 11 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 25\right)}}{3 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-4/3*(48*cosh(x)^6 + 288*cosh(x)*sinh(x)^5 + 48*sinh(x)^6 + 36*(20*cosh(x)^2 - 3)*sinh(x)^4 - 108*cosh(x)^4 + 48*(20*cosh(x)^3 - 9*cosh(x))*sinh(x)^3 + 8*(90*cosh(x)^4 - 81*cosh(x)^2 + 11)*sinh(x)^2 + 88*cosh(x)^2 - 12*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)*log(2*sinh(x)/(cosh(x) - sinh(x))) + 16*(18*cosh(x)^5 - 27*cosh(x)^3 + 11*cosh(x))*sinh(x) - 25)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
62,1,273,0,0.404529," ","integrate((1+coth(x))^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(18 \, \cosh\left(x\right)^{4} + 72 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + 18 \, \sinh\left(x\right)^{4} + 27 \, {\left(4 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 27 \, \cosh\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)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 18 \, {\left(4 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 11\right)}}{3 \, {\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)}}"," ",0,"-4/3*(18*cosh(x)^4 + 72*cosh(x)*sinh(x)^3 + 18*sinh(x)^4 + 27*(4*cosh(x)^2 - 1)*sinh(x)^2 - 27*cosh(x)^2 - 6*(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)*log(2*sinh(x)/(cosh(x) - sinh(x))) + 18*(4*cosh(x)^3 - 3*cosh(x))*sinh(x) + 11)/(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
63,1,142,0,0.391405," ","integrate((1+coth(x))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, \cosh\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)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 8 \, \cosh\left(x\right) \sinh\left(x\right) + 4 \, \sinh\left(x\right)^{2} - 3\right)}}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}"," ",0,"-2*(4*cosh(x)^2 - 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*sinh(x)/(cosh(x) - sinh(x))) + 8*cosh(x)*sinh(x) + 4*sinh(x)^2 - 3)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
64,1,53,0,0.413181," ","integrate((1+coth(x))^2,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1}"," ",0,"2*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*log(2*sinh(x)/(cosh(x) - sinh(x))) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
65,1,26,0,0.427303," ","integrate(1/(1+coth(x)),x, algorithm=""fricas"")","\frac{{\left(2 \, x + 1\right)} \cosh\left(x\right) + {\left(2 \, x - 1\right)} \sinh\left(x\right)}{4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/4*((2*x + 1)*cosh(x) + (2*x - 1)*sinh(x))/(cosh(x) + sinh(x))","B",0
66,1,52,0,0.382174," ","integrate(1/(1+coth(x))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, x - 1\right)} \cosh\left(x\right)^{2} + 2 \, {\left(4 \, x + 1\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(4 \, x - 1\right)} \sinh\left(x\right)^{2} + 4}{16 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"1/16*((4*x - 1)*cosh(x)^2 + 2*(4*x + 1)*cosh(x)*sinh(x) + (4*x - 1)*sinh(x)^2 + 4)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
67,1,86,0,0.384506," ","integrate(1/(1+coth(x))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, x + 1\right)} \cosh\left(x\right)^{3} + 6 \, {\left(6 \, x + 1\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + 2 \, {\left(6 \, x - 1\right)} \sinh\left(x\right)^{3} + 3 \, {\left(2 \, {\left(6 \, x - 1\right)} \cosh\left(x\right)^{2} + 9\right)} \sinh\left(x\right) + 9 \, \cosh\left(x\right)}{96 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3}\right)}}"," ",0,"1/96*(2*(6*x + 1)*cosh(x)^3 + 6*(6*x + 1)*cosh(x)*sinh(x)^2 + 2*(6*x - 1)*sinh(x)^3 + 3*(2*(6*x - 1)*cosh(x)^2 + 9)*sinh(x) + 9*cosh(x))/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)","B",0
68,1,121,0,0.386166," ","integrate(1/(1+coth(x))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, x - 1\right)} \cosh\left(x\right)^{4} + 12 \, {\left(8 \, x + 1\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 3 \, {\left(8 \, x - 1\right)} \sinh\left(x\right)^{4} + 2 \, {\left(9 \, {\left(8 \, x - 1\right)} \cosh\left(x\right)^{2} + 32\right)} \sinh\left(x\right)^{2} + 64 \, \cosh\left(x\right)^{2} + 4 \, {\left(3 \, {\left(8 \, x + 1\right)} \cosh\left(x\right)^{3} + 16 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 36}{384 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}\right)}}"," ",0,"1/384*(3*(8*x - 1)*cosh(x)^4 + 12*(8*x + 1)*cosh(x)*sinh(x)^3 + 3*(8*x - 1)*sinh(x)^4 + 2*(9*(8*x - 1)*cosh(x)^2 + 32)*sinh(x)^2 + 64*cosh(x)^2 + 4*(3*(8*x + 1)*cosh(x)^3 + 16*cosh(x))*sinh(x) - 36)/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)","B",0
69,1,159,0,0.388542," ","integrate(1/(1+coth(x))^5,x, algorithm=""fricas"")","\frac{12 \, {\left(10 \, x + 1\right)} \cosh\left(x\right)^{5} + 60 \, {\left(10 \, x + 1\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + 12 \, {\left(10 \, x - 1\right)} \sinh\left(x\right)^{5} + 15 \, {\left(8 \, {\left(10 \, x - 1\right)} \cosh\left(x\right)^{2} + 25\right)} \sinh\left(x\right)^{3} + 225 \, \cosh\left(x\right)^{3} + 15 \, {\left(8 \, {\left(10 \, x + 1\right)} \cosh\left(x\right)^{3} + 45 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 5 \, {\left(12 \, {\left(10 \, x - 1\right)} \cosh\left(x\right)^{4} + 225 \, \cosh\left(x\right)^{2} - 100\right)} \sinh\left(x\right) - 100 \, \cosh\left(x\right)}{3840 \, {\left(\cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5}\right)}}"," ",0,"1/3840*(12*(10*x + 1)*cosh(x)^5 + 60*(10*x + 1)*cosh(x)*sinh(x)^4 + 12*(10*x - 1)*sinh(x)^5 + 15*(8*(10*x - 1)*cosh(x)^2 + 25)*sinh(x)^3 + 225*cosh(x)^3 + 15*(8*(10*x + 1)*cosh(x)^3 + 45*cosh(x))*sinh(x)^2 + 5*(12*(10*x - 1)*cosh(x)^4 + 225*cosh(x)^2 - 100)*sinh(x) - 100*cosh(x))/(cosh(x)^5 + 5*cosh(x)^4*sinh(x) + 10*cosh(x)^3*sinh(x)^2 + 10*cosh(x)^2*sinh(x)^3 + 5*cosh(x)*sinh(x)^4 + sinh(x)^5)","B",0
70,1,438,0,0.400978," ","integrate((1+coth(x))^(7/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(2 \, \sqrt{2} {\left(23 \, \sqrt{2} \cosh\left(x\right)^{5} + 115 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{4} + 23 \, \sqrt{2} \sinh\left(x\right)^{5} + 5 \, {\left(46 \, \sqrt{2} \cosh\left(x\right)^{2} - 7 \, \sqrt{2}\right)} \sinh\left(x\right)^{3} - 35 \, \sqrt{2} \cosh\left(x\right)^{3} + 5 \, {\left(46 \, \sqrt{2} \cosh\left(x\right)^{3} - 21 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 5 \, {\left(23 \, \sqrt{2} \cosh\left(x\right)^{4} - 21 \, \sqrt{2} \cosh\left(x\right)^{2} + 3 \, \sqrt{2}\right)} \sinh\left(x\right) + 15 \, \sqrt{2} \cosh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 15 \, {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{4} - 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{4} - 6 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{2} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} + 6 \, {\left(\sqrt{2} \cosh\left(x\right)^{5} - 2 \, \sqrt{2} \cosh\left(x\right)^{3} + \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) - \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)\right)}}{15 \, {\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)}}"," ",0,"-4/15*(2*sqrt(2)*(23*sqrt(2)*cosh(x)^5 + 115*sqrt(2)*cosh(x)*sinh(x)^4 + 23*sqrt(2)*sinh(x)^5 + 5*(46*sqrt(2)*cosh(x)^2 - 7*sqrt(2))*sinh(x)^3 - 35*sqrt(2)*cosh(x)^3 + 5*(46*sqrt(2)*cosh(x)^3 - 21*sqrt(2)*cosh(x))*sinh(x)^2 + 5*(23*sqrt(2)*cosh(x)^4 - 21*sqrt(2)*cosh(x)^2 + 3*sqrt(2))*sinh(x) + 15*sqrt(2)*cosh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 15*(sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^4 - 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x)^3 + 3*(5*sqrt(2)*cosh(x)^4 - 6*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^2 + 3*sqrt(2)*cosh(x)^2 + 6*(sqrt(2)*cosh(x)^5 - 2*sqrt(2)*cosh(x)^3 + sqrt(2)*cosh(x))*sinh(x) - sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(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
71,1,259,0,0.407430," ","integrate((1+coth(x))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \sqrt{2} {\left(4 \, \sqrt{2} \cosh\left(x\right)^{3} + 12 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \sinh\left(x\right)^{3} + 3 \, {\left(4 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right) - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)\right)}}{3 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-2/3*(2*sqrt(2)*(4*sqrt(2)*cosh(x)^3 + 12*sqrt(2)*cosh(x)*sinh(x)^2 + 4*sqrt(2)*sinh(x)^3 + 3*(4*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x) - 3*sqrt(2)*cosh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
72,1,131,0,0.401938," ","integrate((1+coth(x))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1}"," ",0,"-(2*sqrt(2)*(sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
73,1,50,0,0.389888," ","integrate((1+coth(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)"," ",0,"1/2*sqrt(2)*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1)","B",0
74,1,85,0,0.405783," ","integrate(1/(1+coth(x))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right) - 4 \, \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}}}{4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/4*((sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1) - 4*sqrt(sinh(x)/(cosh(x) - sinh(x))))/(cosh(x) + sinh(x))","B",0
75,1,168,0,0.397430," ","integrate(1/(1+coth(x))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(4 \, \sqrt{2} \cosh\left(x\right)^{2} + 8 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + 4 \, \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + \sqrt{2} \sinh\left(x\right)^{3}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{24 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3}\right)}}"," ",0,"-1/24*(2*sqrt(2)*(4*sqrt(2)*cosh(x)^2 + 8*sqrt(2)*cosh(x)*sinh(x) + 4*sqrt(2)*sinh(x)^2 - sqrt(2))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*(sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x)^2*sinh(x) + 3*sqrt(2)*cosh(x)*sinh(x)^2 + sqrt(2)*sinh(x)^3)*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)","B",0
76,1,266,0,0.404277," ","integrate(1/(1+coth(x))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(23 \, \sqrt{2} \cosh\left(x\right)^{4} + 92 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + 23 \, \sqrt{2} \sinh\left(x\right)^{4} + {\left(138 \, \sqrt{2} \cosh\left(x\right)^{2} - 11 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} - 11 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(46 \, \sqrt{2} \cosh\left(x\right)^{3} - 11 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, \sqrt{2}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 15 \, {\left(\sqrt{2} \cosh\left(x\right)^{5} + 5 \, \sqrt{2} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, \sqrt{2} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, \sqrt{2} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{4} + \sqrt{2} \sinh\left(x\right)^{5}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{240 \, {\left(\cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5}\right)}}"," ",0,"-1/240*(2*sqrt(2)*(23*sqrt(2)*cosh(x)^4 + 92*sqrt(2)*cosh(x)*sinh(x)^3 + 23*sqrt(2)*sinh(x)^4 + (138*sqrt(2)*cosh(x)^2 - 11*sqrt(2))*sinh(x)^2 - 11*sqrt(2)*cosh(x)^2 + 2*(46*sqrt(2)*cosh(x)^3 - 11*sqrt(2)*cosh(x))*sinh(x) + 3*sqrt(2))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 15*(sqrt(2)*cosh(x)^5 + 5*sqrt(2)*cosh(x)^4*sinh(x) + 10*sqrt(2)*cosh(x)^3*sinh(x)^2 + 10*sqrt(2)*cosh(x)^2*sinh(x)^3 + 5*sqrt(2)*cosh(x)*sinh(x)^4 + sqrt(2)*sinh(x)^5)*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^5 + 5*cosh(x)^4*sinh(x) + 10*cosh(x)^3*sinh(x)^2 + 10*cosh(x)^2*sinh(x)^3 + 5*cosh(x)*sinh(x)^4 + sinh(x)^5)","B",0
77,1,2748,0,0.456316," ","integrate((a+b*coth(d*x+c))^5,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{8} + 24 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \sinh\left(d x + c\right)^{8} - 12 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 12 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} - 7 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(7 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 60 \, a^{3} b^{2} + 40 \, a b^{4} + 6 \, {\left(30 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 2 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(35 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 2 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x - 30 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 24 \, {\left(7 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{5} - 10 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 2 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x - 4 \, {\left(45 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 25 \, a b^{4} + 3 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(21 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{6} - 45 \, a^{3} b^{2} - 15 \, a^{2} b^{3} - 25 \, a b^{4} - 3 \, b^{5} - 45 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x + 9 \, {\left(30 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 2 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5} - 7 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5} + 6 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, a^{4} b + 30 \, a^{2} b^{3} + 3 \, b^{5} + 35 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{4} b - 10 \, a^{2} b^{3} - b^{5} - 15 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x \cosh\left(d x + c\right)^{7} - 9 \, {\left(5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(30 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 20 \, a b^{4} + 2 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(45 \, a^{3} b^{2} + 15 \, a^{2} b^{3} + 25 \, a b^{4} + 3 \, b^{5} + 3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\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,"1/3*(3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^8 + 24*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*sinh(d*x + c)^8 - 12*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^6 - 12*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 - 7*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^2 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*sinh(d*x + c)^6 + 24*(7*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^3 - 3*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 60*a^3*b^2 + 40*a*b^4 + 6*(30*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 2*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^4 + 6*(35*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^4 + 30*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 2*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x - 30*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 24*(7*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^5 - 10*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^3 + (30*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 2*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x - 4*(45*a^3*b^2 + 15*a^2*b^3 + 25*a*b^4 + 3*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^2 + 4*(21*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^6 - 45*a^3*b^2 - 15*a^2*b^3 - 25*a*b^4 - 3*b^5 - 45*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^4 - 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x + 9*(30*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 2*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^8 + 8*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a^4*b + 10*a^2*b^3 + b^5)*sinh(d*x + c)^8 - 4*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^6 - 4*(5*a^4*b + 10*a^2*b^3 + b^5 - 7*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^3 - 3*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 5*a^4*b + 10*a^2*b^3 + b^5 + 6*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^4 + 2*(15*a^4*b + 30*a^2*b^3 + 3*b^5 + 35*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^4 - 30*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^5 - 10*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^3 + 3*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^2 + 4*(7*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^6 - 5*a^4*b - 10*a^2*b^3 - b^5 - 15*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^4 + 9*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^7 - 3*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^5 + 3*(5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c)^3 - (5*a^4*b + 10*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x*cosh(d*x + c)^7 - 9*(5*a^3*b^2 + 5*a^2*b^3 + 5*a*b^4 + b^5 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^5 + 3*(30*a^3*b^2 + 20*a^2*b^3 + 20*a*b^4 + 2*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c)^3 - (45*a^3*b^2 + 15*a^2*b^3 + 25*a*b^4 + 3*b^5 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(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
78,1,1396,0,0.422088," ","integrate((a+b*coth(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{6} + 18 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \sinh\left(d x + c\right)^{6} - 3 \, {\left(12 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 12 \, a^{2} b^{2} - 8 \, a b^{3} - 4 \, b^{4} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{4} - 36 \, a^{2} b^{2} - 8 \, b^{4} + 12 \, {\left(5 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(12 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x + 3 \, {\left(24 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{4} + 24 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x - 6 \, {\left(12 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} b + a b^{3}\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{3} b + a b^{3} - 5 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{3} b - a b^{3} + 4 \, {\left(5 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} b + a b^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + a 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) + 6 \, {\left(3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(12 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 8 \, a b^{3} + 4 \, b^{4} + 3 \, {\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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*(3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)^6 + 18*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*sinh(d*x + c)^6 - 3*(12*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^4 + 3*(15*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)^2 - 12*a^2*b^2 - 8*a*b^3 - 4*b^4 - 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*sinh(d*x + c)^4 - 36*a^2*b^2 - 8*b^4 + 12*(5*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)^3 - (12*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x + 3*(24*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2 + 3*(15*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)^4 + 24*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x - 6*(12*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((a^3*b + a*b^3)*cosh(d*x + c)^6 + 6*(a^3*b + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3*b + a*b^3)*sinh(d*x + c)^6 - 3*(a^3*b + a*b^3)*cosh(d*x + c)^4 - 3*(a^3*b + a*b^3 - 5*(a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^3*b - a*b^3 + 4*(5*(a^3*b + a*b^3)*cosh(d*x + c)^3 - 3*(a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^3*b + a*b^3)*cosh(d*x + c)^2 + 3*(5*(a^3*b + a*b^3)*cosh(d*x + c)^4 + a^3*b + a*b^3 - 6*(a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 6*((a^3*b + a*b^3)*cosh(d*x + c)^5 - 2*(a^3*b + a*b^3)*cosh(d*x + c)^3 + (a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 6*(3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x*cosh(d*x + c)^5 - 2*(12*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^3 + (24*a^2*b^2 + 8*a*b^3 + 4*b^4 + 3*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(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
79,1,654,0,0.425719," ","integrate((a+b*coth(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x \sinh\left(d x + c\right)^{4} + 6 \, a b^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x - 2 \, {\left(3 \, a b^{2} + b^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 3 \, a b^{2} - b^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b + b^{3} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(3 \, a^{2} b + b^{3} - 3 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} b + 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({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, a b^{2} + b^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x*cosh(d*x + c)^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x*sinh(d*x + c)^4 + 6*a*b^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x - 2*(3*a*b^2 + b^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x)*cosh(d*x + c)^2 + 2*(3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x*cosh(d*x + c)^2 - 3*a*b^2 - b^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x)*sinh(d*x + c)^2 + ((3*a^2*b + b^3)*cosh(d*x + c)^4 + 4*(3*a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2*b + b^3)*sinh(d*x + c)^4 + 3*a^2*b + b^3 - 2*(3*a^2*b + b^3)*cosh(d*x + c)^2 - 2*(3*a^2*b + b^3 - 3*(3*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((3*a^2*b + b^3)*cosh(d*x + c)^3 - (3*a^2*b + 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*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x*cosh(d*x + c)^3 - (3*a*b^2 + b^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^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
80,1,205,0,0.406748," ","integrate((a+b*coth(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} d x - 2 \, b^{2} + 2 \, {\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\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 \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,"((a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + 2*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c) + (a^2 - 2*a*b + b^2)*d*x*sinh(d*x + c)^2 - (a^2 - 2*a*b + b^2)*d*x - 2*b^2 + 2*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 - a*b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - 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
81,1,62,0,0.449049," ","integrate(1/(a+b*coth(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} d x - b \log\left(\frac{2 \, {\left(b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{2} - b^{2}\right)} d}"," ",0,"((a + b)*d*x - b*log(2*(b*cosh(d*x + c) + a*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))))/((a^2 - b^2)*d)","A",0
82,1,426,0,0.424652," ","integrate(1/(a+b*coth(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \sinh\left(d x + c\right)^{2} - 2 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d x + 2 \, {\left(a^{2} b - a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} d}"," ",0,"((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^2 - 2*a*b^2 + 2*b^3 - (a^3 + a^2*b - a*b^2 - b^3)*d*x + 2*(a^2*b - a*b^2 - (a^2*b + a*b^2)*cosh(d*x + c)^2 - 2*(a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) - (a^2*b + a*b^2)*sinh(d*x + c)^2)*log(2*(b*cosh(d*x + c) + a*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))))/((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*d*cosh(d*x + c)^2 + 2*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c) + (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*d*sinh(d*x + c)^2 - (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*d)","B",0
83,1,1431,0,0.436200," ","integrate(1/(a+b*coth(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x \sinh\left(d x + c\right)^{4} + 6 \, a^{3} b^{2} - 12 \, a^{2} b^{3} + 6 \, a b^{4} + {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} d x - 2 \, {\left(3 \, a^{3} b^{2} - a^{2} b^{3} - 3 \, a b^{4} + b^{5} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(3 \, a^{3} b^{2} - a^{2} b^{3} - 3 \, a b^{4} + b^{5} - 3 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d x\right)} \sinh\left(d x + c\right)^{2} - {\left(3 \, a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5} + {\left(3 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5} - 3 \, {\left(3 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} b^{2} - a^{2} b^{3} - 3 \, a b^{4} + b^{5} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{8} + 2 \, a^{7} b - 2 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 2 \, a b^{7} - b^{8}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 2 \, a^{7} b - 2 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 2 \, a b^{7} - b^{8}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{8} + 2 \, a^{7} b - 2 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 2 \, a b^{7} - b^{8}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{8} + 2 \, a^{7} b - 2 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 2 \, a b^{7} - b^{8}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{8} - 2 \, a^{7} b - 2 \, a^{6} b^{2} + 6 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 2 \, a b^{7} - b^{8}\right)} d + 4 \, {\left({\left(a^{8} + 2 \, a^{7} b - 2 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 2 \, a b^{7} - b^{8}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x*cosh(d*x + c)^4 + 4*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x*sinh(d*x + c)^4 + 6*a^3*b^2 - 12*a^2*b^3 + 6*a*b^4 + (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*d*x - 2*(3*a^3*b^2 - a^2*b^3 - 3*a*b^4 + b^5 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*x)*cosh(d*x + c)^2 - 2*(3*a^3*b^2 - a^2*b^3 - 3*a*b^4 + b^5 - 3*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*x)*sinh(d*x + c)^2 - (3*a^4*b - 6*a^3*b^2 + 4*a^2*b^3 - 2*a*b^4 + b^5 + (3*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 + b^5)*cosh(d*x + c)^4 + 4*(3*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 + b^5)*sinh(d*x + c)^4 - 2*(3*a^4*b - 2*a^2*b^3 - b^5)*cosh(d*x + c)^2 - 2*(3*a^4*b - 2*a^2*b^3 - b^5 - 3*(3*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((3*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 + b^5)*cosh(d*x + c)^3 - (3*a^4*b - 2*a^2*b^3 - b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*cosh(d*x + c) + a*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))) + 4*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x*cosh(d*x + c)^3 - (3*a^3*b^2 - a^2*b^3 - 3*a*b^4 + b^5 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 2*a^7*b - 2*a^6*b^2 - 6*a^5*b^3 + 6*a^3*b^5 + 2*a^2*b^6 - 2*a*b^7 - b^8)*d*cosh(d*x + c)^4 + 4*(a^8 + 2*a^7*b - 2*a^6*b^2 - 6*a^5*b^3 + 6*a^3*b^5 + 2*a^2*b^6 - 2*a*b^7 - b^8)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^8 + 2*a^7*b - 2*a^6*b^2 - 6*a^5*b^3 + 6*a^3*b^5 + 2*a^2*b^6 - 2*a*b^7 - b^8)*d*sinh(d*x + c)^4 - 2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cosh(d*x + c)^2 + 2*(3*(a^8 + 2*a^7*b - 2*a^6*b^2 - 6*a^5*b^3 + 6*a^3*b^5 + 2*a^2*b^6 - 2*a*b^7 - b^8)*d*cosh(d*x + c)^2 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d)*sinh(d*x + c)^2 + (a^8 - 2*a^7*b - 2*a^6*b^2 + 6*a^5*b^3 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8)*d + 4*((a^8 + 2*a^7*b - 2*a^6*b^2 - 6*a^5*b^3 + 6*a^3*b^5 + 2*a^2*b^6 - 2*a*b^7 - b^8)*d*cosh(d*x + c)^3 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
84,1,3698,0,0.503009," ","integrate(1/(a+b*coth(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right)^{6} + 18 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \sinh\left(d x + c\right)^{6} - 36 \, a^{5} b^{2} + 108 \, a^{4} b^{3} - 116 \, a^{3} b^{4} + 60 \, a^{2} b^{5} - 24 \, a b^{6} + 8 \, b^{7} - 3 \, {\left(12 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 4 \, a b^{6} - 4 \, b^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(12 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 4 \, a b^{6} - 4 \, b^{7} - 15 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7}\right)} d x\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(5 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(12 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 4 \, a b^{6} - 4 \, b^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} + a^{6} b - 3 \, a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + 3 \, a^{2} b^{5} - a b^{6} - b^{7}\right)} d x + 3 \, {\left(24 \, a^{5} b^{2} - 32 \, a^{4} b^{3} - 12 \, a^{3} b^{4} + 28 \, a^{2} b^{5} - 12 \, a b^{6} + 4 \, b^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + a^{5} b^{2} - 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5} + 3 \, a b^{6} + b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(24 \, a^{5} b^{2} - 32 \, a^{4} b^{3} - 12 \, a^{3} b^{4} + 28 \, a^{2} b^{5} - 12 \, a b^{6} + 4 \, b^{7} + 15 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{7} + 3 \, a^{6} b + a^{5} b^{2} - 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5} + 3 \, a b^{6} + b^{7}\right)} d x - 6 \, {\left(12 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 4 \, a b^{6} - 4 \, b^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} - a b^{6} - {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{6} - 6 \, {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} - {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(a^{6} b + a^{5} b^{2} - a^{2} b^{5} - a b^{6}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{6} b + a^{5} b^{2} - a^{2} b^{5} - a b^{6} - 5 \, {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(5 \, {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} b + a^{5} b^{2} - a^{2} b^{5} - a b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} b - a^{5} b^{2} - a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{6} b - a^{5} b^{2} - a^{2} b^{5} + a b^{6} + 5 \, {\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{6} b + a^{5} b^{2} - a^{2} b^{5} - a b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left({\left(a^{6} b + 3 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{6} b + a^{5} b^{2} - a^{2} b^{5} - a b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} b - a^{5} b^{2} - a^{2} b^{5} + a b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 6 \, {\left(3 \, {\left(a^{7} + 7 \, a^{6} b + 21 \, a^{5} b^{2} + 35 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 21 \, a^{2} b^{5} + 7 \, a b^{6} + b^{7}\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(12 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - 16 \, a^{3} b^{4} + 4 \, a b^{6} - 4 \, b^{7} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{5} b^{2} - 32 \, a^{4} b^{3} - 12 \, a^{3} b^{4} + 28 \, a^{2} b^{5} - 12 \, a b^{6} + 4 \, b^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + a^{5} b^{2} - 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5} + 3 \, a b^{6} + b^{7}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{11} + a^{10} b - 5 \, a^{9} b^{2} - 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} + 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} - 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} + 5 \, a^{2} b^{9} - a b^{10} - b^{11}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{11} + a^{10} b - 5 \, a^{9} b^{2} - 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} + 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} - 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} + 5 \, a^{2} b^{9} - a b^{10} - b^{11}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{11} - a^{10} b - 5 \, a^{9} b^{2} + 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} - 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} + 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} - 5 \, a^{2} b^{9} - a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{11} + a^{10} b - 5 \, a^{9} b^{2} - 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} + 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} - 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} + 5 \, a^{2} b^{9} - a b^{10} - b^{11}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{11} + a^{10} b - 5 \, a^{9} b^{2} - 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} + 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} - 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} + 5 \, a^{2} b^{9} - a b^{10} - b^{11}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{11} - a^{10} b - 5 \, a^{9} b^{2} + 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} - 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} + 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} - 5 \, a^{2} b^{9} - a b^{10} + b^{11}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{11} - 3 \, a^{10} b - a^{9} b^{2} + 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} - 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} + 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} + a^{2} b^{9} + 3 \, a b^{10} - b^{11}\right)} d + 6 \, {\left({\left(a^{11} + 3 \, a^{10} b - a^{9} b^{2} - 11 \, a^{8} b^{3} - 6 \, a^{7} b^{4} + 14 \, a^{6} b^{5} + 14 \, a^{5} b^{6} - 6 \, a^{4} b^{7} - 11 \, a^{3} b^{8} - a^{2} b^{9} + 3 \, a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{11} + a^{10} b - 5 \, a^{9} b^{2} - 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} + 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} - 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} + 5 \, a^{2} b^{9} - a b^{10} - b^{11}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{11} - a^{10} b - 5 \, a^{9} b^{2} + 5 \, a^{8} b^{3} + 10 \, a^{7} b^{4} - 10 \, a^{6} b^{5} - 10 \, a^{5} b^{6} + 10 \, a^{4} b^{7} + 5 \, a^{3} b^{8} - 5 \, a^{2} b^{9} - a b^{10} + b^{11}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/3*(3*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)^6 + 18*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 3*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*sinh(d*x + c)^6 - 36*a^5*b^2 + 108*a^4*b^3 - 116*a^3*b^4 + 60*a^2*b^5 - 24*a*b^6 + 8*b^7 - 3*(12*a^5*b^2 + 4*a^4*b^3 - 16*a^3*b^4 + 4*a*b^6 - 4*b^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7)*d*x)*cosh(d*x + c)^4 - 3*(12*a^5*b^2 + 4*a^4*b^3 - 16*a^3*b^4 + 4*a*b^6 - 4*b^7 - 15*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)^2 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7)*d*x)*sinh(d*x + c)^4 + 12*(5*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)^3 - (12*a^5*b^2 + 4*a^4*b^3 - 16*a^3*b^4 + 4*a*b^6 - 4*b^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^7 + a^6*b - 3*a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 + 3*a^2*b^5 - a*b^6 - b^7)*d*x + 3*(24*a^5*b^2 - 32*a^4*b^3 - 12*a^3*b^4 + 28*a^2*b^5 - 12*a*b^6 + 4*b^7 + 3*(a^7 + 3*a^6*b + a^5*b^2 - 5*a^4*b^3 - 5*a^3*b^4 + a^2*b^5 + 3*a*b^6 + b^7)*d*x)*cosh(d*x + c)^2 + 3*(24*a^5*b^2 - 32*a^4*b^3 - 12*a^3*b^4 + 28*a^2*b^5 - 12*a*b^6 + 4*b^7 + 15*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)^4 + 3*(a^7 + 3*a^6*b + a^5*b^2 - 5*a^4*b^3 - 5*a^3*b^4 + a^2*b^5 + 3*a*b^6 + b^7)*d*x - 6*(12*a^5*b^2 + 4*a^4*b^3 - 16*a^3*b^4 + 4*a*b^6 - 4*b^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*(a^6*b - 3*a^5*b^2 + 4*a^4*b^3 - 4*a^3*b^4 + 3*a^2*b^5 - a*b^6 - (a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)^6 - 6*(a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)*sinh(d*x + c)^5 - (a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*sinh(d*x + c)^6 + 3*(a^6*b + a^5*b^2 - a^2*b^5 - a*b^6)*cosh(d*x + c)^4 + 3*(a^6*b + a^5*b^2 - a^2*b^5 - a*b^6 - 5*(a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 4*(5*(a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)^3 - 3*(a^6*b + a^5*b^2 - a^2*b^5 - a*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^6*b - a^5*b^2 - a^2*b^5 + a*b^6)*cosh(d*x + c)^2 - 3*(a^6*b - a^5*b^2 - a^2*b^5 + a*b^6 + 5*(a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)^4 - 6*(a^6*b + a^5*b^2 - a^2*b^5 - a*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 6*((a^6*b + 3*a^5*b^2 + 4*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5 + a*b^6)*cosh(d*x + c)^5 - 2*(a^6*b + a^5*b^2 - a^2*b^5 - a*b^6)*cosh(d*x + c)^3 + (a^6*b - a^5*b^2 - a^2*b^5 + a*b^6)*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*cosh(d*x + c) + a*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))) + 6*(3*(a^7 + 7*a^6*b + 21*a^5*b^2 + 35*a^4*b^3 + 35*a^3*b^4 + 21*a^2*b^5 + 7*a*b^6 + b^7)*d*x*cosh(d*x + c)^5 - 2*(12*a^5*b^2 + 4*a^4*b^3 - 16*a^3*b^4 + 4*a*b^6 - 4*b^7 + 3*(a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7)*d*x)*cosh(d*x + c)^3 + (24*a^5*b^2 - 32*a^4*b^3 - 12*a^3*b^4 + 28*a^2*b^5 - 12*a*b^6 + 4*b^7 + 3*(a^7 + 3*a^6*b + a^5*b^2 - 5*a^4*b^3 - 5*a^3*b^4 + a^2*b^5 + 3*a*b^6 + b^7)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)^6 + 6*(a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*sinh(d*x + c)^6 - 3*(a^11 + a^10*b - 5*a^9*b^2 - 5*a^8*b^3 + 10*a^7*b^4 + 10*a^6*b^5 - 10*a^5*b^6 - 10*a^4*b^7 + 5*a^3*b^8 + 5*a^2*b^9 - a*b^10 - b^11)*d*cosh(d*x + c)^4 + 3*(5*(a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)^2 - (a^11 + a^10*b - 5*a^9*b^2 - 5*a^8*b^3 + 10*a^7*b^4 + 10*a^6*b^5 - 10*a^5*b^6 - 10*a^4*b^7 + 5*a^3*b^8 + 5*a^2*b^9 - a*b^10 - b^11)*d)*sinh(d*x + c)^4 + 3*(a^11 - a^10*b - 5*a^9*b^2 + 5*a^8*b^3 + 10*a^7*b^4 - 10*a^6*b^5 - 10*a^5*b^6 + 10*a^4*b^7 + 5*a^3*b^8 - 5*a^2*b^9 - a*b^10 + b^11)*d*cosh(d*x + c)^2 + 4*(5*(a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)^3 - 3*(a^11 + a^10*b - 5*a^9*b^2 - 5*a^8*b^3 + 10*a^7*b^4 + 10*a^6*b^5 - 10*a^5*b^6 - 10*a^4*b^7 + 5*a^3*b^8 + 5*a^2*b^9 - a*b^10 - b^11)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)^4 - 6*(a^11 + a^10*b - 5*a^9*b^2 - 5*a^8*b^3 + 10*a^7*b^4 + 10*a^6*b^5 - 10*a^5*b^6 - 10*a^4*b^7 + 5*a^3*b^8 + 5*a^2*b^9 - a*b^10 - b^11)*d*cosh(d*x + c)^2 + (a^11 - a^10*b - 5*a^9*b^2 + 5*a^8*b^3 + 10*a^7*b^4 - 10*a^6*b^5 - 10*a^5*b^6 + 10*a^4*b^7 + 5*a^3*b^8 - 5*a^2*b^9 - a*b^10 + b^11)*d)*sinh(d*x + c)^2 - (a^11 - 3*a^10*b - a^9*b^2 + 11*a^8*b^3 - 6*a^7*b^4 - 14*a^6*b^5 + 14*a^5*b^6 + 6*a^4*b^7 - 11*a^3*b^8 + a^2*b^9 + 3*a*b^10 - b^11)*d + 6*((a^11 + 3*a^10*b - a^9*b^2 - 11*a^8*b^3 - 6*a^7*b^4 + 14*a^6*b^5 + 14*a^5*b^6 - 6*a^4*b^7 - 11*a^3*b^8 - a^2*b^9 + 3*a*b^10 + b^11)*d*cosh(d*x + c)^5 - 2*(a^11 + a^10*b - 5*a^9*b^2 - 5*a^8*b^3 + 10*a^7*b^4 + 10*a^6*b^5 - 10*a^5*b^6 - 10*a^4*b^7 + 5*a^3*b^8 + 5*a^2*b^9 - a*b^10 - b^11)*d*cosh(d*x + c)^3 + (a^11 - a^10*b - 5*a^9*b^2 + 5*a^8*b^3 + 10*a^7*b^4 - 10*a^6*b^5 - 10*a^5*b^6 + 10*a^4*b^7 + 5*a^3*b^8 - 5*a^2*b^9 - a*b^10 + b^11)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
85,1,49,0,0.405985," ","integrate(1/(4+6*coth(d*x+c)),x, algorithm=""fricas"")","-\frac{5 \, d x - 3 \, \log\left(\frac{2 \, {\left(3 \, \cosh\left(d x + c\right) + 2 \, \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{10 \, d}"," ",0,"-1/10*(5*d*x - 3*log(2*(3*cosh(d*x + c) + 2*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))))/d","A",0
86,1,48,0,0.402684," ","integrate(1/(4-6*coth(d*x+c)),x, algorithm=""fricas"")","\frac{d x - 3 \, \log\left(\frac{2 \, {\left(3 \, \cosh\left(d x + c\right) - 2 \, \sinh\left(d x + c\right)\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{10 \, d}"," ",0,"1/10*(d*x - 3*log(2*(3*cosh(d*x + c) - 2*sinh(d*x + c))/(cosh(d*x + c) - sinh(d*x + c))))/d","A",0
87,1,2231,0,0.509325," ","integrate((a+b*coth(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(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) + a\right)} \sqrt{a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right) + \sqrt{a - b} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} - 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} - {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a \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) + a - b\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 4 \, {\left({\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, d}, -\frac{2 \, \sqrt{-a - b} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a\right)} \sqrt{-a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + b^{2}}\right) - \sqrt{a - b} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} - 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} - {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a \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) + a - b\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 4 \, {\left({\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, d}, -\frac{2 \, \sqrt{-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 + b\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, a b - b^{2}}\right) - \sqrt{a + b} \log\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(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) + a\right)} \sqrt{a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}{4 \, d}, -\frac{\sqrt{-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 + b\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, a b - b^{2}}\right) + \sqrt{-a - b} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a\right)} \sqrt{-a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + b^{2}}\right)}{2 \, d}\right]"," ",0,"[1/4*(sqrt(a + b)*log(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 4*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 + 2*a^2 - b^2 + 2*((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - (2*a + b)*cosh(d*x + c)^2 + (6*(a + b)*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 2*(2*(a + b)*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)) + sqrt(a - b)*log(((2*a^2 - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 - b^2)*sinh(d*x + c)^4 - 4*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(2*a^2 - b^2)*cosh(d*x + c)^2 - 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 2*a^2 - 4*a*b + 2*b^2 - 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 - b)*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 2*a + b)*sinh(d*x + c)^2 + 2*(2*a*cosh(d*x + c)^3 - (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + a - b)*sqrt(a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 4*((2*a^2 - b^2)*cosh(d*x + c)^3 - 2*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/d, -1/4*(2*sqrt(-a - b)*arctan(((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)*sqrt(-a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 - a^2 + b^2)) - sqrt(a - b)*log(((2*a^2 - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 - b^2)*sinh(d*x + c)^4 - 4*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(2*a^2 - b^2)*cosh(d*x + c)^2 - 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 2*a^2 - 4*a*b + 2*b^2 - 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 - b)*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 2*a + b)*sinh(d*x + c)^2 + 2*(2*a*cosh(d*x + c)^3 - (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + a - b)*sqrt(a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 4*((2*a^2 - b^2)*cosh(d*x + c)^3 - 2*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/d, -1/4*(2*sqrt(-a + b)*arctan(-(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + b)*sqrt(-a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 - b^2)*cosh(d*x + c)^2 + 2*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - b^2)*sinh(d*x + c)^2 - a^2 + 2*a*b - b^2)) - sqrt(a + b)*log(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 4*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 + 2*a^2 - b^2 + 2*((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - (2*a + b)*cosh(d*x + c)^2 + (6*(a + b)*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 2*(2*(a + b)*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)))/d, -1/2*(sqrt(-a + b)*arctan(-(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + b)*sqrt(-a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 - b^2)*cosh(d*x + c)^2 + 2*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - b^2)*sinh(d*x + c)^2 - a^2 + 2*a*b - b^2)) + sqrt(-a - b)*arctan(((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)*sqrt(-a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 - a^2 + b^2)))/d]","B",0
88,1,2307,0,0.498271," ","integrate(1/(a+b*coth(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} {\left(a - b\right)} \log\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(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) + a\right)} \sqrt{a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right) + {\left(a + b\right)} \sqrt{a - b} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} - 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} - {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a \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) + a - b\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 4 \, {\left({\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, {\left(a^{2} - b^{2}\right)} d}, -\frac{2 \, {\left(a - b\right)} \sqrt{-a - b} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a\right)} \sqrt{-a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + b^{2}}\right) - {\left(a + b\right)} \sqrt{a - b} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} - 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} - {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a \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) + a - b\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 4 \, {\left({\left(2 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4}}\right)}{4 \, {\left(a^{2} - b^{2}\right)} d}, -\frac{2 \, {\left(a + b\right)} \sqrt{-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 + b\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, a b - b^{2}}\right) - \sqrt{a + b} {\left(a - b\right)} \log\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(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) + a\right)} \sqrt{a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}{4 \, {\left(a^{2} - b^{2}\right)} d}, -\frac{{\left(a + b\right)} \sqrt{-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 + b\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 2 \, a b - b^{2}}\right) + {\left(a - b\right)} \sqrt{-a - b} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a\right)} \sqrt{-a - b} \sqrt{\frac{b \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)}{\sinh\left(d x + c\right)}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} + b^{2}}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}\right]"," ",0,"[1/4*(sqrt(a + b)*(a - b)*log(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 4*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 + 2*a^2 - b^2 + 2*((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - (2*a + b)*cosh(d*x + c)^2 + (6*(a + b)*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 2*(2*(a + b)*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)) + (a + b)*sqrt(a - b)*log(((2*a^2 - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 - b^2)*sinh(d*x + c)^4 - 4*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(2*a^2 - b^2)*cosh(d*x + c)^2 - 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 2*a^2 - 4*a*b + 2*b^2 - 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 - b)*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 2*a + b)*sinh(d*x + c)^2 + 2*(2*a*cosh(d*x + c)^3 - (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + a - b)*sqrt(a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 4*((2*a^2 - b^2)*cosh(d*x + c)^3 - 2*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/((a^2 - b^2)*d), -1/4*(2*(a - b)*sqrt(-a - b)*arctan(((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)*sqrt(-a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 - a^2 + b^2)) - (a + b)*sqrt(a - b)*log(((2*a^2 - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 - b^2)*sinh(d*x + c)^4 - 4*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(2*a^2 - b^2)*cosh(d*x + c)^2 - 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 2*a^2 - 4*a*b + 2*b^2 - 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 - b)*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 2*a + b)*sinh(d*x + c)^2 + 2*(2*a*cosh(d*x + c)^3 - (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + a - b)*sqrt(a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 4*((2*a^2 - b^2)*cosh(d*x + c)^3 - 2*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*cosh(d*x + c)^3*sinh(d*x + c) + 6*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4)))/((a^2 - b^2)*d), -1/4*(2*(a + b)*sqrt(-a + b)*arctan(-(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + b)*sqrt(-a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 - b^2)*cosh(d*x + c)^2 + 2*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - b^2)*sinh(d*x + c)^2 - a^2 + 2*a*b - b^2)) - sqrt(a + b)*(a - b)*log(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 4*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 + 2*a^2 - b^2 + 2*((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - (2*a + b)*cosh(d*x + c)^2 + (6*(a + b)*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 2*(2*(a + b)*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c)) + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)))/((a^2 - b^2)*d), -1/2*((a + b)*sqrt(-a + b)*arctan(-(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + b)*sqrt(-a + b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 - b^2)*cosh(d*x + c)^2 + 2*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - b^2)*sinh(d*x + c)^2 - a^2 + 2*a*b - b^2)) + (a - b)*sqrt(-a - b)*arctan(((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)*sqrt(-a - b)*sqrt((b*cosh(d*x + c) + a*sinh(d*x + c))/sinh(d*x + c))/((a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 - a^2 + b^2)))/((a^2 - b^2)*d)]","B",0
89,1,93,0,0.388601," ","integrate(sinh(x)^4/(1+coth(x)),x, algorithm=""fricas"")","\frac{5 \, \cosh\left(x\right)^{5} + 25 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + 5 \, {\left(2 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{3} - 45 \, \cosh\left(x\right)^{3} + 5 \, {\left(10 \, \cosh\left(x\right)^{3} - 27 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 60 \, {\left(2 \, x + 1\right)} \cosh\left(x\right) + 5 \, {\left(\cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} + 24 \, x - 12\right)} \sinh\left(x\right)}{384 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/384*(5*cosh(x)^5 + 25*cosh(x)*sinh(x)^4 + sinh(x)^5 + 5*(2*cosh(x)^2 - 3)*sinh(x)^3 - 45*cosh(x)^3 + 5*(10*cosh(x)^3 - 27*cosh(x))*sinh(x)^2 + 60*(2*x + 1)*cosh(x) + 5*(cosh(x)^4 - 9*cosh(x)^2 + 24*x - 12)*sinh(x))/(cosh(x) + sinh(x))","B",0
90,1,60,0,0.398051," ","integrate(sinh(x)^3/(1+coth(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{4} + 16 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 10\right)} \sinh\left(x\right)^{2} - 20 \, \cosh\left(x\right)^{2} + 16 \, {\left(\cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 45}{120 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/120*(cosh(x)^4 + 16*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 10)*sinh(x)^2 - 20*cosh(x)^2 + 16*(cosh(x)^3 - 5*cosh(x))*sinh(x) - 45)/(cosh(x) + sinh(x))","B",0
91,1,50,0,0.395480," ","integrate(sinh(x)^2/(1+coth(x)),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} - 6 \, {\left(2 \, x + 1\right)} \cosh\left(x\right) + 3 \, {\left(\cosh\left(x\right)^{2} - 4 \, x + 2\right)} \sinh\left(x\right)}{32 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/32*(3*cosh(x)^3 + 9*cosh(x)*sinh(x)^2 + sinh(x)^3 - 6*(2*x + 1)*cosh(x) + 3*(cosh(x)^2 - 4*x + 2)*sinh(x))/(cosh(x) + sinh(x))","A",0
92,1,25,0,0.392804," ","integrate(sinh(x)/(1+coth(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 3}{6 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/6*(cosh(x)^2 + 4*cosh(x)*sinh(x) + sinh(x)^2 + 3)/(cosh(x) + sinh(x))","A",0
93,1,9,0,0.429127," ","integrate(csch(x)/(1+coth(x)),x, algorithm=""fricas"")","-\frac{1}{\cosh\left(x\right) + \sinh\left(x\right)}"," ",0,"-1/(cosh(x) + sinh(x))","A",0
94,1,18,0,0.412045," ","integrate(csch(x)^2/(1+coth(x)),x, algorithm=""fricas"")","-2 \, x + \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-2*x + log(2*sinh(x)/(cosh(x) - sinh(x)))","B",0
95,1,77,0,0.388806," ","integrate(csch(x)^3/(1+coth(x)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) - 2 \, \cosh\left(x\right) - 2 \, \sinh\left(x\right)}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1}"," ",0,"((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*log(cosh(x) + sinh(x) + 1) - (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*log(cosh(x) + sinh(x) - 1) - 2*cosh(x) - 2*sinh(x))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
96,1,55,0,0.399457," ","integrate(csch(x)^4/(1+coth(x)),x, algorithm=""fricas"")","-\frac{2}{\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,"-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
97,1,1279,0,0.428029," ","integrate(sinh(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5} - 7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - a^{4} b + 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - a b^{4} - b^{5} + 2 \, {\left(35 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{5} + a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 4 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, a^{5} + a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 4 \, a b^{4} + 3 \, b^{5} - 15 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} x \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 64 \, {\left(b^{5} \cosh\left(x\right)^{4} + 4 \, b^{5} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, b^{5} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, b^{5} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{5} \sinh\left(x\right)^{4}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 8 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{5} - a^{4} b - 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 4 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} x \cosh\left(x\right)^{3} + {\left(2 \, a^{5} + a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 4 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{4}\right)}}"," ",0,"1/64*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^8 + 8*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^7 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^8 - 4*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x)^6 - 4*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5 - 7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^6 + 8*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*x*cosh(x)^4 + 8*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 - 3*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x))*sinh(x)^5 - a^5 - a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - a*b^4 - b^5 + 2*(35*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 - 30*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x)^2 + 4*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*x)*sinh(x)^4 + 8*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 - 10*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x)^3 + 4*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*x*cosh(x))*sinh(x)^3 + 4*(2*a^5 + a^4*b - 6*a^3*b^2 - 4*a^2*b^3 + 4*a*b^4 + 3*b^5)*cosh(x)^2 + 4*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 + 2*a^5 + a^4*b - 6*a^3*b^2 - 4*a^2*b^3 + 4*a*b^4 + 3*b^5 - 15*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x)^4 + 12*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*x*cosh(x)^2)*sinh(x)^2 - 64*(b^5*cosh(x)^4 + 4*b^5*cosh(x)^3*sinh(x) + 6*b^5*cosh(x)^2*sinh(x)^2 + 4*b^5*cosh(x)*sinh(x)^3 + b^5*sinh(x)^4)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + 8*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^7 - 3*(2*a^5 - a^4*b - 6*a^3*b^2 + 4*a^2*b^3 + 4*a*b^4 - 3*b^5)*cosh(x)^5 + 4*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*x*cosh(x)^3 + (2*a^5 + a^4*b - 6*a^3*b^2 - 4*a^2*b^3 + 4*a*b^4 + 3*b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3*sinh(x) + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x)^2 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^4)","B",0
98,1,1859,0,0.455044," ","integrate(sinh(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{6} + a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 24 \, {\left(b^{4} \cosh\left(x\right)^{3} + 3 \, b^{4} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, b^{4} \cosh\left(x\right) \sinh\left(x\right)^{2} + b^{4} \sinh\left(x\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\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} - 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\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) + 6 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{3}\right)}}, \frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{6} + a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 48 \, {\left(b^{4} \cosh\left(x\right)^{3} + 3 \, b^{4} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, b^{4} \cosh\left(x\right) \sinh\left(x\right)^{2} + b^{4} \sinh\left(x\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right) + 6 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(3 \, a^{5} - a^{4} b - 10 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} - 5 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + a^{4} b - 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + 7 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{3}\right)}}\right]"," ",0,"[1/24*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 + 6*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^5 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^6 + a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^4 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5)*cosh(x)^2 - 3*(3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 + 6*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^2)*sinh(x)^2 + 24*(b^4*cosh(x)^3 + 3*b^4*cosh(x)^2*sinh(x) + 3*b^4*cosh(x)*sinh(x)^2 + b^4*sinh(x)^3)*sqrt(a^2 - b^2)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)) + 6*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 - 2*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^3 - (3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x) + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^2 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^3), 1/24*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 + 6*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^5 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^6 + a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^4 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 - 3*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5)*cosh(x)^2 - 3*(3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 + 6*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^2)*sinh(x)^2 + 48*(b^4*cosh(x)^3 + 3*b^4*cosh(x)^2*sinh(x) + 3*b^4*cosh(x)*sinh(x)^2 + b^4*sinh(x)^3)*sqrt(-a^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))) + 6*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 - 2*(3*a^5 - a^4*b - 10*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 - 5*b^5)*cosh(x)^3 - (3*a^5 + a^4*b - 10*a^3*b^2 - 6*a^2*b^3 + 7*a*b^4 + 5*b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x) + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^2 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^3)]","B",0
99,1,331,0,0.406229," ","integrate(sinh(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} x \cosh\left(x\right)^{2} - a^{3} - a^{2} b + a b^{2} + b^{3} + 2 \, {\left(3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} x\right)} \sinh\left(x\right)^{2} - 8 \, {\left(b^{3} \cosh\left(x\right)^{2} + 2 \, b^{3} \cosh\left(x\right) \sinh\left(x\right) + b^{3} \sinh\left(x\right)^{2}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{2}\right)}}"," ",0,"1/8*((a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^4 - 4*(a^3 - 3*a*b^2 - 2*b^3)*x*cosh(x)^2 - a^3 - a^2*b + a*b^2 + b^3 + 2*(3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 - 2*(a^3 - 3*a*b^2 - 2*b^3)*x)*sinh(x)^2 - 8*(b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + 4*((a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*x*cosh(x))*sinh(x))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^2)","B",0
100,1,431,0,0.436877," ","integrate(sinh(x)/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{a^{3} + a^{2} b - a b^{2} - b^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{2} - 2 \, {\left(b^{2} \cosh\left(x\right) + b^{2} \sinh\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\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} + 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}\right)}{2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)\right)}}, \frac{a^{3} + a^{2} b - a b^{2} - b^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b^{2} \cosh\left(x\right) + b^{2} \sinh\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right)}{2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/2*(a^3 + a^2*b - a*b^2 - b^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x) + (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^2 - 2*(b^2*cosh(x) + b^2*sinh(x))*sqrt(a^2 - b^2)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)), 1/2*(a^3 + a^2*b - a*b^2 - b^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x) + (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^2 + 4*(b^2*cosh(x) + b^2*sinh(x))*sqrt(-a^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x))]","B",0
101,1,147,0,0.403369," ","integrate(csch(x)/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{{\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} - 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\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^{2} - b^{2}}}, \frac{2 \, \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right)}{a^{2} - b^{2}}\right]"," ",0,"[log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b))/sqrt(a^2 - b^2), 2*sqrt(-a^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x)))/(a^2 - b^2)]","A",0
102,1,43,0,0.406281," ","integrate(csch(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{\log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{b}"," ",0,"-(log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - log(2*sinh(x)/(cosh(x) - sinh(x))))/b","B",0
103,1,384,0,0.449532," ","integrate(csch(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \log\left(\frac{{\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} - 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}\right) - 2 \, b \cosh\left(x\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)} \log\left(\cosh\left(x\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)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) - 2 \, b \sinh\left(x\right)}{b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2} - b^{2}}, \frac{2 \, \sqrt{-a^{2} + b^{2}} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right) - 2 \, b \cosh\left(x\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)} \log\left(\cosh\left(x\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)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) - 2 \, b \sinh\left(x\right)}{b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2} - b^{2}}\right]"," ",0,"[(sqrt(a^2 - b^2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)) - 2*b*cosh(x) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*log(cosh(x) + sinh(x) + 1) - (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*log(cosh(x) + sinh(x) - 1) - 2*b*sinh(x))/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2 - b^2), (2*sqrt(-a^2 + b^2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))) - 2*b*cosh(x) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*log(cosh(x) + sinh(x) + 1) - (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*log(cosh(x) + sinh(x) - 1) - 2*b*sinh(x))/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2 - b^2)]","B",0
104,1,434,0,0.416877," ","integrate(csch(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + 2 \, {\left(a b - b^{2}\right)} \sinh\left(x\right)^{2} - 2 \, a b - {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{b^{3} \cosh\left(x\right)^{4} + 4 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{3} \sinh\left(x\right)^{4} - 2 \, b^{3} \cosh\left(x\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(x\right)^{2} - b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b^{3} \cosh\left(x\right)^{3} - b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)}"," ",0,"(2*(a*b - b^2)*cosh(x)^2 + 4*(a*b - b^2)*cosh(x)*sinh(x) + 2*(a*b - b^2)*sinh(x)^2 - 2*a*b - ((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 - 2*(a^2 - b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + ((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 - 2*(a^2 - b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*log(2*sinh(x)/(cosh(x) - sinh(x))))/(b^3*cosh(x)^4 + 4*b^3*cosh(x)*sinh(x)^3 + b^3*sinh(x)^4 - 2*b^3*cosh(x)^2 + b^3 + 2*(3*b^3*cosh(x)^2 - b^3)*sinh(x)^2 + 4*(b^3*cosh(x)^3 - b^3*cosh(x))*sinh(x))","B",0
105,1,92,0,0.407202," ","integrate(cosh(x)^4/(1+coth(x)),x, algorithm=""fricas"")","\frac{5 \, \cosh\left(x\right)^{5} + 25 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + {\left(10 \, \cosh\left(x\right)^{2} + 9\right)} \sinh\left(x\right)^{3} + 27 \, \cosh\left(x\right)^{3} + {\left(50 \, \cosh\left(x\right)^{3} + 81 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 12 \, {\left(2 \, x + 1\right)} \cosh\left(x\right) + {\left(5 \, \cosh\left(x\right)^{4} + 27 \, \cosh\left(x\right)^{2} + 24 \, x - 12\right)} \sinh\left(x\right)}{384 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/384*(5*cosh(x)^5 + 25*cosh(x)*sinh(x)^4 + sinh(x)^5 + (10*cosh(x)^2 + 9)*sinh(x)^3 + 27*cosh(x)^3 + (50*cosh(x)^3 + 81*cosh(x))*sinh(x)^2 + 12*(2*x + 1)*cosh(x) + (5*cosh(x)^4 + 27*cosh(x)^2 + 24*x - 12)*sinh(x))/(cosh(x) + sinh(x))","B",0
106,1,56,0,0.371961," ","integrate(cosh(x)^3/(1+coth(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{4} + \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} + 5\right)} \sinh\left(x\right)^{2} + 5 \, \cosh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)}{30 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/30*(cosh(x)^4 + cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 5)*sinh(x)^2 + 5*cosh(x)^2 + (cosh(x)^3 + 5*cosh(x))*sinh(x))/(cosh(x) + sinh(x))","B",0
107,1,51,0,0.401685," ","integrate(cosh(x)^2/(1+coth(x)),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + 2 \, {\left(2 \, x + 1\right)} \cosh\left(x\right) + {\left(3 \, \cosh\left(x\right)^{2} + 4 \, x - 2\right)} \sinh\left(x\right)}{32 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/32*(3*cosh(x)^3 + 9*cosh(x)*sinh(x)^2 + sinh(x)^3 + 2*(2*x + 1)*cosh(x) + (3*cosh(x)^2 + 4*x - 2)*sinh(x))/(cosh(x) + sinh(x))","A",0
108,1,23,0,0.409664," ","integrate(cosh(x)/(1+coth(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{2} + \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}{3 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/3*(cosh(x)^2 + cosh(x)*sinh(x) + sinh(x)^2)/(cosh(x) + sinh(x))","A",0
109,1,23,0,0.386510," ","integrate(sech(x)/(1+coth(x)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right)}"," ",0,"(2*(cosh(x) + sinh(x))*arctan(cosh(x) + sinh(x)) + 1)/(cosh(x) + sinh(x))","B",0
110,1,78,0,0.414577," ","integrate(sech(x)^2/(1+coth(x)),x, algorithm=""fricas"")","-\frac{2 \, x \cosh\left(x\right)^{2} + 4 \, x \cosh\left(x\right) \sinh\left(x\right) + 2 \, x \sinh\left(x\right)^{2} - {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, x + 2}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1}"," ",0,"-(2*x*cosh(x)^2 + 4*x*cosh(x)*sinh(x) + 2*x*sinh(x)^2 - (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*log(2*cosh(x)/(cosh(x) - sinh(x))) + 2*x + 2)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)","B",0
111,1,140,0,0.380354," ","integrate(sech(x)^3/(1+coth(x)),x, algorithm=""fricas"")","-\frac{\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 3 \, {\left(\cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right) + 3 \, \cosh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}"," ",0,"-(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + 3*(cosh(x)^2 + 1)*sinh(x) + 3*cosh(x))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)","B",0
112,1,84,0,0.366828," ","integrate(sech(x)^4/(1+coth(x)),x, algorithm=""fricas"")","-\frac{4 \, {\left(\cosh\left(x\right) + 2 \, \sinh\left(x\right)\right)}}{3 \, {\left(\cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + {\left(10 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{3} + {\left(10 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right) + 4 \, \cosh\left(x\right)\right)}}"," ",0,"-4/3*(cosh(x) + 2*sinh(x))/(cosh(x)^5 + 5*cosh(x)*sinh(x)^4 + sinh(x)^5 + (10*cosh(x)^2 + 3)*sinh(x)^3 + 3*cosh(x)^3 + (10*cosh(x)^3 + 9*cosh(x))*sinh(x)^2 + (5*cosh(x)^4 + 9*cosh(x)^2 + 2)*sinh(x) + 4*cosh(x))","B",0
113,1,231,0,0.434772," ","integrate(sech(x)^2*(1+coth(x))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \log\left(\frac{2 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} + 3 \, \cosh\left(x\right)^{2} + 6 \, \cosh\left(x\right) \sinh\left(x\right) + 3 \, \sinh\left(x\right)^{2} - 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \log\left(-\frac{2 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, \cosh\left(x\right)^{2} - 6 \, \cosh\left(x\right) \sinh\left(x\right) - 3 \, \sinh\left(x\right)^{2} + 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}"," ",0,"1/4*(4*sqrt(2)*(sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*log((2*sqrt(2)*(sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) + 3*cosh(x)^2 + 6*cosh(x)*sinh(x) + 3*sinh(x)^2 - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*log(-(2*sqrt(2)*(sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*cosh(x)^2 - 6*cosh(x)*sinh(x) - 3*sinh(x)^2 + 1)/(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
114,1,1229,0,0.425337," ","integrate(cosh(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5} + 7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - a^{4} b + 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - a b^{4} - b^{5} + 2 \, {\left(35 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(2 \, a^{5} + 3 \, a^{4} b - 2 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} - 2 \, a^{5} - 3 \, a^{4} b + 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5} + 15 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} x \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 64 \, {\left(a^{4} b \cosh\left(x\right)^{4} + 4 \, a^{4} b \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, a^{4} b \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, a^{4} b \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{4} b \sinh\left(x\right)^{4}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 8 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} x \cosh\left(x\right)^{3} - {\left(2 \, a^{5} + 3 \, a^{4} b - 2 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{4}\right)}}"," ",0,"1/64*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^8 + 8*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^7 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^8 + 4*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x)^6 + 4*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5 + 7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^6 + 8*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*x*cosh(x)^4 + 8*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 + 3*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x))*sinh(x)^5 - a^5 - a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - a*b^4 - b^5 + 2*(35*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 + 30*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x)^2 + 4*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*x)*sinh(x)^4 + 8*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 + 10*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x)^3 + 4*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*x*cosh(x))*sinh(x)^3 - 4*(2*a^5 + 3*a^4*b - 2*a^3*b^2 - 4*a^2*b^3 + b^5)*cosh(x)^2 + 4*(7*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 - 2*a^5 - 3*a^4*b + 2*a^3*b^2 + 4*a^2*b^3 - b^5 + 15*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x)^4 + 12*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*x*cosh(x)^2)*sinh(x)^2 - 64*(a^4*b*cosh(x)^4 + 4*a^4*b*cosh(x)^3*sinh(x) + 6*a^4*b*cosh(x)^2*sinh(x)^2 + 4*a^4*b*cosh(x)*sinh(x)^3 + a^4*b*sinh(x)^4)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + 8*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^7 + 3*(2*a^5 - 3*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 - b^5)*cosh(x)^5 + 4*(3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*x*cosh(x)^3 - (2*a^5 + 3*a^4*b - 2*a^3*b^2 - 4*a^2*b^3 + b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3*sinh(x) + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x)^2 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^4)","B",0
115,1,1873,0,0.444360," ","integrate(cosh(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{6} - a^{5} - a^{4} b + 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5} + 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 24 \, {\left(a^{3} b \cosh\left(x\right)^{3} + 3 \, a^{3} b \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{3} b \sinh\left(x\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\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} + 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\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) + 6 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{3}\right)}}, \frac{{\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \sinh\left(x\right)^{6} - a^{5} - a^{4} b + 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5} + 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5} - 5 \, {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 48 \, {\left(a^{3} b \cosh\left(x\right)^{3} + 3 \, a^{3} b \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{3} b \sinh\left(x\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right) + 6 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} - 5 \, a^{4} b - 2 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 5 \, a^{4} b - 2 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - a b^{4} + b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{3}\right)}}\right]"," ",0,"[1/24*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 + 6*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^5 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^6 - a^5 - a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - a*b^4 - b^5 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5 + 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5)*cosh(x)^2 - 3*(3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 - 6*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^2)*sinh(x)^2 + 24*(a^3*b*cosh(x)^3 + 3*a^3*b*cosh(x)^2*sinh(x) + 3*a^3*b*cosh(x)*sinh(x)^2 + a^3*b*sinh(x)^3)*sqrt(a^2 - b^2)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)) + 6*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 + 2*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^3 - (3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x) + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^2 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^3), 1/24*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^6 + 6*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)*sinh(x)^5 + (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*sinh(x)^6 - a^5 - a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - a*b^4 - b^5 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5 + 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 + 3*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5)*cosh(x)^2 - 3*(3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5 - 5*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 - 6*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^2)*sinh(x)^2 - 48*(a^3*b*cosh(x)^3 + 3*a^3*b*cosh(x)^2*sinh(x) + 3*a^3*b*cosh(x)*sinh(x)^2 + a^3*b*sinh(x)^3)*sqrt(-a^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))) + 6*((a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*cosh(x)^5 + 2*(3*a^5 - 5*a^4*b - 2*a^3*b^2 + 6*a^2*b^3 - a*b^4 - b^5)*cosh(x)^3 - (3*a^5 + 5*a^4*b - 2*a^3*b^2 - 6*a^2*b^3 - a*b^4 + b^5)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2*sinh(x) + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^2 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^3)]","B",0
116,1,334,0,0.409517," ","integrate(cosh(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} x \cosh\left(x\right)^{2} - a^{3} - a^{2} b + a b^{2} + b^{3} + 2 \, {\left(3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} x\right)} \sinh\left(x\right)^{2} - 8 \, {\left(a^{2} b \cosh\left(x\right)^{2} + 2 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right) + a^{2} b \sinh\left(x\right)^{2}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{2}\right)}}"," ",0,"1/8*((a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*x*cosh(x)^2 - a^3 - a^2*b + a*b^2 + b^3 + 2*(3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 2*(a^3 + 2*a^2*b + a*b^2)*x)*sinh(x)^2 - 8*(a^2*b*cosh(x)^2 + 2*a^2*b*cosh(x)*sinh(x) + a^2*b*sinh(x)^2)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + 4*((a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 + 2*(a^3 + 2*a^2*b + a*b^2)*x*cosh(x))*sinh(x))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^2)","B",0
117,1,431,0,0.422934," ","integrate(cosh(x)/(a+b*coth(x)),x, algorithm=""fricas"")","\left[-\frac{a^{3} + a^{2} b - a b^{2} - b^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(a b \cosh\left(x\right) + a b \sinh\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{{\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} - 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}\right)}{2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)\right)}}, -\frac{a^{3} + a^{2} b - a b^{2} - b^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b \cosh\left(x\right) + a b \sinh\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right)}{2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/2*(a^3 + a^2*b - a*b^2 - b^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x) - (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^2 + 2*(a*b*cosh(x) + a*b*sinh(x))*sqrt(a^2 - b^2)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)), -1/2*(a^3 + a^2*b - a*b^2 - b^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)*sinh(x) - (a^3 - a^2*b - a*b^2 + b^3)*sinh(x)^2 + 4*(a*b*cosh(x) + a*b*sinh(x))*sqrt(-a^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x) + (a^4 - 2*a^2*b^2 + b^4)*sinh(x))]","B",0
118,1,200,0,0.464088," ","integrate(sech(x)/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} b \log\left(\frac{{\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} + 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}\right) + 2 \, {\left(a^{2} - b^{2}\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{a^{3} - a b^{2}}, -\frac{2 \, {\left(\sqrt{-a^{2} + b^{2}} b \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right) - {\left(a^{2} - b^{2}\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)\right)}}{a^{3} - a b^{2}}\right]"," ",0,"[(sqrt(a^2 - b^2)*b*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)) + 2*(a^2 - b^2)*arctan(cosh(x) + sinh(x)))/(a^3 - a*b^2), -2*(sqrt(-a^2 + b^2)*b*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))) - (a^2 - b^2)*arctan(cosh(x) + sinh(x)))/(a^3 - a*b^2)]","A",0
119,1,117,0,0.437332," ","integrate(sech(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","-\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)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\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)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, a}{a^{2} \cosh\left(x\right)^{2} + 2 \, a^{2} \cosh\left(x\right) \sinh\left(x\right) + a^{2} \sinh\left(x\right)^{2} + a^{2}}"," ",0,"-((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*log(2*cosh(x)/(cosh(x) - sinh(x))) + 2*a)/(a^2*cosh(x)^2 + 2*a^2*cosh(x)*sinh(x) + a^2*sinh(x)^2 + a^2)","B",0
120,1,856,0,0.468630," ","integrate(sech(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} - 2 \, a b\right)} \sinh\left(x\right)^{3} + {\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^{2} - b^{2}} \log\left(\frac{{\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} + 2 \, \sqrt{a^{2} - b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + a - b}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}\right) + {\left({\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right) + {\left(3 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b\right)} \sinh\left(x\right)}{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} + 2 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)}, \frac{{\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} - 2 \, a b\right)} \sinh\left(x\right)^{3} - 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^{2} + b^{2}} \arctan\left(\frac{\sqrt{-a^{2} + b^{2}}}{{\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - {\left(a^{2} + 2 \, a b\right)} \cosh\left(x\right) + {\left(3 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b\right)} \sinh\left(x\right)}{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} + 2 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + 2 \, {\left(3 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right]"," ",0,"[((a^2 - 2*a*b)*cosh(x)^3 + 3*(a^2 - 2*a*b)*cosh(x)*sinh(x)^2 + (a^2 - 2*a*b)*sinh(x)^3 + (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^2 - b^2)*log(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + 2*sqrt(a^2 - b^2)*(cosh(x) + sinh(x)) + a - b)/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)) + ((a^2 - 2*b^2)*cosh(x)^4 + 4*(a^2 - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - 2*b^2)*sinh(x)^4 + 2*(a^2 - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - 2*b^2)*cosh(x)^2 + a^2 - 2*b^2)*sinh(x)^2 + a^2 - 2*b^2 + 4*((a^2 - 2*b^2)*cosh(x)^3 + (a^2 - 2*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (a^2 + 2*a*b)*cosh(x) + (3*(a^2 - 2*a*b)*cosh(x)^2 - a^2 - 2*a*b)*sinh(x))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + 2*a^3*cosh(x)^2 + a^3 + 2*(3*a^3*cosh(x)^2 + a^3)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + a^3*cosh(x))*sinh(x)), ((a^2 - 2*a*b)*cosh(x)^3 + 3*(a^2 - 2*a*b)*cosh(x)*sinh(x)^2 + (a^2 - 2*a*b)*sinh(x)^3 - 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^2 + b^2)*arctan(sqrt(-a^2 + b^2)/((a + b)*cosh(x) + (a + b)*sinh(x))) + ((a^2 - 2*b^2)*cosh(x)^4 + 4*(a^2 - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - 2*b^2)*sinh(x)^4 + 2*(a^2 - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - 2*b^2)*cosh(x)^2 + a^2 - 2*b^2)*sinh(x)^2 + a^2 - 2*b^2 + 4*((a^2 - 2*b^2)*cosh(x)^3 + (a^2 - 2*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (a^2 + 2*a*b)*cosh(x) + (3*(a^2 - 2*a*b)*cosh(x)^2 - a^2 - 2*a*b)*sinh(x))/(a^3*cosh(x)^4 + 4*a^3*cosh(x)*sinh(x)^3 + a^3*sinh(x)^4 + 2*a^3*cosh(x)^2 + a^3 + 2*(3*a^3*cosh(x)^2 + a^3)*sinh(x)^2 + 4*(a^3*cosh(x)^3 + a^3*cosh(x))*sinh(x))]","B",0
121,1,909,0,0.422126," ","integrate(sech(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(x\right)^{4} + 24 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, a^{3} - 6 \, a b^{2} + 6 \, {\left(2 \, a^{3} + a^{2} b - 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(2 \, a^{3} + a^{2} b - 2 \, a b^{2} + 6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{2} b - b^{3} + 5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b - b^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - 3 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{2} b - b^{3} + 5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b - b^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 12 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + a^{2} b - 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left(a^{4} \cosh\left(x\right)^{6} + 6 \, a^{4} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{4} \sinh\left(x\right)^{6} + 3 \, a^{4} \cosh\left(x\right)^{4} + 3 \, a^{4} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a^{4} \cosh\left(x\right)^{2} + a^{4}\right)} \sinh\left(x\right)^{4} + a^{4} + 4 \, {\left(5 \, a^{4} \cosh\left(x\right)^{3} + 3 \, a^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{4} \cosh\left(x\right)^{4} + 6 \, a^{4} \cosh\left(x\right)^{2} + a^{4}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a^{4} \cosh\left(x\right)^{5} + 2 \, a^{4} \cosh\left(x\right)^{3} + a^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/3*(6*(a^2*b - a*b^2)*cosh(x)^4 + 24*(a^2*b - a*b^2)*cosh(x)*sinh(x)^3 + 6*(a^2*b - a*b^2)*sinh(x)^4 + 4*a^3 - 6*a*b^2 + 6*(2*a^3 + a^2*b - 2*a*b^2)*cosh(x)^2 + 6*(2*a^3 + a^2*b - 2*a*b^2 + 6*(a^2*b - a*b^2)*cosh(x)^2)*sinh(x)^2 + 3*((a^2*b - b^3)*cosh(x)^6 + 6*(a^2*b - b^3)*cosh(x)*sinh(x)^5 + (a^2*b - b^3)*sinh(x)^6 + 3*(a^2*b - b^3)*cosh(x)^4 + 3*(a^2*b - b^3 + 5*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^2*b - b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^3 + a^2*b - b^3 + 3*(a^2*b - b^3)*cosh(x)^2 + 3*(5*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 6*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^2*b - b^3)*cosh(x)^5 + 2*(a^2*b - b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - 3*((a^2*b - b^3)*cosh(x)^6 + 6*(a^2*b - b^3)*cosh(x)*sinh(x)^5 + (a^2*b - b^3)*sinh(x)^6 + 3*(a^2*b - b^3)*cosh(x)^4 + 3*(a^2*b - b^3 + 5*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^2*b - b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^3 + a^2*b - b^3 + 3*(a^2*b - b^3)*cosh(x)^2 + 3*(5*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 6*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^2*b - b^3)*cosh(x)^5 + 2*(a^2*b - b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 12*(2*(a^2*b - a*b^2)*cosh(x)^3 + (2*a^3 + a^2*b - 2*a*b^2)*cosh(x))*sinh(x))/(a^4*cosh(x)^6 + 6*a^4*cosh(x)*sinh(x)^5 + a^4*sinh(x)^6 + 3*a^4*cosh(x)^4 + 3*a^4*cosh(x)^2 + 3*(5*a^4*cosh(x)^2 + a^4)*sinh(x)^4 + a^4 + 4*(5*a^4*cosh(x)^3 + 3*a^4*cosh(x))*sinh(x)^3 + 3*(5*a^4*cosh(x)^4 + 6*a^4*cosh(x)^2 + a^4)*sinh(x)^2 + 6*(a^4*cosh(x)^5 + 2*a^4*cosh(x)^3 + a^4*cosh(x))*sinh(x))","B",0
122,1,41,0,0.414849," ","integrate(sech(x)/(I+2*coth(x)),x, algorithm=""fricas"")","-\frac{2}{5} \, \sqrt{5} \log\left(\left(\frac{2}{5} i + \frac{1}{5}\right) \, \sqrt{5} + e^{x}\right) + \frac{2}{5} \, \sqrt{5} \log\left(-\left(\frac{2}{5} i + \frac{1}{5}\right) \, \sqrt{5} + e^{x}\right) + \log\left(e^{x} + i\right) - \log\left(e^{x} - i\right)"," ",0,"-2/5*sqrt(5)*log((2/5*I + 1/5)*sqrt(5) + e^x) + 2/5*sqrt(5)*log(-(2/5*I + 1/5)*sqrt(5) + e^x) + log(e^x + I) - log(e^x - I)","A",0
123,1,571,0,0.421546," ","integrate(tanh(x)^4/(1+coth(x)),x, algorithm=""fricas"")","\frac{54 \, x \cosh\left(x\right)^{8} + 432 \, x \cosh\left(x\right) \sinh\left(x\right)^{7} + 54 \, x \sinh\left(x\right)^{8} + 3 \, {\left(54 \, x + 17\right)} \cosh\left(x\right)^{6} + 3 \, {\left(504 \, x \cosh\left(x\right)^{2} + 54 \, x + 17\right)} \sinh\left(x\right)^{6} + 18 \, {\left(168 \, x \cosh\left(x\right)^{3} + {\left(54 \, x + 17\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 81 \, {\left(2 \, x + 1\right)} \cosh\left(x\right)^{4} + 9 \, {\left(420 \, x \cosh\left(x\right)^{4} + 5 \, {\left(54 \, x + 17\right)} \cosh\left(x\right)^{2} + 18 \, x + 9\right)} \sinh\left(x\right)^{4} + 12 \, {\left(252 \, x \cosh\left(x\right)^{5} + 5 \, {\left(54 \, x + 17\right)} \cosh\left(x\right)^{3} + 27 \, {\left(2 \, x + 1\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(54 \, x + 65\right)} \cosh\left(x\right)^{2} + {\left(1512 \, x \cosh\left(x\right)^{6} + 45 \, {\left(54 \, x + 17\right)} \cosh\left(x\right)^{4} + 486 \, {\left(2 \, x + 1\right)} \cosh\left(x\right)^{2} + 54 \, x + 65\right)} \sinh\left(x\right)^{2} - 24 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(70 \, \cosh\left(x\right)^{4} + 45 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 18 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 6 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(216 \, x \cosh\left(x\right)^{7} + 9 \, {\left(54 \, x + 17\right)} \cosh\left(x\right)^{5} + 162 \, {\left(2 \, x + 1\right)} \cosh\left(x\right)^{3} + {\left(54 \, x + 65\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3}{12 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(70 \, \cosh\left(x\right)^{4} + 45 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 18 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 6 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"1/12*(54*x*cosh(x)^8 + 432*x*cosh(x)*sinh(x)^7 + 54*x*sinh(x)^8 + 3*(54*x + 17)*cosh(x)^6 + 3*(504*x*cosh(x)^2 + 54*x + 17)*sinh(x)^6 + 18*(168*x*cosh(x)^3 + (54*x + 17)*cosh(x))*sinh(x)^5 + 81*(2*x + 1)*cosh(x)^4 + 9*(420*x*cosh(x)^4 + 5*(54*x + 17)*cosh(x)^2 + 18*x + 9)*sinh(x)^4 + 12*(252*x*cosh(x)^5 + 5*(54*x + 17)*cosh(x)^3 + 27*(2*x + 1)*cosh(x))*sinh(x)^3 + (54*x + 65)*cosh(x)^2 + (1512*x*cosh(x)^6 + 45*(54*x + 17)*cosh(x)^4 + 486*(2*x + 1)*cosh(x)^2 + 54*x + 65)*sinh(x)^2 - 24*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 3)*sinh(x)^6 + 3*cosh(x)^6 + 2*(28*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + (70*cosh(x)^4 + 45*cosh(x)^2 + 3)*sinh(x)^4 + 3*cosh(x)^4 + 4*(14*cosh(x)^5 + 15*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 45*cosh(x)^4 + 18*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(4*cosh(x)^7 + 9*cosh(x)^5 + 6*cosh(x)^3 + cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 2*(216*x*cosh(x)^7 + 9*(54*x + 17)*cosh(x)^5 + 162*(2*x + 1)*cosh(x)^3 + (54*x + 65)*cosh(x))*sinh(x) + 3)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 3)*sinh(x)^6 + 3*cosh(x)^6 + 2*(28*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + (70*cosh(x)^4 + 45*cosh(x)^2 + 3)*sinh(x)^4 + 3*cosh(x)^4 + 4*(14*cosh(x)^5 + 15*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 45*cosh(x)^4 + 18*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(4*cosh(x)^7 + 9*cosh(x)^5 + 6*cosh(x)^3 + cosh(x))*sinh(x))","B",0
124,1,354,0,0.410000," ","integrate(tanh(x)^3/(1+coth(x)),x, algorithm=""fricas"")","-\frac{14 \, x \cosh\left(x\right)^{6} + 84 \, x \cosh\left(x\right) \sinh\left(x\right)^{5} + 14 \, x \sinh\left(x\right)^{6} + {\left(28 \, x + 1\right)} \cosh\left(x\right)^{4} + {\left(210 \, x \cosh\left(x\right)^{2} + 28 \, x + 1\right)} \sinh\left(x\right)^{4} + 4 \, {\left(70 \, x \cosh\left(x\right)^{3} + {\left(28 \, x + 1\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, {\left(7 \, x + 5\right)} \cosh\left(x\right)^{2} + 2 \, {\left(105 \, x \cosh\left(x\right)^{4} + 3 \, {\left(28 \, x + 1\right)} \cosh\left(x\right)^{2} + 7 \, x + 5\right)} \sinh\left(x\right)^{2} - 8 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + {\left(15 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right)^{4} + 2 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 12 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 4 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left(21 \, x \cosh\left(x\right)^{5} + {\left(28 \, x + 1\right)} \cosh\left(x\right)^{3} + {\left(7 \, x + 5\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}{4 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + {\left(15 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right)^{4} + 2 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 12 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 4 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/4*(14*x*cosh(x)^6 + 84*x*cosh(x)*sinh(x)^5 + 14*x*sinh(x)^6 + (28*x + 1)*cosh(x)^4 + (210*x*cosh(x)^2 + 28*x + 1)*sinh(x)^4 + 4*(70*x*cosh(x)^3 + (28*x + 1)*cosh(x))*sinh(x)^3 + 2*(7*x + 5)*cosh(x)^2 + 2*(105*x*cosh(x)^4 + 3*(28*x + 1)*cosh(x)^2 + 7*x + 5)*sinh(x)^2 - 8*(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + (15*cosh(x)^2 + 2)*sinh(x)^4 + 2*cosh(x)^4 + 4*(5*cosh(x)^3 + 2*cosh(x))*sinh(x)^3 + (15*cosh(x)^4 + 12*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(3*cosh(x)^5 + 4*cosh(x)^3 + cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 4*(21*x*cosh(x)^5 + (28*x + 1)*cosh(x)^3 + (7*x + 5)*cosh(x))*sinh(x) + 1)/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + (15*cosh(x)^2 + 2)*sinh(x)^4 + 2*cosh(x)^4 + 4*(5*cosh(x)^3 + 2*cosh(x))*sinh(x)^3 + (15*cosh(x)^4 + 12*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(3*cosh(x)^5 + 4*cosh(x)^3 + cosh(x))*sinh(x))","B",0
125,1,186,0,0.437204," ","integrate(tanh(x)^2/(1+coth(x)),x, algorithm=""fricas"")","\frac{10 \, x \cosh\left(x\right)^{4} + 40 \, x \cosh\left(x\right) \sinh\left(x\right)^{3} + 10 \, x \sinh\left(x\right)^{4} + {\left(10 \, x + 9\right)} \cosh\left(x\right)^{2} + {\left(60 \, x \cosh\left(x\right)^{2} + 10 \, x + 9\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} + {\left(6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(20 \, x \cosh\left(x\right)^{3} + {\left(10 \, x + 9\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"1/4*(10*x*cosh(x)^4 + 40*x*cosh(x)*sinh(x)^3 + 10*x*sinh(x)^4 + (10*x + 9)*cosh(x)^2 + (60*x*cosh(x)^2 + 10*x + 9)*sinh(x)^2 - 4*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(2*cosh(x)^3 + cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 2*(20*x*cosh(x)^3 + (10*x + 9)*cosh(x))*sinh(x) + 1)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(2*cosh(x)^3 + cosh(x))*sinh(x))","B",0
126,1,73,0,0.406539," ","integrate(tanh(x)/(1+coth(x)),x, algorithm=""fricas"")","-\frac{6 \, x \cosh\left(x\right)^{2} + 12 \, x \cosh\left(x\right) \sinh\left(x\right) + 6 \, x \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}\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 1}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"-1/4*(6*x*cosh(x)^2 + 12*x*cosh(x)*sinh(x) + 6*x*sinh(x)^2 - 4*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)*log(2*cosh(x)/(cosh(x) - sinh(x))) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
127,1,26,0,0.407742," ","integrate(1/(1+coth(x)),x, algorithm=""fricas"")","\frac{{\left(2 \, x + 1\right)} \cosh\left(x\right) + {\left(2 \, x - 1\right)} \sinh\left(x\right)}{4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/4*((2*x + 1)*cosh(x) + (2*x - 1)*sinh(x))/(cosh(x) + sinh(x))","B",0
128,1,26,0,0.396632," ","integrate(coth(x)/(1+coth(x)),x, algorithm=""fricas"")","\frac{{\left(2 \, x - 1\right)} \cosh\left(x\right) + {\left(2 \, x + 1\right)} \sinh\left(x\right)}{4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/4*((2*x - 1)*cosh(x) + (2*x + 1)*sinh(x))/(cosh(x) + sinh(x))","B",0
129,1,73,0,0.417682," ","integrate(coth(x)^2/(1+coth(x)),x, algorithm=""fricas"")","-\frac{6 \, x \cosh\left(x\right)^{2} + 12 \, x \cosh\left(x\right) \sinh\left(x\right) + 6 \, x \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}\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - 1}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"-1/4*(6*x*cosh(x)^2 + 12*x*cosh(x)*sinh(x) + 6*x*sinh(x)^2 - 4*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)*log(2*sinh(x)/(cosh(x) - sinh(x))) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
130,1,196,0,0.421510," ","integrate(coth(x)^3/(1+coth(x)),x, algorithm=""fricas"")","\frac{10 \, x \cosh\left(x\right)^{4} + 40 \, x \cosh\left(x\right) \sinh\left(x\right)^{3} + 10 \, x \sinh\left(x\right)^{4} - {\left(10 \, x + 9\right)} \cosh\left(x\right)^{2} + {\left(60 \, x \cosh\left(x\right)^{2} - 10 \, x - 9\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} + {\left(6 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(20 \, x \cosh\left(x\right)^{3} - {\left(10 \, x + 9\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"1/4*(10*x*cosh(x)^4 + 40*x*cosh(x)*sinh(x)^3 + 10*x*sinh(x)^4 - (10*x + 9)*cosh(x)^2 + (60*x*cosh(x)^2 - 10*x - 9)*sinh(x)^2 - 4*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 - 1)*sinh(x)^2 - cosh(x)^2 + 2*(2*cosh(x)^3 - cosh(x))*sinh(x))*log(2*sinh(x)/(cosh(x) - sinh(x))) + 2*(20*x*cosh(x)^3 - (10*x + 9)*cosh(x))*sinh(x) + 1)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 - 1)*sinh(x)^2 - cosh(x)^2 + 2*(2*cosh(x)^3 - cosh(x))*sinh(x))","B",0
131,1,357,0,0.409514," ","integrate(coth(x)^4/(1+coth(x)),x, algorithm=""fricas"")","-\frac{14 \, x \cosh\left(x\right)^{6} + 84 \, x \cosh\left(x\right) \sinh\left(x\right)^{5} + 14 \, x \sinh\left(x\right)^{6} - {\left(28 \, x + 1\right)} \cosh\left(x\right)^{4} + {\left(210 \, x \cosh\left(x\right)^{2} - 28 \, x - 1\right)} \sinh\left(x\right)^{4} + 4 \, {\left(70 \, x \cosh\left(x\right)^{3} - {\left(28 \, x + 1\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, {\left(7 \, x + 5\right)} \cosh\left(x\right)^{2} + 2 \, {\left(105 \, x \cosh\left(x\right)^{4} - 3 \, {\left(28 \, x + 1\right)} \cosh\left(x\right)^{2} + 7 \, x + 5\right)} \sinh\left(x\right)^{2} - 8 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + {\left(15 \, \cosh\left(x\right)^{2} - 2\right)} \sinh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} - 12 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} - 4 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left(21 \, x \cosh\left(x\right)^{5} - {\left(28 \, x + 1\right)} \cosh\left(x\right)^{3} + {\left(7 \, x + 5\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 1}{4 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + {\left(15 \, \cosh\left(x\right)^{2} - 2\right)} \sinh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} - 12 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} - 4 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/4*(14*x*cosh(x)^6 + 84*x*cosh(x)*sinh(x)^5 + 14*x*sinh(x)^6 - (28*x + 1)*cosh(x)^4 + (210*x*cosh(x)^2 - 28*x - 1)*sinh(x)^4 + 4*(70*x*cosh(x)^3 - (28*x + 1)*cosh(x))*sinh(x)^3 + 2*(7*x + 5)*cosh(x)^2 + 2*(105*x*cosh(x)^4 - 3*(28*x + 1)*cosh(x)^2 + 7*x + 5)*sinh(x)^2 - 8*(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + (15*cosh(x)^2 - 2)*sinh(x)^4 - 2*cosh(x)^4 + 4*(5*cosh(x)^3 - 2*cosh(x))*sinh(x)^3 + (15*cosh(x)^4 - 12*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(3*cosh(x)^5 - 4*cosh(x)^3 + cosh(x))*sinh(x))*log(2*sinh(x)/(cosh(x) - sinh(x))) + 4*(21*x*cosh(x)^5 - (28*x + 1)*cosh(x)^3 + (7*x + 5)*cosh(x))*sinh(x) - 1)/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + (15*cosh(x)^2 - 2)*sinh(x)^4 - 2*cosh(x)^4 + 4*(5*cosh(x)^3 - 2*cosh(x))*sinh(x)^3 + (15*cosh(x)^4 - 12*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(3*cosh(x)^5 - 4*cosh(x)^3 + cosh(x))*sinh(x))","B",0
132,1,259,0,0.387386," ","integrate(coth(x)*(1+coth(x))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} + 15 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + 5 \, \sqrt{2} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right) - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{3 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-1/3*(2*sqrt(2)*(5*sqrt(2)*cosh(x)^3 + 15*sqrt(2)*cosh(x)*sinh(x)^2 + 5*sqrt(2)*sinh(x)^3 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x) - 3*sqrt(2)*cosh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
133,1,131,0,0.396817," ","integrate(coth(x)*(1+coth(x))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}"," ",0,"-1/2*(4*sqrt(2)*(sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
134,1,85,0,0.395844," ","integrate(coth(x)/(1+coth(x))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cosh\left(x\right) + \sqrt{2} \sinh\left(x\right)\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right) + 4 \, \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}}}{4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"1/4*((sqrt(2)*cosh(x) + sqrt(2)*sinh(x))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1) + 4*sqrt(sinh(x)/(cosh(x) - sinh(x))))/(cosh(x) + sinh(x))","B",0
135,1,166,0,0.402768," ","integrate(coth(x)/(1+coth(x))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sqrt{2} \sinh\left(x\right)^{2} + \sqrt{2}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + \sqrt{2} \sinh\left(x\right)^{3}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{24 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3}\right)}}"," ",0,"-1/24*(2*sqrt(2)*(2*sqrt(2)*cosh(x)^2 + 4*sqrt(2)*cosh(x)*sinh(x) + 2*sqrt(2)*sinh(x)^2 + sqrt(2))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*(sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x)^2*sinh(x) + 3*sqrt(2)*cosh(x)*sinh(x)^2 + sqrt(2)*sinh(x)^3)*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)","B",0
136,1,436,0,0.403696," ","integrate(coth(x)^2*(1+coth(x))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(9 \, \sqrt{2} \cosh\left(x\right)^{5} + 45 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{4} + 9 \, \sqrt{2} \sinh\left(x\right)^{5} + 10 \, {\left(9 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{3} - 10 \, \sqrt{2} \cosh\left(x\right)^{3} + 30 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 5 \, {\left(9 \, \sqrt{2} \cosh\left(x\right)^{4} - 6 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right) + 5 \, \sqrt{2} \cosh\left(x\right)\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 5 \, {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{4} - 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{4} - 6 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{2} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} + 6 \, {\left(\sqrt{2} \cosh\left(x\right)^{5} - 2 \, \sqrt{2} \cosh\left(x\right)^{3} + \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) - \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{5 \, {\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)}}"," ",0,"-1/5*(2*sqrt(2)*(9*sqrt(2)*cosh(x)^5 + 45*sqrt(2)*cosh(x)*sinh(x)^4 + 9*sqrt(2)*sinh(x)^5 + 10*(9*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^3 - 10*sqrt(2)*cosh(x)^3 + 30*(3*sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x)^2 + 5*(9*sqrt(2)*cosh(x)^4 - 6*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x) + 5*sqrt(2)*cosh(x))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 5*(sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^4 - 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x)^3 + 3*(5*sqrt(2)*cosh(x)^4 - 6*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^2 + 3*sqrt(2)*cosh(x)^2 + 6*(sqrt(2)*cosh(x)^5 - 2*sqrt(2)*cosh(x)^3 + sqrt(2)*cosh(x))*sinh(x) - sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(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
137,1,242,0,0.398150," ","integrate(coth(x)^2*(1+coth(x))^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + \sqrt{2} \sinh\left(x\right)^{3}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{6 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-1/6*(8*sqrt(2)*(sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x)^2*sinh(x) + 3*sqrt(2)*cosh(x)*sinh(x)^2 + sqrt(2)*sinh(x)^3)*sqrt(sinh(x)/(cosh(x) - sinh(x))) - 3*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
138,1,189,0,0.402746," ","integrate(coth(x)^2/(1+coth(x))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} + 10 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + 5 \, \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} - {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + \sqrt{2} \sinh\left(x\right)^{3} + {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right) - \sqrt{2} \cosh\left(x\right)\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)\right)}}"," ",0,"-1/4*(2*sqrt(2)*(5*sqrt(2)*cosh(x)^2 + 10*sqrt(2)*cosh(x)*sinh(x) + 5*sqrt(2)*sinh(x)^2 - sqrt(2))*sqrt(sinh(x)/(cosh(x) - sinh(x))) - (sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x)*sinh(x)^2 + sqrt(2)*sinh(x)^3 + (3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x) - sqrt(2)*cosh(x))*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))","B",0
139,1,166,0,0.410221," ","integrate(coth(x)^2/(1+coth(x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(8 \, \sqrt{2} \cosh\left(x\right)^{2} + 16 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + 8 \, \sqrt{2} \sinh\left(x\right)^{2} + \sqrt{2}\right)} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} + 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + \sqrt{2} \sinh\left(x\right)^{3}\right)} \log\left(2 \, \sqrt{2} \sqrt{\frac{\sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 2 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} - 1\right)}{24 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3}\right)}}"," ",0,"1/24*(2*sqrt(2)*(8*sqrt(2)*cosh(x)^2 + 16*sqrt(2)*cosh(x)*sinh(x) + 8*sqrt(2)*sinh(x)^2 + sqrt(2))*sqrt(sinh(x)/(cosh(x) - sinh(x))) + 3*(sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x)^2*sinh(x) + 3*sqrt(2)*cosh(x)*sinh(x)^2 + sqrt(2)*sinh(x)^3)*log(2*sqrt(2)*sqrt(sinh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x)) + 2*cosh(x)^2 + 4*cosh(x)*sinh(x) + 2*sinh(x)^2 - 1))/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)","B",0
140,1,1294,0,0.453126," ","integrate(tanh(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right)^{6} + 18 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right) \sinh\left(x\right)^{5} + 3 \, {\left(a^{5} + a^{4} b\right)} x \sinh\left(x\right)^{6} + 8 \, a^{5} - 2 \, a^{3} b^{2} - 6 \, a b^{4} + 3 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 2 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)^{4} + 3 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 2 \, a b^{4} + 15 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right)^{2} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \sinh\left(x\right)^{4} + 12 \, {\left(5 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right)^{3} + {\left(4 \, a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 2 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(4 \, a^{5} - 2 \, a^{4} b + 2 \, a^{2} b^{3} - 4 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(15 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right)^{4} + 4 \, a^{5} - 2 \, a^{4} b + 2 \, a^{2} b^{3} - 4 \, a b^{4} + 6 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 2 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \sinh\left(x\right)^{2} + 3 \, {\left(a^{5} + a^{4} b\right)} x - 3 \, {\left(b^{5} \cosh\left(x\right)^{6} + 6 \, b^{5} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{5} \sinh\left(x\right)^{6} + 3 \, b^{5} \cosh\left(x\right)^{4} + 3 \, b^{5} \cosh\left(x\right)^{2} + b^{5} + 3 \, {\left(5 \, b^{5} \cosh\left(x\right)^{2} + b^{5}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{5} \cosh\left(x\right)^{3} + 3 \, b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{5} \cosh\left(x\right)^{4} + 6 \, b^{5} \cosh\left(x\right)^{2} + b^{5}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b^{5} \cosh\left(x\right)^{5} + 2 \, b^{5} \cosh\left(x\right)^{3} + b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - 3 \, {\left({\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} b - b^{5}\right)} \sinh\left(x\right)^{6} + a^{4} b - b^{5} + 3 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} b - b^{5} + 5 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{4} b - b^{5} + 5 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} b - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 6 \, {\left(3 \, {\left(a^{5} + a^{4} b\right)} x \cosh\left(x\right)^{5} + 2 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 2 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{5} - 2 \, a^{4} b + 2 \, a^{2} b^{3} - 4 \, a b^{4} + 3 \, {\left(a^{5} + a^{4} b\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{6} - a^{4} b^{2}\right)} \sinh\left(x\right)^{6} + a^{6} - a^{4} b^{2} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{6} - a^{4} b^{2} + 5 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{6} - a^{4} b^{2} + 5 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"1/3*(3*(a^5 + a^4*b)*x*cosh(x)^6 + 18*(a^5 + a^4*b)*x*cosh(x)*sinh(x)^5 + 3*(a^5 + a^4*b)*x*sinh(x)^6 + 8*a^5 - 2*a^3*b^2 - 6*a*b^4 + 3*(4*a^5 - 2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 2*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x)^4 + 3*(4*a^5 - 2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 2*a*b^4 + 15*(a^5 + a^4*b)*x*cosh(x)^2 + 3*(a^5 + a^4*b)*x)*sinh(x)^4 + 12*(5*(a^5 + a^4*b)*x*cosh(x)^3 + (4*a^5 - 2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 2*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x))*sinh(x)^3 + 3*(4*a^5 - 2*a^4*b + 2*a^2*b^3 - 4*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x)^2 + 3*(15*(a^5 + a^4*b)*x*cosh(x)^4 + 4*a^5 - 2*a^4*b + 2*a^2*b^3 - 4*a*b^4 + 6*(4*a^5 - 2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 2*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x)^2 + 3*(a^5 + a^4*b)*x)*sinh(x)^2 + 3*(a^5 + a^4*b)*x - 3*(b^5*cosh(x)^6 + 6*b^5*cosh(x)*sinh(x)^5 + b^5*sinh(x)^6 + 3*b^5*cosh(x)^4 + 3*b^5*cosh(x)^2 + b^5 + 3*(5*b^5*cosh(x)^2 + b^5)*sinh(x)^4 + 4*(5*b^5*cosh(x)^3 + 3*b^5*cosh(x))*sinh(x)^3 + 3*(5*b^5*cosh(x)^4 + 6*b^5*cosh(x)^2 + b^5)*sinh(x)^2 + 6*(b^5*cosh(x)^5 + 2*b^5*cosh(x)^3 + b^5*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - 3*((a^4*b - b^5)*cosh(x)^6 + 6*(a^4*b - b^5)*cosh(x)*sinh(x)^5 + (a^4*b - b^5)*sinh(x)^6 + a^4*b - b^5 + 3*(a^4*b - b^5)*cosh(x)^4 + 3*(a^4*b - b^5 + 5*(a^4*b - b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^4*b - b^5)*cosh(x)^3 + 3*(a^4*b - b^5)*cosh(x))*sinh(x)^3 + 3*(a^4*b - b^5)*cosh(x)^2 + 3*(a^4*b - b^5 + 5*(a^4*b - b^5)*cosh(x)^4 + 6*(a^4*b - b^5)*cosh(x)^2)*sinh(x)^2 + 6*((a^4*b - b^5)*cosh(x)^5 + 2*(a^4*b - b^5)*cosh(x)^3 + (a^4*b - b^5)*cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 6*(3*(a^5 + a^4*b)*x*cosh(x)^5 + 2*(4*a^5 - 2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 2*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x)^3 + (4*a^5 - 2*a^4*b + 2*a^2*b^3 - 4*a*b^4 + 3*(a^5 + a^4*b)*x)*cosh(x))*sinh(x))/((a^6 - a^4*b^2)*cosh(x)^6 + 6*(a^6 - a^4*b^2)*cosh(x)*sinh(x)^5 + (a^6 - a^4*b^2)*sinh(x)^6 + a^6 - a^4*b^2 + 3*(a^6 - a^4*b^2)*cosh(x)^4 + 3*(a^6 - a^4*b^2 + 5*(a^6 - a^4*b^2)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^6 - a^4*b^2)*cosh(x)^3 + 3*(a^6 - a^4*b^2)*cosh(x))*sinh(x)^3 + 3*(a^6 - a^4*b^2)*cosh(x)^2 + 3*(a^6 - a^4*b^2 + 5*(a^6 - a^4*b^2)*cosh(x)^4 + 6*(a^6 - a^4*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((a^6 - a^4*b^2)*cosh(x)^5 + 2*(a^6 - a^4*b^2)*cosh(x)^3 + (a^6 - a^4*b^2)*cosh(x))*sinh(x))","B",0
141,1,637,0,0.434747," ","integrate(tanh(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{{\left(a^{4} + a^{3} b\right)} x \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} + a^{3} b\right)} x \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} + a^{3} b\right)} x \sinh\left(x\right)^{4} + 2 \, a^{3} b - 2 \, a b^{3} - 2 \, {\left(a^{4} - a^{3} b - a^{2} b^{2} + a b^{3} - {\left(a^{4} + a^{3} b\right)} x\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{4} - a^{3} b - a^{2} b^{2} + a b^{3} - 3 \, {\left(a^{4} + a^{3} b\right)} x \cosh\left(x\right)^{2} - {\left(a^{4} + a^{3} b\right)} x\right)} \sinh\left(x\right)^{2} + {\left(a^{4} + a^{3} b\right)} x - {\left(b^{4} \cosh\left(x\right)^{4} + 4 \, b^{4} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{4} \sinh\left(x\right)^{4} + 2 \, b^{4} \cosh\left(x\right)^{2} + b^{4} + 2 \, {\left(3 \, b^{4} \cosh\left(x\right)^{2} + b^{4}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b^{4} \cosh\left(x\right)^{3} + b^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left({\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} - b^{4}\right)} \sinh\left(x\right)^{4} + a^{4} - b^{4} + 2 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} - b^{4} + 3 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left({\left(a^{4} + a^{3} b\right)} x \cosh\left(x\right)^{3} - {\left(a^{4} - a^{3} b - a^{2} b^{2} + a b^{3} - {\left(a^{4} + a^{3} b\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{a^{5} - a^{3} b^{2} + {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} - a^{3} b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} - a^{3} b^{2} + 3 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}"," ",0,"-((a^4 + a^3*b)*x*cosh(x)^4 + 4*(a^4 + a^3*b)*x*cosh(x)*sinh(x)^3 + (a^4 + a^3*b)*x*sinh(x)^4 + 2*a^3*b - 2*a*b^3 - 2*(a^4 - a^3*b - a^2*b^2 + a*b^3 - (a^4 + a^3*b)*x)*cosh(x)^2 - 2*(a^4 - a^3*b - a^2*b^2 + a*b^3 - 3*(a^4 + a^3*b)*x*cosh(x)^2 - (a^4 + a^3*b)*x)*sinh(x)^2 + (a^4 + a^3*b)*x - (b^4*cosh(x)^4 + 4*b^4*cosh(x)*sinh(x)^3 + b^4*sinh(x)^4 + 2*b^4*cosh(x)^2 + b^4 + 2*(3*b^4*cosh(x)^2 + b^4)*sinh(x)^2 + 4*(b^4*cosh(x)^3 + b^4*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - ((a^4 - b^4)*cosh(x)^4 + 4*(a^4 - b^4)*cosh(x)*sinh(x)^3 + (a^4 - b^4)*sinh(x)^4 + a^4 - b^4 + 2*(a^4 - b^4)*cosh(x)^2 + 2*(a^4 - b^4 + 3*(a^4 - b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 - b^4)*cosh(x)^3 + (a^4 - b^4)*cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 4*((a^4 + a^3*b)*x*cosh(x)^3 - (a^4 - a^3*b - a^2*b^2 + a*b^3 - (a^4 + a^3*b)*x)*cosh(x))*sinh(x))/(a^5 - a^3*b^2 + (a^5 - a^3*b^2)*cosh(x)^4 + 4*(a^5 - a^3*b^2)*cosh(x)*sinh(x)^3 + (a^5 - a^3*b^2)*sinh(x)^4 + 2*(a^5 - a^3*b^2)*cosh(x)^2 + 2*(a^5 - a^3*b^2 + 3*(a^5 - a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 - a^3*b^2)*cosh(x)^3 + (a^5 - a^3*b^2)*cosh(x))*sinh(x))","B",0
142,1,264,0,0.440328," ","integrate(tanh(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a^{3} + a^{2} b\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b\right)} x \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{3} + a^{2} b\right)} x \sinh\left(x\right)^{2} + 2 \, a^{3} - 2 \, a b^{2} + {\left(a^{3} + a^{2} b\right)} x - {\left(b^{3} \cosh\left(x\right)^{2} + 2 \, b^{3} \cosh\left(x\right) \sinh\left(x\right) + b^{3} \sinh\left(x\right)^{2} + b^{3}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(a^{2} b - b^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{2}\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{4} - a^{2} b^{2} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{4} - a^{2} b^{2}\right)} \sinh\left(x\right)^{2}}"," ",0,"((a^3 + a^2*b)*x*cosh(x)^2 + 2*(a^3 + a^2*b)*x*cosh(x)*sinh(x) + (a^3 + a^2*b)*x*sinh(x)^2 + 2*a^3 - 2*a*b^2 + (a^3 + a^2*b)*x - (b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2 + b^3)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - (a^2*b - b^3 + (a^2*b - b^3)*cosh(x)^2 + 2*(a^2*b - b^3)*cosh(x)*sinh(x) + (a^2*b - b^3)*sinh(x)^2)*log(2*cosh(x)/(cosh(x) - sinh(x))))/(a^4 - a^2*b^2 + (a^4 - a^2*b^2)*cosh(x)^2 + 2*(a^4 - a^2*b^2)*cosh(x)*sinh(x) + (a^4 - a^2*b^2)*sinh(x)^2)","B",0
143,1,73,0,0.454272," ","integrate(tanh(x)/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{b^{2} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(a^{2} + a b\right)} x + {\left(a^{2} - b^{2}\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{3} - a b^{2}}"," ",0,"(b^2*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - (a^2 + a*b)*x + (a^2 - b^2)*log(2*cosh(x)/(cosh(x) - sinh(x))))/(a^3 - a*b^2)","A",0
144,1,42,0,0.401601," ","integrate(1/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} x - b \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{2} - b^{2}}"," ",0,"((a + b)*x - b*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))))/(a^2 - b^2)","A",0
145,1,43,0,0.438712," ","integrate(coth(x)/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} x - a \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{2} - b^{2}}"," ",0,"-((a + b)*x - a*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))))/(a^2 - b^2)","A",0
146,1,76,0,0.440492," ","integrate(coth(x)^2/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{a^{2} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(a b + b^{2}\right)} x - {\left(a^{2} - b^{2}\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{2} b - b^{3}}"," ",0,"-(a^2*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - (a*b + b^2)*x - (a^2 - b^2)*log(2*sinh(x)/(cosh(x) - sinh(x))))/(a^2*b - b^3)","A",0
147,1,271,0,0.446453," ","integrate(coth(x)^3/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a b^{2} + b^{3}\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} + b^{3}\right)} x \cosh\left(x\right) \sinh\left(x\right) + {\left(a b^{2} + b^{3}\right)} x \sinh\left(x\right)^{2} + 2 \, a^{2} b - 2 \, b^{3} - {\left(a b^{2} + b^{3}\right)} x - {\left(a^{3} \cosh\left(x\right)^{2} + 2 \, a^{3} \cosh\left(x\right) \sinh\left(x\right) + a^{3} \sinh\left(x\right)^{2} - a^{3}\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(a^{3} - a b^{2} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{3} - a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{2} b^{2} - b^{4} - {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b^{2} - b^{4}\right)} \sinh\left(x\right)^{2}}"," ",0,"((a*b^2 + b^3)*x*cosh(x)^2 + 2*(a*b^2 + b^3)*x*cosh(x)*sinh(x) + (a*b^2 + b^3)*x*sinh(x)^2 + 2*a^2*b - 2*b^3 - (a*b^2 + b^3)*x - (a^3*cosh(x)^2 + 2*a^3*cosh(x)*sinh(x) + a^3*sinh(x)^2 - a^3)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) - (a^3 - a*b^2 - (a^3 - a*b^2)*cosh(x)^2 - 2*(a^3 - a*b^2)*cosh(x)*sinh(x) - (a^3 - a*b^2)*sinh(x)^2)*log(2*sinh(x)/(cosh(x) - sinh(x))))/(a^2*b^2 - b^4 - (a^2*b^2 - b^4)*cosh(x)^2 - 2*(a^2*b^2 - b^4)*cosh(x)*sinh(x) - (a^2*b^2 - b^4)*sinh(x)^2)","B",0
148,1,648,0,0.449864," ","integrate(coth(x)^4/(a+b*coth(x)),x, algorithm=""fricas"")","\frac{{\left(a b^{3} + b^{4}\right)} x \cosh\left(x\right)^{4} + 4 \, {\left(a b^{3} + b^{4}\right)} x \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{3} + b^{4}\right)} x \sinh\left(x\right)^{4} - 2 \, a^{3} b + 2 \, a b^{3} + 2 \, {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4} - {\left(a b^{3} + b^{4}\right)} x\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4} + 3 \, {\left(a b^{3} + b^{4}\right)} x \cosh\left(x\right)^{2} - {\left(a b^{3} + b^{4}\right)} x\right)} \sinh\left(x\right)^{2} + {\left(a b^{3} + b^{4}\right)} x - {\left(a^{4} \cosh\left(x\right)^{4} + 4 \, a^{4} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{4} \sinh\left(x\right)^{4} - 2 \, a^{4} \cosh\left(x\right)^{2} + a^{4} + 2 \, {\left(3 \, a^{4} \cosh\left(x\right)^{2} - a^{4}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{4} \cosh\left(x\right)^{3} - a^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + {\left({\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} - b^{4}\right)} \sinh\left(x\right)^{4} + a^{4} - b^{4} - 2 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{4} - b^{4} - 3 \, {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} - b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{4} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left({\left(a b^{3} + b^{4}\right)} x \cosh\left(x\right)^{3} + {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4} - {\left(a b^{3} + b^{4}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{a^{2} b^{3} - b^{5} + {\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} b^{3} - b^{5}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b^{3} - b^{5} - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} b^{3} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}"," ",0,"((a*b^3 + b^4)*x*cosh(x)^4 + 4*(a*b^3 + b^4)*x*cosh(x)*sinh(x)^3 + (a*b^3 + b^4)*x*sinh(x)^4 - 2*a^3*b + 2*a*b^3 + 2*(a^3*b - a^2*b^2 - a*b^3 + b^4 - (a*b^3 + b^4)*x)*cosh(x)^2 + 2*(a^3*b - a^2*b^2 - a*b^3 + b^4 + 3*(a*b^3 + b^4)*x*cosh(x)^2 - (a*b^3 + b^4)*x)*sinh(x)^2 + (a*b^3 + b^4)*x - (a^4*cosh(x)^4 + 4*a^4*cosh(x)*sinh(x)^3 + a^4*sinh(x)^4 - 2*a^4*cosh(x)^2 + a^4 + 2*(3*a^4*cosh(x)^2 - a^4)*sinh(x)^2 + 4*(a^4*cosh(x)^3 - a^4*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + ((a^4 - b^4)*cosh(x)^4 + 4*(a^4 - b^4)*cosh(x)*sinh(x)^3 + (a^4 - b^4)*sinh(x)^4 + a^4 - b^4 - 2*(a^4 - b^4)*cosh(x)^2 - 2*(a^4 - b^4 - 3*(a^4 - b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 - b^4)*cosh(x)^3 - (a^4 - b^4)*cosh(x))*sinh(x))*log(2*sinh(x)/(cosh(x) - sinh(x))) + 4*((a*b^3 + b^4)*x*cosh(x)^3 + (a^3*b - a^2*b^2 - a*b^3 + b^4 - (a*b^3 + b^4)*x)*cosh(x))*sinh(x))/(a^2*b^3 - b^5 + (a^2*b^3 - b^5)*cosh(x)^4 + 4*(a^2*b^3 - b^5)*cosh(x)*sinh(x)^3 + (a^2*b^3 - b^5)*sinh(x)^4 - 2*(a^2*b^3 - b^5)*cosh(x)^2 - 2*(a^2*b^3 - b^5 - 3*(a^2*b^3 - b^5)*cosh(x)^2)*sinh(x)^2 + 4*((a^2*b^3 - b^5)*cosh(x)^3 - (a^2*b^3 - b^5)*cosh(x))*sinh(x))","B",0
149,1,1299,0,0.457123," ","integrate(coth(x)^5/(a+b*coth(x)),x, algorithm=""fricas"")","-\frac{3 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right)^{6} + 18 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right) \sinh\left(x\right)^{5} + 3 \, {\left(a b^{4} + b^{5}\right)} x \sinh\left(x\right)^{6} + 6 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5} + 3 \, {\left(2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)^{4} + 3 \, {\left(2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} - 4 \, b^{5} + 15 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right)^{2} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \sinh\left(x\right)^{4} + 12 \, {\left(5 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right)^{3} + {\left(2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(15 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right)^{4} - 4 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a b^{4} + 4 \, b^{5} + 6 \, {\left(2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \sinh\left(x\right)^{2} - 3 \, {\left(a b^{4} + b^{5}\right)} x - 3 \, {\left(a^{5} \cosh\left(x\right)^{6} + 6 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{5} \sinh\left(x\right)^{6} - 3 \, a^{5} \cosh\left(x\right)^{4} + 3 \, a^{5} \cosh\left(x\right)^{2} - a^{5} + 3 \, {\left(5 \, a^{5} \cosh\left(x\right)^{2} - a^{5}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{5} \cosh\left(x\right)^{3} - 3 \, a^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{5} \cosh\left(x\right)^{4} - 6 \, a^{5} \cosh\left(x\right)^{2} + a^{5}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a^{5} \cosh\left(x\right)^{5} - 2 \, a^{5} \cosh\left(x\right)^{3} + a^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} - a b^{4}\right)} \sinh\left(x\right)^{6} - a^{5} + a b^{4} - 3 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{5} - a b^{4} - 5 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{5} - a b^{4} + 5 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 6 \, {\left(3 \, {\left(a b^{4} + b^{5}\right)} x \cosh\left(x\right)^{5} + 2 \, {\left(2 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a b^{4} - 4 \, b^{5} - 3 \, {\left(a b^{4} + b^{5}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{6} - a^{2} b^{4} + b^{6} - 3 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{2} b^{4} - b^{6} - 5 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{2} b^{4} - b^{6} + 5 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/3*(3*(a*b^4 + b^5)*x*cosh(x)^6 + 18*(a*b^4 + b^5)*x*cosh(x)*sinh(x)^5 + 3*(a*b^4 + b^5)*x*sinh(x)^6 + 6*a^4*b + 2*a^2*b^3 - 8*b^5 + 3*(2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x)^4 + 3*(2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - 4*b^5 + 15*(a*b^4 + b^5)*x*cosh(x)^2 - 3*(a*b^4 + b^5)*x)*sinh(x)^4 + 12*(5*(a*b^4 + b^5)*x*cosh(x)^3 + (2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x))*sinh(x)^3 - 3*(4*a^4*b - 2*a^3*b^2 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x)^2 + 3*(15*(a*b^4 + b^5)*x*cosh(x)^4 - 4*a^4*b + 2*a^3*b^2 - 2*a*b^4 + 4*b^5 + 6*(2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x)^2 + 3*(a*b^4 + b^5)*x)*sinh(x)^2 - 3*(a*b^4 + b^5)*x - 3*(a^5*cosh(x)^6 + 6*a^5*cosh(x)*sinh(x)^5 + a^5*sinh(x)^6 - 3*a^5*cosh(x)^4 + 3*a^5*cosh(x)^2 - a^5 + 3*(5*a^5*cosh(x)^2 - a^5)*sinh(x)^4 + 4*(5*a^5*cosh(x)^3 - 3*a^5*cosh(x))*sinh(x)^3 + 3*(5*a^5*cosh(x)^4 - 6*a^5*cosh(x)^2 + a^5)*sinh(x)^2 + 6*(a^5*cosh(x)^5 - 2*a^5*cosh(x)^3 + a^5*cosh(x))*sinh(x))*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))) + 3*((a^5 - a*b^4)*cosh(x)^6 + 6*(a^5 - a*b^4)*cosh(x)*sinh(x)^5 + (a^5 - a*b^4)*sinh(x)^6 - a^5 + a*b^4 - 3*(a^5 - a*b^4)*cosh(x)^4 - 3*(a^5 - a*b^4 - 5*(a^5 - a*b^4)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 - a*b^4)*cosh(x)^3 - 3*(a^5 - a*b^4)*cosh(x))*sinh(x)^3 + 3*(a^5 - a*b^4)*cosh(x)^2 + 3*(a^5 - a*b^4 + 5*(a^5 - a*b^4)*cosh(x)^4 - 6*(a^5 - a*b^4)*cosh(x)^2)*sinh(x)^2 + 6*((a^5 - a*b^4)*cosh(x)^5 - 2*(a^5 - a*b^4)*cosh(x)^3 + (a^5 - a*b^4)*cosh(x))*sinh(x))*log(2*sinh(x)/(cosh(x) - sinh(x))) + 6*(3*(a*b^4 + b^5)*x*cosh(x)^5 + 2*(2*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x)^3 - (4*a^4*b - 2*a^3*b^2 + 2*a*b^4 - 4*b^5 - 3*(a*b^4 + b^5)*x)*cosh(x))*sinh(x))/((a^2*b^4 - b^6)*cosh(x)^6 + 6*(a^2*b^4 - b^6)*cosh(x)*sinh(x)^5 + (a^2*b^4 - b^6)*sinh(x)^6 - a^2*b^4 + b^6 - 3*(a^2*b^4 - b^6)*cosh(x)^4 - 3*(a^2*b^4 - b^6 - 5*(a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^2*b^4 - b^6)*cosh(x)^3 - 3*(a^2*b^4 - b^6)*cosh(x))*sinh(x)^3 + 3*(a^2*b^4 - b^6)*cosh(x)^2 + 3*(a^2*b^4 - b^6 + 5*(a^2*b^4 - b^6)*cosh(x)^4 - 6*(a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^2 + 6*((a^2*b^4 - b^6)*cosh(x)^5 - 2*(a^2*b^4 - b^6)*cosh(x)^3 + (a^2*b^4 - b^6)*cosh(x))*sinh(x))","B",0
150,1,184,0,0.402604," ","integrate(x*csch(x)^2/(a+b*coth(x))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a + b\right)} x \cosh\left(x\right)^{2} + 4 \, {\left(a + b\right)} x \cosh\left(x\right) \sinh\left(x\right) + 2 \, {\left(a + b\right)} x \sinh\left(x\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)} \log\left(\frac{2 \, {\left(b \cosh\left(x\right) + a \sinh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a^{3} - a^{2} b - a b^{2} + b^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \sinh\left(x\right)^{2}}"," ",0,"(2*(a + b)*x*cosh(x)^2 + 4*(a + b)*x*cosh(x)*sinh(x) + 2*(a + b)*x*sinh(x)^2 - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a + b)*log(2*(b*cosh(x) + a*sinh(x))/(cosh(x) - sinh(x))))/(a^3 - a^2*b - a*b^2 + b^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)*sinh(x) - (a^3 + a^2*b - a*b^2 - b^3)*sinh(x)^2)","B",0
151,1,28,0,0.388009," ","integrate(x^3*coth(a+2*log(x)),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(x^{4} e^{\left(2 \, a\right)} + 2 \, \log\left(x^{4} e^{\left(2 \, a\right)} - 1\right)\right)} e^{\left(-2 \, a\right)}"," ",0,"1/4*(x^4*e^(2*a) + 2*log(x^4*e^(2*a) - 1))*e^(-2*a)","A",0
152,1,62,0,0.402366," ","integrate(x^2*coth(a+2*log(x)),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{3} e^{\left(2 \, a\right)} + 6 \, \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} + 3 \, e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} - 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right)\right)} e^{\left(-2 \, a\right)}"," ",0,"1/6*(2*x^3*e^(2*a) + 6*arctan(x*e^(1/2*a))*e^(1/2*a) + 3*e^(1/2*a)*log((x^2*e^a - 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)))*e^(-2*a)","A",0
153,1,33,0,0.428728," ","integrate(x*coth(a+2*log(x)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} e^{a} - \log\left(x^{2} e^{a} + 1\right) + \log\left(x^{2} e^{a} - 1\right)\right)} e^{\left(-a\right)}"," ",0,"1/2*(x^2*e^a - log(x^2*e^a + 1) + log(x^2*e^a - 1))*e^(-a)","A",0
154,1,58,0,0.406519," ","integrate(coth(a+2*log(x)),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(2 \, \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} - 2 \, x e^{a} - e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} - 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right)\right)} e^{\left(-a\right)}"," ",0,"-1/2*(2*arctan(x*e^(1/2*a))*e^(1/2*a) - 2*x*e^a - e^(1/2*a)*log((x^2*e^a - 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)))*e^(-a)","B",0
155,1,18,0,0.424038," ","integrate(coth(a+2*log(x))/x,x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{4} e^{\left(2 \, a\right)} - 1\right) - \log\left(x\right)"," ",0,"1/2*log(x^4*e^(2*a) - 1) - log(x)","A",0
156,1,54,0,0.418243," ","integrate(coth(a+2*log(x))/x^2,x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} + x e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} - 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right) + 2}{2 \, x}"," ",0,"1/2*(2*x*arctan(x*e^(1/2*a))*e^(1/2*a) + x*e^(1/2*a)*log((x^2*e^a - 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)) + 2)/x","A",0
157,1,38,0,0.407205," ","integrate(coth(a+2*log(x))/x^3,x, algorithm=""fricas"")","-\frac{x^{2} e^{a} \log\left(x^{2} e^{a} + 1\right) - x^{2} e^{a} \log\left(x^{2} e^{a} - 1\right) - 1}{2 \, x^{2}}"," ",0,"-1/2*(x^2*e^a*log(x^2*e^a + 1) - x^2*e^a*log(x^2*e^a - 1) - 1)/x^2","B",0
158,1,61,0,0.388948," ","integrate(x^3*coth(a+2*log(x))^2,x, algorithm=""fricas"")","\frac{x^{8} e^{\left(4 \, a\right)} - x^{4} e^{\left(2 \, a\right)} + 4 \, {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \log\left(x^{4} e^{\left(2 \, a\right)} - 1\right) - 4}{4 \, {\left(x^{4} e^{\left(4 \, a\right)} - e^{\left(2 \, a\right)}\right)}}"," ",0,"1/4*(x^8*e^(4*a) - x^4*e^(2*a) + 4*(x^4*e^(2*a) - 1)*log(x^4*e^(2*a) - 1) - 4)/(x^4*e^(4*a) - e^(2*a))","A",0
159,1,104,0,0.413516," ","integrate(x^2*coth(a+2*log(x))^2,x, algorithm=""fricas"")","\frac{4 \, x^{7} e^{\left(4 \, a\right)} - 16 \, x^{3} e^{\left(2 \, a\right)} + 18 \, {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} + 9 \, {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} - 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right)}{12 \, {\left(x^{4} e^{\left(4 \, a\right)} - e^{\left(2 \, a\right)}\right)}}"," ",0,"1/12*(4*x^7*e^(4*a) - 16*x^3*e^(2*a) + 18*(x^4*e^(2*a) - 1)*arctan(x*e^(1/2*a))*e^(1/2*a) + 9*(x^4*e^(2*a) - 1)*e^(1/2*a)*log((x^2*e^a - 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)))/(x^4*e^(4*a) - e^(2*a))","B",0
160,1,74,0,0.400654," ","integrate(x*coth(a+2*log(x))^2,x, algorithm=""fricas"")","\frac{x^{6} e^{\left(3 \, a\right)} - 3 \, x^{2} e^{a} - {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \log\left(x^{2} e^{a} + 1\right) + {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \log\left(x^{2} e^{a} - 1\right)}{2 \, {\left(x^{4} e^{\left(3 \, a\right)} - e^{a}\right)}}"," ",0,"1/2*(x^6*e^(3*a) - 3*x^2*e^a - (x^4*e^(2*a) - 1)*log(x^2*e^a + 1) + (x^4*e^(2*a) - 1)*log(x^2*e^a - 1))/(x^4*e^(3*a) - e^a)","B",0
161,1,97,0,0.408405," ","integrate(coth(a+2*log(x))^2,x, algorithm=""fricas"")","\frac{4 \, x^{5} e^{\left(3 \, a\right)} - 2 \, {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} + {\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} - 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right) - 8 \, x e^{a}}{4 \, {\left(x^{4} e^{\left(3 \, a\right)} - e^{a}\right)}}"," ",0,"1/4*(4*x^5*e^(3*a) - 2*(x^4*e^(2*a) - 1)*arctan(x*e^(1/2*a))*e^(1/2*a) + (x^4*e^(2*a) - 1)*e^(1/2*a)*log((x^2*e^a - 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)) - 8*x*e^a)/(x^4*e^(3*a) - e^a)","B",0
162,1,28,0,0.432253," ","integrate(coth(a+2*log(x))^2/x,x, algorithm=""fricas"")","\frac{{\left(x^{4} e^{\left(2 \, a\right)} - 1\right)} \log\left(x\right) - 1}{x^{4} e^{\left(2 \, a\right)} - 1}"," ",0,"((x^4*e^(2*a) - 1)*log(x) - 1)/(x^4*e^(2*a) - 1)","B",0
163,1,97,0,0.412546," ","integrate(coth(a+2*log(x))^2/x^2,x, algorithm=""fricas"")","-\frac{8 \, x^{4} e^{\left(2 \, a\right)} + 2 \, {\left(x^{5} e^{\left(2 \, a\right)} - x\right)} \arctan\left(x e^{\left(\frac{1}{2} \, a\right)}\right) e^{\left(\frac{1}{2} \, a\right)} - {\left(x^{5} e^{\left(2 \, a\right)} - x\right)} e^{\left(\frac{1}{2} \, a\right)} \log\left(\frac{x^{2} e^{a} + 2 \, x e^{\left(\frac{1}{2} \, a\right)} + 1}{x^{2} e^{a} - 1}\right) - 4}{4 \, {\left(x^{5} e^{\left(2 \, a\right)} - x\right)}}"," ",0,"-1/4*(8*x^4*e^(2*a) + 2*(x^5*e^(2*a) - x)*arctan(x*e^(1/2*a))*e^(1/2*a) - (x^5*e^(2*a) - x)*e^(1/2*a)*log((x^2*e^a + 2*x*e^(1/2*a) + 1)/(x^2*e^a - 1)) - 4)/(x^5*e^(2*a) - x)","A",0
164,1,82,0,0.396306," ","integrate(coth(a+2*log(x))^2/x^3,x, algorithm=""fricas"")","-\frac{3 \, x^{4} e^{\left(2 \, a\right)} - {\left(x^{6} e^{\left(3 \, a\right)} - x^{2} e^{a}\right)} \log\left(x^{2} e^{a} + 1\right) + {\left(x^{6} e^{\left(3 \, a\right)} - x^{2} e^{a}\right)} \log\left(x^{2} e^{a} - 1\right) - 1}{2 \, {\left(x^{6} e^{\left(2 \, a\right)} - x^{2}\right)}}"," ",0,"-1/2*(3*x^4*e^(2*a) - (x^6*e^(3*a) - x^2*e^a)*log(x^2*e^a + 1) + (x^6*e^(3*a) - x^2*e^a)*log(x^2*e^a - 1) - 1)/(x^6*e^(2*a) - x^2)","A",0
165,0,0,0,0.405070," ","integrate((e*x)^m*coth(a+2*log(x)),x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(a + 2 \, \log\left(x\right)\right), x\right)"," ",0,"integral((e*x)^m*coth(a + 2*log(x)), x)","F",0
166,0,0,0,0.404042," ","integrate((e*x)^m*coth(a+2*log(x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(a + 2 \, \log\left(x\right)\right)^{2}, x\right)"," ",0,"integral((e*x)^m*coth(a + 2*log(x))^2, x)","F",0
167,0,0,0,0.398713," ","integrate((e*x)^m*coth(a+2*log(x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(a + 2 \, \log\left(x\right)\right)^{3}, x\right)"," ",0,"integral((e*x)^m*coth(a + 2*log(x))^3, x)","F",0
168,0,0,0,0.406621," ","integrate(coth(a+b*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(b \log\left(x\right) + a\right)^{p}, x\right)"," ",0,"integral(coth(b*log(x) + a)^p, x)","F",0
169,0,0,0,0.406752," ","integrate((e*x)^m*coth(a+b*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(b \log\left(x\right) + a\right)^{p}, x\right)"," ",0,"integral((e*x)^m*coth(b*log(x) + a)^p, x)","F",0
170,0,0,0,0.408938," ","integrate(coth(a+1/2*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + \frac{1}{2} \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 1/2*log(x))^p, x)","F",0
171,0,0,0,0.442209," ","integrate(coth(a+1/4*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + \frac{1}{4} \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 1/4*log(x))^p, x)","F",0
172,0,0,0,0.856715," ","integrate(coth(a+1/6*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + \frac{1}{6} \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 1/6*log(x))^p, x)","F",0
173,0,0,0,1.748685," ","integrate(coth(a+1/8*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + \frac{1}{8} \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 1/8*log(x))^p, x)","F",0
174,0,0,0,0.414955," ","integrate(coth(a+log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + log(x))^p, x)","F",0
175,0,0,0,0.406158," ","integrate(coth(a+2*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + 2 \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 2*log(x))^p, x)","F",0
176,0,0,0,0.422344," ","integrate(coth(a+3*log(x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(a + 3 \, \log\left(x\right)\right)^{p}, x\right)"," ",0,"integral(coth(a + 3*log(x))^p, x)","F",0
177,0,0,0,0.402756," ","integrate(x^3*coth(d*(a+b*log(c*x^n))),x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \coth\left(b d \log\left(c x^{n}\right) + a d\right), x\right)"," ",0,"integral(x^3*coth(b*d*log(c*x^n) + a*d), x)","F",0
178,0,0,0,0.436515," ","integrate(x^2*coth(d*(a+b*log(c*x^n))),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \coth\left(b d \log\left(c x^{n}\right) + a d\right), x\right)"," ",0,"integral(x^2*coth(b*d*log(c*x^n) + a*d), x)","F",0
179,0,0,0,0.442095," ","integrate(x*coth(d*(a+b*log(c*x^n))),x, algorithm=""fricas"")","{\rm integral}\left(x \coth\left(b d \log\left(c x^{n}\right) + a d\right), x\right)"," ",0,"integral(x*coth(b*d*log(c*x^n) + a*d), x)","F",0
180,0,0,0,0.402179," ","integrate(coth(d*(a+b*log(c*x^n))),x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(b d \log\left(c x^{n}\right) + a d\right), x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d), x)","F",0
181,1,76,0,0.414922," ","integrate(coth(d*(a+b*log(c*x^n)))/x,x, algorithm=""fricas"")","-\frac{b d n \log\left(x\right) - \log\left(\frac{2 \, \sinh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right)}{\cosh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right) - \sinh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right)}\right)}{b d n}"," ",0,"-(b*d*n*log(x) - log(2*sinh(b*d*n*log(x) + b*d*log(c) + a*d)/(cosh(b*d*n*log(x) + b*d*log(c) + a*d) - sinh(b*d*n*log(x) + b*d*log(c) + a*d))))/(b*d*n)","B",0
182,0,0,0,0.410889," ","integrate(coth(d*(a+b*log(c*x^n)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b d \log\left(c x^{n}\right) + a d\right)}{x^{2}}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)/x^2, x)","F",0
183,0,0,0,0.415451," ","integrate(coth(d*(a+b*log(c*x^n)))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b d \log\left(c x^{n}\right) + a d\right)}{x^{3}}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)/x^3, x)","F",0
184,0,0,0,0.411406," ","integrate(x^3*coth(d*(a+b*log(c*x^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}, x\right)"," ",0,"integral(x^3*coth(b*d*log(c*x^n) + a*d)^2, x)","F",0
185,0,0,0,0.421588," ","integrate(x^2*coth(d*(a+b*log(c*x^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}, x\right)"," ",0,"integral(x^2*coth(b*d*log(c*x^n) + a*d)^2, x)","F",0
186,0,0,0,0.411864," ","integrate(x*coth(d*(a+b*log(c*x^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(x \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}, x\right)"," ",0,"integral(x*coth(b*d*log(c*x^n) + a*d)^2, x)","F",0
187,0,0,0,0.416790," ","integrate(coth(d*(a+b*log(c*x^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)^2, x)","F",0
188,1,72,0,0.430694," ","integrate(coth(d*(a+b*log(c*x^n)))^2/x,x, algorithm=""fricas"")","\frac{{\left(b d n \log\left(x\right) + 1\right)} \sinh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right) - \cosh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right)}{b d n \sinh\left(b d n \log\left(x\right) + b d \log\left(c\right) + a d\right)}"," ",0,"((b*d*n*log(x) + 1)*sinh(b*d*n*log(x) + b*d*log(c) + a*d) - cosh(b*d*n*log(x) + b*d*log(c) + a*d))/(b*d*n*sinh(b*d*n*log(x) + b*d*log(c) + a*d))","B",0
189,0,0,0,0.416414," ","integrate(coth(d*(a+b*log(c*x^n)))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)^2/x^2, x)","F",0
190,0,0,0,0.534543," ","integrate(coth(d*(a+b*log(c*x^n)))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)^2/x^3, x)","F",0
191,1,572,0,0.631716," ","integrate(coth(a+b*log(c*x^n))^3/x,x, algorithm=""fricas"")","-\frac{b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} \log\left(x\right) + 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \log\left(x\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + b n \log\left(x\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 2 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n \log\left(x\right) + 2 \, {\left(3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} \log\left(x\right) - b n \log\left(x\right) + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 1\right)} \log\left(\frac{2 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}\right) + 4 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} \log\left(x\right) - {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 2 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, {\left(3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n + 4 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}"," ",0,"-(b*n*cosh(b*n*log(x) + b*log(c) + a)^4*log(x) + 4*b*n*cosh(b*n*log(x) + b*log(c) + a)*log(x)*sinh(b*n*log(x) + b*log(c) + a)^3 + b*n*log(x)*sinh(b*n*log(x) + b*log(c) + a)^4 - 2*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^2 + b*n*log(x) + 2*(3*b*n*cosh(b*n*log(x) + b*log(c) + a)^2*log(x) - b*n*log(x) + 1)*sinh(b*n*log(x) + b*log(c) + a)^2 - (cosh(b*n*log(x) + b*log(c) + a)^4 + 4*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + sinh(b*n*log(x) + b*log(c) + a)^4 + 2*(3*cosh(b*n*log(x) + b*log(c) + a)^2 - 1)*sinh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)^2 + 4*(cosh(b*n*log(x) + b*log(c) + a)^3 - cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 1)*log(2*sinh(b*n*log(x) + b*log(c) + a)/(cosh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a))) + 4*(b*n*cosh(b*n*log(x) + b*log(c) + a)^3*log(x) - (b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a))/(b*n*cosh(b*n*log(x) + b*log(c) + a)^4 + 4*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + b*n*sinh(b*n*log(x) + b*log(c) + a)^4 - 2*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 2*(3*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 - b*n)*sinh(b*n*log(x) + b*log(c) + a)^2 + b*n + 4*(b*n*cosh(b*n*log(x) + b*log(c) + a)^3 - b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a))","B",0
192,1,171,0,0.511919," ","integrate(coth(a+b*log(c*x^n))^4/x,x, algorithm=""fricas"")","\frac{{\left(3 \, b n \log\left(x\right) + 4\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 12 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 3 \, {\left({\left(3 \, b n \log\left(x\right) + 4\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 3 \, b n \log\left(x\right) - 4\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{3 \, {\left(b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 3 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)}}"," ",0,"1/3*((3*b*n*log(x) + 4)*sinh(b*n*log(x) + b*log(c) + a)^3 - 4*cosh(b*n*log(x) + b*log(c) + a)^3 - 12*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^2 + 3*((3*b*n*log(x) + 4)*cosh(b*n*log(x) + b*log(c) + a)^2 - 3*b*n*log(x) - 4)*sinh(b*n*log(x) + b*log(c) + a))/(b*n*sinh(b*n*log(x) + b*log(c) + a)^3 + 3*(b*n*cosh(b*n*log(x) + b*log(c) + a)^2 - b*n)*sinh(b*n*log(x) + b*log(c) + a))","B",0
193,1,1576,0,0.423241," ","integrate(coth(a+b*log(c*x^n))^5/x,x, algorithm=""fricas"")","-\frac{b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} \log\left(x\right) + 8 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \log\left(x\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} + b n \log\left(x\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} - 4 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 4 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} \log\left(x\right) - b n \log\left(x\right) + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 8 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} \log\left(x\right) - 3 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 2 \, {\left(3 \, b n \log\left(x\right) - 2\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, {\left(35 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} \log\left(x\right) - 30 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 3 \, b n \log\left(x\right) - 2\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 8 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} \log\left(x\right) - 10 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + {\left(3 \, b n \log\left(x\right) - 2\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 4 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n \log\left(x\right) + 4 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} \log\left(x\right) - 15 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 3 \, {\left(3 \, b n \log\left(x\right) - 2\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n \log\left(x\right) + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} + 8 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} + 4 \, {\left(7 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} - 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 8 \, {\left(7 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 2 \, {\left(35 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 30 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 3\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 6 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 8 \, {\left(7 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} - 10 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 4 \, {\left(7 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} - 15 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 9 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 8 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} - 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 1\right)} \log\left(\frac{2 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}\right) + 8 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} \log\left(x\right) - 3 \, {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + {\left(3 \, b n \log\left(x\right) - 2\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - {\left(b n \log\left(x\right) - 1\right)} \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} + 8 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} + b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{8} - 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 4 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 6 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 8 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 2 \, {\left(35 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 30 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 3 \, b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 8 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} - 10 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 4 \, {\left(7 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} - 15 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 9 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n + 8 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} - 3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}"," ",0,"-(b*n*cosh(b*n*log(x) + b*log(c) + a)^8*log(x) + 8*b*n*cosh(b*n*log(x) + b*log(c) + a)*log(x)*sinh(b*n*log(x) + b*log(c) + a)^7 + b*n*log(x)*sinh(b*n*log(x) + b*log(c) + a)^8 - 4*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^6 + 4*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^2*log(x) - b*n*log(x) + 1)*sinh(b*n*log(x) + b*log(c) + a)^6 + 8*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^3*log(x) - 3*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^5 + 2*(3*b*n*log(x) - 2)*cosh(b*n*log(x) + b*log(c) + a)^4 + 2*(35*b*n*cosh(b*n*log(x) + b*log(c) + a)^4*log(x) - 30*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^2 + 3*b*n*log(x) - 2)*sinh(b*n*log(x) + b*log(c) + a)^4 + 8*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^5*log(x) - 10*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^3 + (3*b*n*log(x) - 2)*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^3 - 4*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^2 + b*n*log(x) + 4*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^6*log(x) - 15*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^4 + 3*(3*b*n*log(x) - 2)*cosh(b*n*log(x) + b*log(c) + a)^2 - b*n*log(x) + 1)*sinh(b*n*log(x) + b*log(c) + a)^2 - (cosh(b*n*log(x) + b*log(c) + a)^8 + 8*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^7 + sinh(b*n*log(x) + b*log(c) + a)^8 + 4*(7*cosh(b*n*log(x) + b*log(c) + a)^2 - 1)*sinh(b*n*log(x) + b*log(c) + a)^6 - 4*cosh(b*n*log(x) + b*log(c) + a)^6 + 8*(7*cosh(b*n*log(x) + b*log(c) + a)^3 - 3*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^5 + 2*(35*cosh(b*n*log(x) + b*log(c) + a)^4 - 30*cosh(b*n*log(x) + b*log(c) + a)^2 + 3)*sinh(b*n*log(x) + b*log(c) + a)^4 + 6*cosh(b*n*log(x) + b*log(c) + a)^4 + 8*(7*cosh(b*n*log(x) + b*log(c) + a)^5 - 10*cosh(b*n*log(x) + b*log(c) + a)^3 + 3*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^3 + 4*(7*cosh(b*n*log(x) + b*log(c) + a)^6 - 15*cosh(b*n*log(x) + b*log(c) + a)^4 + 9*cosh(b*n*log(x) + b*log(c) + a)^2 - 1)*sinh(b*n*log(x) + b*log(c) + a)^2 - 4*cosh(b*n*log(x) + b*log(c) + a)^2 + 8*(cosh(b*n*log(x) + b*log(c) + a)^7 - 3*cosh(b*n*log(x) + b*log(c) + a)^5 + 3*cosh(b*n*log(x) + b*log(c) + a)^3 - cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 1)*log(2*sinh(b*n*log(x) + b*log(c) + a)/(cosh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a))) + 8*(b*n*cosh(b*n*log(x) + b*log(c) + a)^7*log(x) - 3*(b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a)^5 + (3*b*n*log(x) - 2)*cosh(b*n*log(x) + b*log(c) + a)^3 - (b*n*log(x) - 1)*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a))/(b*n*cosh(b*n*log(x) + b*log(c) + a)^8 + 8*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^7 + b*n*sinh(b*n*log(x) + b*log(c) + a)^8 - 4*b*n*cosh(b*n*log(x) + b*log(c) + a)^6 + 4*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 - b*n)*sinh(b*n*log(x) + b*log(c) + a)^6 + 6*b*n*cosh(b*n*log(x) + b*log(c) + a)^4 + 8*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^3 - 3*b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^5 + 2*(35*b*n*cosh(b*n*log(x) + b*log(c) + a)^4 - 30*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 3*b*n)*sinh(b*n*log(x) + b*log(c) + a)^4 - 4*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 8*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^5 - 10*b*n*cosh(b*n*log(x) + b*log(c) + a)^3 + 3*b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^3 + 4*(7*b*n*cosh(b*n*log(x) + b*log(c) + a)^6 - 15*b*n*cosh(b*n*log(x) + b*log(c) + a)^4 + 9*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 - b*n)*sinh(b*n*log(x) + b*log(c) + a)^2 + b*n + 8*(b*n*cosh(b*n*log(x) + b*log(c) + a)^7 - 3*b*n*cosh(b*n*log(x) + b*log(c) + a)^5 + 3*b*n*cosh(b*n*log(x) + b*log(c) + a)^3 - b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a))","B",0
194,0,0,0,0.528481," ","integrate((e*x)^m*coth(d*(a+b*log(c*x^n))),x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(b d \log\left(c x^{n}\right) + a d\right), x\right)"," ",0,"integral((e*x)^m*coth(b*d*log(c*x^n) + a*d), x)","F",0
195,0,0,0,0.574916," ","integrate((e*x)^m*coth(d*(a+b*log(c*x^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{2}, x\right)"," ",0,"integral((e*x)^m*coth(b*d*log(c*x^n) + a*d)^2, x)","F",0
196,0,0,0,0.463522," ","integrate((e*x)^m*coth(d*(a+b*log(c*x^n)))^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{3}, x\right)"," ",0,"integral((e*x)^m*coth(b*d*log(c*x^n) + a*d)^3, x)","F",0
197,0,0,0,0.402919," ","integrate(coth(d*(a+b*log(c*x^n)))^p,x, algorithm=""fricas"")","{\rm integral}\left(\coth\left(b d \log\left(c x^{n}\right) + a d\right)^{p}, x\right)"," ",0,"integral(coth(b*d*log(c*x^n) + a*d)^p, x)","F",0
198,0,0,0,0.431092," ","integrate((e*x)^m*coth(d*(a+b*log(c*x^n)))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \coth\left(b d \log\left(c x^{n}\right) + a d\right)^{p}, x\right)"," ",0,"integral((e*x)^m*coth(b*d*log(c*x^n) + a*d)^p, x)","F",0
199,1,626,0,0.454382," ","integrate(coth(a+b*log(c*x^n))^(5/2)/x,x, algorithm=""fricas"")","\frac{6 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) - 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 3 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) - 8 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - 4 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}} + 4}{6 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - b n\right)}}"," ",0,"1/6*(6*(cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) - 4*cosh(b*n*log(x) + b*log(c) + a)^2 - 3*(cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) - 8*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - 4*sinh(b*n*log(x) + b*log(c) + a)^2 - 4*(cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 + 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a)) + 4)/(b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 2*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + b*n*sinh(b*n*log(x) + b*log(c) + a)^2 - b*n)","B",0
200,1,334,0,0.472531," ","integrate(coth(a+b*log(c*x^n))^(3/2)/x,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}} + 2 \, \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) + \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right)}{2 \, b n}"," ",0,"-1/2*(4*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a)) + 2*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) + log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))))/(b*n)","B",0
201,1,305,0,0.449520," ","integrate(coth(a+b*log(c*x^n))^(1/2)/x,x, algorithm=""fricas"")","\frac{2 \, \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) - \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right)}{2 \, b n}"," ",0,"1/2*(2*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) - log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))))/(b*n)","B",0
202,1,303,0,0.489969," ","integrate(1/x/coth(a+b*log(c*x^n))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) + \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right)}{2 \, b n}"," ",0,"-1/2*(2*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) + log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))))/(b*n)","B",0
203,1,625,0,0.459771," ","integrate(1/x/coth(a+b*log(c*x^n))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) - 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) - 8 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - 4 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}} - 4}{2 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n\right)}}"," ",0,"1/2*(2*(cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 + 1)*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) - 4*cosh(b*n*log(x) + b*log(c) + a)^2 - (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 + 1)*log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) - 8*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - 4*sinh(b*n*log(x) + b*log(c) + a)^2 - 4*(cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a)) - 4)/(b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 2*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + b*n*sinh(b*n*log(x) + b*log(c) + a)^2 + b*n)","B",0
204,1,1104,0,0.525365," ","integrate(1/x/coth(a+b*log(c*x^n))^(5/2),x, algorithm=""fricas"")","-\frac{4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 16 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 4 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 8 \, {\left(3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 6 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 1\right)} \arctan\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) + 8 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 3 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 1\right)} \log\left(-\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) - \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}}\right) + 16 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 1\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 2 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 4 \, {\left(\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + 1\right)} \sqrt{\frac{\cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{\sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}} + 4}{6 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + b n \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 2 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, {\left(3 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + b n + 4 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)}}"," ",0,"-1/6*(4*cosh(b*n*log(x) + b*log(c) + a)^4 + 16*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + 4*sinh(b*n*log(x) + b*log(c) + a)^4 + 8*(3*cosh(b*n*log(x) + b*log(c) + a)^2 + 1)*sinh(b*n*log(x) + b*log(c) + a)^2 + 6*(cosh(b*n*log(x) + b*log(c) + a)^4 + 4*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + sinh(b*n*log(x) + b*log(c) + a)^4 + 2*(3*cosh(b*n*log(x) + b*log(c) + a)^2 + 1)*sinh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)^2 + 4*(cosh(b*n*log(x) + b*log(c) + a)^3 + cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 1)*arctan(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) + 8*cosh(b*n*log(x) + b*log(c) + a)^2 + 3*(cosh(b*n*log(x) + b*log(c) + a)^4 + 4*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + sinh(b*n*log(x) + b*log(c) + a)^4 + 2*(3*cosh(b*n*log(x) + b*log(c) + a)^2 + 1)*sinh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)^2 + 4*(cosh(b*n*log(x) + b*log(c) + a)^3 + cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 1)*log(-cosh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) - sinh(b*n*log(x) + b*log(c) + a)^2 + (cosh(b*n*log(x) + b*log(c) + a)^2 + 2*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)^2 - 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a))) + 16*(cosh(b*n*log(x) + b*log(c) + a)^3 + cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 4*(cosh(b*n*log(x) + b*log(c) + a)^4 + 4*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + sinh(b*n*log(x) + b*log(c) + a)^4 + 2*(3*cosh(b*n*log(x) + b*log(c) + a)^2 - 1)*sinh(b*n*log(x) + b*log(c) + a)^2 - 2*cosh(b*n*log(x) + b*log(c) + a)^2 + 4*(cosh(b*n*log(x) + b*log(c) + a)^3 - cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a) + 1)*sqrt(cosh(b*n*log(x) + b*log(c) + a)/sinh(b*n*log(x) + b*log(c) + a)) + 4)/(b*n*cosh(b*n*log(x) + b*log(c) + a)^4 + 4*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^3 + b*n*sinh(b*n*log(x) + b*log(c) + a)^4 + 2*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 2*(3*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + b*n)*sinh(b*n*log(x) + b*log(c) + a)^2 + b*n + 4*(b*n*cosh(b*n*log(x) + b*log(c) + a)^3 + b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a))","B",0
205,1,8951,0,2.028258," ","integrate(coth(x)^5/(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c + 2 \, c^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2} + 4 \, {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) - 2 \, {\left(c^{2} \cosh\left(x\right)^{4} + 4 \, c^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + c^{2} \sinh\left(x\right)^{4} - 2 \, c^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c^{2} \cosh\left(x\right)^{2} - c^{2}\right)} \sinh\left(x\right)^{2} + c^{2} + 4 \, {\left(c^{2} \cosh\left(x\right)^{3} - c^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) + 4 \, \sqrt{2} {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \sinh\left(x\right)^{4} + {\left(a + b\right)} c^{2} + c^{3} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3} - 3 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{3} - {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{4 \, {\left(c^{2} \cosh\left(x\right)^{4} + 4 \, c^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + c^{2} \sinh\left(x\right)^{4} - 2 \, c^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c^{2} \cosh\left(x\right)^{2} - c^{2}\right)} \sinh\left(x\right)^{2} + c^{2} + 4 \, {\left(c^{2} \cosh\left(x\right)^{3} - c^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c + 2 \, c^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2} + 4 \, {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \sinh\left(x\right)^{4} + {\left(a + b\right)} c^{2} + c^{3} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3} - 3 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{3} - {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c + 2 \, c^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2} + 4 \, {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) - {\left(c^{2} \cosh\left(x\right)^{4} + 4 \, c^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + c^{2} \sinh\left(x\right)^{4} - 2 \, c^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c^{2} \cosh\left(x\right)^{2} - c^{2}\right)} \sinh\left(x\right)^{2} + c^{2} + 4 \, {\left(c^{2} \cosh\left(x\right)^{3} - c^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \sinh\left(x\right)^{4} + {\left(a + b\right)} c^{2} + c^{3} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3} - 3 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{3} - {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left(c^{2} \cosh\left(x\right)^{4} + 4 \, c^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + c^{2} \sinh\left(x\right)^{4} - 2 \, c^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c^{2} \cosh\left(x\right)^{2} - c^{2}\right)} \sinh\left(x\right)^{2} + c^{2} + 4 \, {\left(c^{2} \cosh\left(x\right)^{3} - c^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c + 2 \, c^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2} + 4 \, {\left({\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2} - {\left(2 \, a + b\right)} c - 2 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \sinh\left(x\right)^{4} + {\left(a + b\right)} c^{2} + c^{3} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left({\left(a + b\right)} c^{2} + c^{3} - 3 \, {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)^{3} - {\left({\left(a + b\right)} c^{2} + c^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/8*(((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^4 + 4*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)*sinh(x)^3 + (a*b + b^2 - (2*a + b)*c - 2*c^2)*sinh(x)^4 - 2*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 + 2*(3*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 - a*b - b^2 + (2*a + b)*c + 2*c^2)*sinh(x)^2 + a*b + b^2 - (2*a + b)*c - 2*c^2 + 4*((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^3 - (a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x))*sinh(x))*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) - 2*(c^2*cosh(x)^4 + 4*c^2*cosh(x)*sinh(x)^3 + c^2*sinh(x)^4 - 2*c^2*cosh(x)^2 + 2*(3*c^2*cosh(x)^2 - c^2)*sinh(x)^2 + c^2 + 4*(c^2*cosh(x)^3 - c^2*cosh(x))*sinh(x))*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 4*sqrt(2)*((a + b)*c + c^2)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(((a + b)*c^2 + c^3)*cosh(x)^4 + 4*((a + b)*c^2 + c^3)*cosh(x)*sinh(x)^3 + ((a + b)*c^2 + c^3)*sinh(x)^4 + (a + b)*c^2 + c^3 - 2*((a + b)*c^2 + c^3)*cosh(x)^2 - 2*((a + b)*c^2 + c^3 - 3*((a + b)*c^2 + c^3)*cosh(x)^2)*sinh(x)^2 + 4*(((a + b)*c^2 + c^3)*cosh(x)^3 - ((a + b)*c^2 + c^3)*cosh(x))*sinh(x)), -1/8*(4*(c^2*cosh(x)^4 + 4*c^2*cosh(x)*sinh(x)^3 + c^2*sinh(x)^4 - 2*c^2*cosh(x)^2 + 2*(3*c^2*cosh(x)^2 - c^2)*sinh(x)^2 + c^2 + 4*(c^2*cosh(x)^3 - c^2*cosh(x))*sinh(x))*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) + ((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^4 + 4*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)*sinh(x)^3 + (a*b + b^2 - (2*a + b)*c - 2*c^2)*sinh(x)^4 - 2*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 + 2*(3*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 - a*b - b^2 + (2*a + b)*c + 2*c^2)*sinh(x)^2 + a*b + b^2 - (2*a + b)*c - 2*c^2 + 4*((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^3 - (a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x))*sinh(x))*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 4*sqrt(2)*((a + b)*c + c^2)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(((a + b)*c^2 + c^3)*cosh(x)^4 + 4*((a + b)*c^2 + c^3)*cosh(x)*sinh(x)^3 + ((a + b)*c^2 + c^3)*sinh(x)^4 + (a + b)*c^2 + c^3 - 2*((a + b)*c^2 + c^3)*cosh(x)^2 - 2*((a + b)*c^2 + c^3 - 3*((a + b)*c^2 + c^3)*cosh(x)^2)*sinh(x)^2 + 4*(((a + b)*c^2 + c^3)*cosh(x)^3 - ((a + b)*c^2 + c^3)*cosh(x))*sinh(x)), -1/4*(((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^4 + 4*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)*sinh(x)^3 + (a*b + b^2 - (2*a + b)*c - 2*c^2)*sinh(x)^4 - 2*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 + 2*(3*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 - a*b - b^2 + (2*a + b)*c + 2*c^2)*sinh(x)^2 + a*b + b^2 - (2*a + b)*c - 2*c^2 + 4*((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^3 - (a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x))*sinh(x))*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))) - (c^2*cosh(x)^4 + 4*c^2*cosh(x)*sinh(x)^3 + c^2*sinh(x)^4 - 2*c^2*cosh(x)^2 + 2*(3*c^2*cosh(x)^2 - c^2)*sinh(x)^2 + c^2 + 4*(c^2*cosh(x)^3 - c^2*cosh(x))*sinh(x))*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 2*sqrt(2)*((a + b)*c + c^2)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(((a + b)*c^2 + c^3)*cosh(x)^4 + 4*((a + b)*c^2 + c^3)*cosh(x)*sinh(x)^3 + ((a + b)*c^2 + c^3)*sinh(x)^4 + (a + b)*c^2 + c^3 - 2*((a + b)*c^2 + c^3)*cosh(x)^2 - 2*((a + b)*c^2 + c^3 - 3*((a + b)*c^2 + c^3)*cosh(x)^2)*sinh(x)^2 + 4*(((a + b)*c^2 + c^3)*cosh(x)^3 - ((a + b)*c^2 + c^3)*cosh(x))*sinh(x)), -1/4*(2*(c^2*cosh(x)^4 + 4*c^2*cosh(x)*sinh(x)^3 + c^2*sinh(x)^4 - 2*c^2*cosh(x)^2 + 2*(3*c^2*cosh(x)^2 - c^2)*sinh(x)^2 + c^2 + 4*(c^2*cosh(x)^3 - c^2*cosh(x))*sinh(x))*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) + ((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^4 + 4*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)*sinh(x)^3 + (a*b + b^2 - (2*a + b)*c - 2*c^2)*sinh(x)^4 - 2*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 + 2*(3*(a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^2 - a*b - b^2 + (2*a + b)*c + 2*c^2)*sinh(x)^2 + a*b + b^2 - (2*a + b)*c - 2*c^2 + 4*((a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x)^3 - (a*b + b^2 - (2*a + b)*c - 2*c^2)*cosh(x))*sinh(x))*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))) + 2*sqrt(2)*((a + b)*c + c^2)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(((a + b)*c^2 + c^3)*cosh(x)^4 + 4*((a + b)*c^2 + c^3)*cosh(x)*sinh(x)^3 + ((a + b)*c^2 + c^3)*sinh(x)^4 + (a + b)*c^2 + c^3 - 2*((a + b)*c^2 + c^3)*cosh(x)^2 - 2*((a + b)*c^2 + c^3 - 3*((a + b)*c^2 + c^3)*cosh(x)^2)*sinh(x)^2 + 4*(((a + b)*c^2 + c^3)*cosh(x)^3 - ((a + b)*c^2 + c^3)*cosh(x))*sinh(x))]","B",0
206,1,6695,0,1.415795," ","integrate(coth(x)^3/(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a + b + c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \sqrt{a + b + c} c \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, {\left({\left(a + b\right)} c + c^{2}\right)}}, -\frac{2 \, \sqrt{-a - b - c} c \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left(a + b + c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right)}{4 \, {\left({\left(a + b\right)} c + c^{2}\right)}}, \frac{2 \, {\left(a + b + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + \sqrt{a + b + c} c \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, {\left({\left(a + b\right)} c + c^{2}\right)}}, -\frac{\sqrt{-a - b - c} c \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left(a + b + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right)}{2 \, {\left({\left(a + b\right)} c + c^{2}\right)}}\right]"," ",0,"[1/4*((a + b + c)*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + sqrt(a + b + c)*c*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a + b)*c + c^2), -1/4*(2*sqrt(-a - b - c)*c*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - (a + b + c)*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)))/((a + b)*c + c^2), 1/4*(2*(a + b + c)*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))) + sqrt(a + b + c)*c*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a + b)*c + c^2), -1/2*(sqrt(-a - b - c)*c*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - (a + b + c)*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))))/((a + b)*c + c^2)]","B",0
207,1,1752,0,1.096561," ","integrate(coth(x)/(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, \sqrt{a + b + c}}, -\frac{\sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right)}{2 \, {\left(a + b + c\right)}}\right]"," ",0,"[1/4*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/sqrt(a + b + c), -1/2*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)))/(a + b + c)]","B",0
208,1,6705,0,1.394552," ","integrate(tanh(x)/(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a + b + c\right)} \sqrt{a} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{3} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 8 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{5} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \sqrt{a + b + c} a \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, {\left(a^{2} + a b + a c\right)}}, -\frac{2 \, a \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left(a + b + c\right)} \sqrt{a} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{3} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 8 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{5} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right)}{4 \, {\left(a^{2} + a b + a c\right)}}, \frac{2 \, \sqrt{-a} {\left(a + b + c\right)} \arctan\left(\frac{\sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b + a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - a b + 3 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{2} + a^{2} + a b + a c + 8 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + \sqrt{a + b + c} a \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, {\left(a^{2} + a b + a c\right)}}, \frac{\sqrt{-a} {\left(a + b + c\right)} \arctan\left(\frac{\sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b + a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - a b + 3 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{2} + a^{2} + a b + a c + 8 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) - a \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right)}{2 \, {\left(a^{2} + a b + a c\right)}}\right]"," ",0,"[1/4*((a + b + c)*sqrt(a)*log(((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^8 + 8*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)*sinh(x)^7 + (8*a^2 + 8*a*b + b^2 + 4*a*c)*sinh(x)^8 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^6 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^6 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^3 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x)^5 + 2*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^4 + 2*(35*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^4 - 30*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*sinh(x)^4 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^5 - 10*(8*a^2 - b^2 - 4*a*c)*cosh(x)^3 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x))*sinh(x)^3 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^6 - 15*(8*a^2 - b^2 - 4*a*c)*cosh(x)^4 + 3*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^2 - 4*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 8*((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^7 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x)^5 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^3 - (8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)) + sqrt(a + b + c)*a*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(a^2 + a*b + a*c), -1/4*(2*a*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - (a + b + c)*sqrt(a)*log(((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^8 + 8*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)*sinh(x)^7 + (8*a^2 + 8*a*b + b^2 + 4*a*c)*sinh(x)^8 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^6 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^6 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^3 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x)^5 + 2*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^4 + 2*(35*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^4 - 30*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*sinh(x)^4 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^5 - 10*(8*a^2 - b^2 - 4*a*c)*cosh(x)^3 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x))*sinh(x)^3 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^6 - 15*(8*a^2 - b^2 - 4*a*c)*cosh(x)^4 + 3*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^2 - 4*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 8*((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^7 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x)^5 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^3 - (8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)))/(a^2 + a*b + a*c), 1/4*(2*sqrt(-a)*(a + b + c)*arctan(1/2*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + a*b + a*c)*cosh(x)^8 + 8*(a^2 + a*b + a*c)*cosh(x)*sinh(x)^7 + (a^2 + a*b + a*c)*sinh(x)^8 - 4*(a^2 - a*c)*cosh(x)^6 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^6 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^3 - 3*(a^2 - a*c)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - a*b + 3*a*c)*cosh(x)^4 + 2*(35*(a^2 + a*b + a*c)*cosh(x)^4 - 30*(a^2 - a*c)*cosh(x)^2 + 3*a^2 - a*b + 3*a*c)*sinh(x)^4 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^5 - 10*(a^2 - a*c)*cosh(x)^3 + (3*a^2 - a*b + 3*a*c)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*c)*cosh(x)^2 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^6 - 15*(a^2 - a*c)*cosh(x)^4 + 3*(3*a^2 - a*b + 3*a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^2 + a^2 + a*b + a*c + 8*((a^2 + a*b + a*c)*cosh(x)^7 - 3*(a^2 - a*c)*cosh(x)^5 + (3*a^2 - a*b + 3*a*c)*cosh(x)^3 - (a^2 - a*c)*cosh(x))*sinh(x))) + sqrt(a + b + c)*a*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(a^2 + a*b + a*c), 1/2*(sqrt(-a)*(a + b + c)*arctan(1/2*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + a*b + a*c)*cosh(x)^8 + 8*(a^2 + a*b + a*c)*cosh(x)*sinh(x)^7 + (a^2 + a*b + a*c)*sinh(x)^8 - 4*(a^2 - a*c)*cosh(x)^6 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^6 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^3 - 3*(a^2 - a*c)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - a*b + 3*a*c)*cosh(x)^4 + 2*(35*(a^2 + a*b + a*c)*cosh(x)^4 - 30*(a^2 - a*c)*cosh(x)^2 + 3*a^2 - a*b + 3*a*c)*sinh(x)^4 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^5 - 10*(a^2 - a*c)*cosh(x)^3 + (3*a^2 - a*b + 3*a*c)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*c)*cosh(x)^2 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^6 - 15*(a^2 - a*c)*cosh(x)^4 + 3*(3*a^2 - a*b + 3*a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^2 + a^2 + a*b + a*c + 8*((a^2 + a*b + a*c)*cosh(x)^7 - 3*(a^2 - a*c)*cosh(x)^5 + (3*a^2 - a*b + 3*a*c)*cosh(x)^3 - (a^2 - a*c)*cosh(x))*sinh(x))) - a*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))))/(a^2 + a*b + a*c)]","B",0
209,1,9148,0,1.920283," ","integrate(tanh(x)^3/(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{3} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 8 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{5} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) - 2 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) + 4 \, \sqrt{2} {\left(a^{2} + a b + a c\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + a^{2} c + 2 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b + a^{2} c + 3 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{4 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{3} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} + b^{2} + 4 \, a c\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 8 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)^{5} + {\left(24 \, a^{2} - 8 \, a b + 3 \, b^{2} + 12 \, a c\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} - b^{2} - 4 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 4 \, \sqrt{2} {\left(a^{2} + a b + a c\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + a^{2} c + 2 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b + a^{2} c + 3 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b + a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - a b + 3 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{2} + a^{2} + a b + a c + 8 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} {\left(a^{2} + a b + a c\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + a^{2} c + 2 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b + a^{2} c + 3 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2} + {\left(2 \, a - b\right)} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{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} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b + a c\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - a b + 3 \, a c\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{2} - a^{2} + a c\right)} \sinh\left(x\right)^{2} + a^{2} + a b + a c + 8 \, {\left({\left(a^{2} + a b + a c\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a c\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - a b + 3 \, a c\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) - 2 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - 2 \, \sqrt{2} {\left(a^{2} + a b + a c\right)} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + a^{2} c + 2 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b + a^{2} c + 3 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b + a^{2} c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/8*(((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^4 + 2*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c + 4*((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x))*sinh(x))*sqrt(a)*log(((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^8 + 8*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)*sinh(x)^7 + (8*a^2 + 8*a*b + b^2 + 4*a*c)*sinh(x)^8 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^6 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^6 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^3 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x)^5 + 2*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^4 + 2*(35*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^4 - 30*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*sinh(x)^4 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^5 - 10*(8*a^2 - b^2 - 4*a*c)*cosh(x)^3 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x))*sinh(x)^3 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^6 - 15*(8*a^2 - b^2 - 4*a*c)*cosh(x)^4 + 3*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^2 + 4*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 8*((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^7 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x)^5 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^3 - (8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)) - 2*(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x))*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 4*sqrt(2)*(a^2 + a*b + a*c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^3 + a^2*b + a^2*c)*cosh(x)^4 + 4*(a^3 + a^2*b + a^2*c)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b + a^2*c)*sinh(x)^4 + a^3 + a^2*b + a^2*c + 2*(a^3 + a^2*b + a^2*c)*cosh(x)^2 + 2*(a^3 + a^2*b + a^2*c + 3*(a^3 + a^2*b + a^2*c)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b + a^2*c)*cosh(x)^3 + (a^3 + a^2*b + a^2*c)*cosh(x))*sinh(x)), -1/8*(4*(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x))*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) + ((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^4 + 2*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c + 4*((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x))*sinh(x))*sqrt(a)*log(((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^8 + 8*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)*sinh(x)^7 + (8*a^2 + 8*a*b + b^2 + 4*a*c)*sinh(x)^8 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^6 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^6 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^3 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x)^5 + 2*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^4 + 2*(35*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^4 - 30*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*sinh(x)^4 + 8*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^5 - 10*(8*a^2 - b^2 - 4*a*c)*cosh(x)^3 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x))*sinh(x)^3 - 4*(8*a^2 - b^2 - 4*a*c)*cosh(x)^2 + 4*(7*(8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^6 - 15*(8*a^2 - b^2 - 4*a*c)*cosh(x)^4 + 3*(24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^2 - 8*a^2 + b^2 + 4*a*c)*sinh(x)^2 + 4*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 8*((8*a^2 + 8*a*b + b^2 + 4*a*c)*cosh(x)^7 - 3*(8*a^2 - b^2 - 4*a*c)*cosh(x)^5 + (24*a^2 - 8*a*b + 3*b^2 + 12*a*c)*cosh(x)^3 - (8*a^2 - b^2 - 4*a*c)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)) + 4*sqrt(2)*(a^2 + a*b + a*c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^3 + a^2*b + a^2*c)*cosh(x)^4 + 4*(a^3 + a^2*b + a^2*c)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b + a^2*c)*sinh(x)^4 + a^3 + a^2*b + a^2*c + 2*(a^3 + a^2*b + a^2*c)*cosh(x)^2 + 2*(a^3 + a^2*b + a^2*c + 3*(a^3 + a^2*b + a^2*c)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b + a^2*c)*cosh(x)^3 + (a^3 + a^2*b + a^2*c)*cosh(x))*sinh(x)), 1/4*(((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^4 + 2*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c + 4*((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x))*sinh(x))*sqrt(-a)*arctan(1/2*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + a*b + a*c)*cosh(x)^8 + 8*(a^2 + a*b + a*c)*cosh(x)*sinh(x)^7 + (a^2 + a*b + a*c)*sinh(x)^8 - 4*(a^2 - a*c)*cosh(x)^6 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^6 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^3 - 3*(a^2 - a*c)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - a*b + 3*a*c)*cosh(x)^4 + 2*(35*(a^2 + a*b + a*c)*cosh(x)^4 - 30*(a^2 - a*c)*cosh(x)^2 + 3*a^2 - a*b + 3*a*c)*sinh(x)^4 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^5 - 10*(a^2 - a*c)*cosh(x)^3 + (3*a^2 - a*b + 3*a*c)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*c)*cosh(x)^2 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^6 - 15*(a^2 - a*c)*cosh(x)^4 + 3*(3*a^2 - a*b + 3*a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^2 + a^2 + a*b + a*c + 8*((a^2 + a*b + a*c)*cosh(x)^7 - 3*(a^2 - a*c)*cosh(x)^5 + (3*a^2 - a*b + 3*a*c)*cosh(x)^3 - (a^2 - a*c)*cosh(x))*sinh(x))) + (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x))*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*(a^2 + a*b + a*c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^3 + a^2*b + a^2*c)*cosh(x)^4 + 4*(a^3 + a^2*b + a^2*c)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b + a^2*c)*sinh(x)^4 + a^3 + a^2*b + a^2*c + 2*(a^3 + a^2*b + a^2*c)*cosh(x)^2 + 2*(a^3 + a^2*b + a^2*c + 3*(a^3 + a^2*b + a^2*c)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b + a^2*c)*cosh(x)^3 + (a^3 + a^2*b + a^2*c)*cosh(x))*sinh(x)), 1/4*(((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^4 + 2*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c)*sinh(x)^2 + 2*a^2 + a*b - b^2 + (2*a - b)*c + 4*((2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x)^3 + (2*a^2 + a*b - b^2 + (2*a - b)*c)*cosh(x))*sinh(x))*sqrt(-a)*arctan(1/2*sqrt(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)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + a*b + a*c)*cosh(x)^8 + 8*(a^2 + a*b + a*c)*cosh(x)*sinh(x)^7 + (a^2 + a*b + a*c)*sinh(x)^8 - 4*(a^2 - a*c)*cosh(x)^6 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^6 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^3 - 3*(a^2 - a*c)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - a*b + 3*a*c)*cosh(x)^4 + 2*(35*(a^2 + a*b + a*c)*cosh(x)^4 - 30*(a^2 - a*c)*cosh(x)^2 + 3*a^2 - a*b + 3*a*c)*sinh(x)^4 + 8*(7*(a^2 + a*b + a*c)*cosh(x)^5 - 10*(a^2 - a*c)*cosh(x)^3 + (3*a^2 - a*b + 3*a*c)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*c)*cosh(x)^2 + 4*(7*(a^2 + a*b + a*c)*cosh(x)^6 - 15*(a^2 - a*c)*cosh(x)^4 + 3*(3*a^2 - a*b + 3*a*c)*cosh(x)^2 - a^2 + a*c)*sinh(x)^2 + a^2 + a*b + a*c + 8*((a^2 + a*b + a*c)*cosh(x)^7 - 3*(a^2 - a*c)*cosh(x)^5 + (3*a^2 - a*b + 3*a*c)*cosh(x)^3 - (a^2 - a*c)*cosh(x))*sinh(x))) - 2*(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x))*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - 2*sqrt(2)*(a^2 + a*b + a*c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^3 + a^2*b + a^2*c)*cosh(x)^4 + 4*(a^3 + a^2*b + a^2*c)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b + a^2*c)*sinh(x)^4 + a^3 + a^2*b + a^2*c + 2*(a^3 + a^2*b + a^2*c)*cosh(x)^2 + 2*(a^3 + a^2*b + a^2*c + 3*(a^3 + a^2*b + a^2*c)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b + a^2*c)*cosh(x)^3 + (a^3 + a^2*b + a^2*c)*cosh(x))*sinh(x))]","B",0
210,1,7964,0,2.308123," ","integrate(coth(x)*(a+b*coth(x)^2+c*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b - 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b + 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 4 \, \sqrt{2} c \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)}}, -\frac{4 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b - 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b + 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{2} - b^{2} - 4 \, a c + 8 \, c^{2}\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 8 \, {\left({\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, b^{2} + 4 \, {\left(3 \, a - 2 \, b\right)} c + 24 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 4 \, \sqrt{2} c \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{8 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)}}, \frac{{\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b - 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b + 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)} \sqrt{a + b + c} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{a + b + c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 2 \, {\left(a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} c \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)}}, -\frac{2 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b + c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b + c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - a + c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b + c\right)} \cosh\left(x\right)^{3} - {\left(a - c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b + c\right)} \sqrt{-a - b - c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b + b c + c^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2} + 2 \, {\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2} + 2 \, {\left(3 \, a + b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + a b - b c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b - 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b + 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{4} + 4 \, {\left(b + 2 \, c\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(b + 2 \, c\right)} \sinh\left(x\right)^{4} - 2 \, {\left(b - 2 \, c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(b + 2 \, c\right)} \cosh\left(x\right)^{2} - b + 2 \, c\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(b + 2 \, c\right)} \cosh\left(x\right)^{3} - {\left(b - 2 \, c\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left({\left(a + b\right)} c + c^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{3} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{2} - a c + c^{2}\right)} \sinh\left(x\right)^{2} + {\left(a + b\right)} c + c^{2} + 8 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a c - c^{2}\right)} \cosh\left(x\right)^{5} + {\left({\left(3 \, a - b\right)} c + 3 \, c^{2}\right)} \cosh\left(x\right)^{3} - {\left(a c - c^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right) + 2 \, \sqrt{2} c \sqrt{\frac{{\left(a + b + c\right)} \cosh\left(x\right)^{4} + {\left(a + b + c\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - c\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b + c\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, c\right)} \sinh\left(x\right)^{2} + 3 \, a - b + 3 \, c}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left(c \cosh\left(x\right)^{4} + 4 \, c \cosh\left(x\right) \sinh\left(x\right)^{3} + c \sinh\left(x\right)^{4} - 2 \, c \cosh\left(x\right)^{2} + 2 \, {\left(3 \, c \cosh\left(x\right)^{2} - c\right)} \sinh\left(x\right)^{2} + 4 \, {\left(c \cosh\left(x\right)^{3} - c \cosh\left(x\right)\right)} \sinh\left(x\right) + c\right)}}\right]"," ",0,"[1/8*(((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b + 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b - 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b + 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c)*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 4*sqrt(2)*c*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c), -1/8*(4*(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c)*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - ((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b + 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b - 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b + 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*log(((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^8 + 8*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)*sinh(x)^7 + (b^2 + 4*(a + 2*b)*c + 8*c^2)*sinh(x)^8 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^6 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^6 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^3 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x)^5 + 2*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^4 + 2*(35*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^4 - 30*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*sinh(x)^4 + 8*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^5 - 10*(b^2 + 4*a*c - 8*c^2)*cosh(x)^3 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x))*sinh(x)^3 - 4*(b^2 + 4*a*c - 8*c^2)*cosh(x)^2 + 4*(7*(b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^6 - 15*(b^2 + 4*a*c - 8*c^2)*cosh(x)^4 + 3*(3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^2 - b^2 - 4*a*c + 8*c^2)*sinh(x)^2 - 4*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + b^2 + 4*(a + 2*b)*c + 8*c^2 + 8*((b^2 + 4*(a + 2*b)*c + 8*c^2)*cosh(x)^7 - 3*(b^2 + 4*a*c - 8*c^2)*cosh(x)^5 + (3*b^2 + 4*(3*a - 2*b)*c + 24*c^2)*cosh(x)^3 - (b^2 + 4*a*c - 8*c^2)*cosh(x))*sinh(x))/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 4*sqrt(2)*c*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c), 1/4*(((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b + 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b - 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b + 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))) + (c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c)*sqrt(a + b + c)*log(((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(a + b + c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 2*(a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*c*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c), -1/4*(2*(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c)*sqrt(-a - b - c)*arctan(sqrt(2)*((a + b + c)*cosh(x)^4 + 4*(a + b + c)*cosh(x)*sinh(x)^3 + (a + b + c)*sinh(x)^4 - 2*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - a + c)*sinh(x)^2 + 4*((a + b + c)*cosh(x)^3 - (a - c)*cosh(x))*sinh(x) + a + b + c)*sqrt(-a - b - c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*sinh(x)^8 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^3 - 3*(a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^4 - 30*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^5 - 10*(a^2 + a*b - b*c - c^2)*cosh(x)^3 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a^2 + a*b - b*c - c^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^6 - 15*(a^2 + a*b - b*c - c^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^2 - a^2 - a*b + b*c + c^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2 + 8*((a^2 + 2*a*b + b^2 + 2*(a + b)*c + c^2)*cosh(x)^7 - 3*(a^2 + a*b - b*c - c^2)*cosh(x)^5 + (3*a^2 + 2*a*b - b^2 + 2*(3*a + b)*c + 3*c^2)*cosh(x)^3 - (a^2 + a*b - b*c - c^2)*cosh(x))*sinh(x))) - ((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b + 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b - 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b + 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*arctan(1/2*sqrt(2)*((b + 2*c)*cosh(x)^4 + 4*(b + 2*c)*cosh(x)*sinh(x)^3 + (b + 2*c)*sinh(x)^4 - 2*(b - 2*c)*cosh(x)^2 + 2*(3*(b + 2*c)*cosh(x)^2 - b + 2*c)*sinh(x)^2 + 4*((b + 2*c)*cosh(x)^3 - (b - 2*c)*cosh(x))*sinh(x) + b + 2*c)*sqrt(-c)*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(((a + b)*c + c^2)*cosh(x)^8 + 8*((a + b)*c + c^2)*cosh(x)*sinh(x)^7 + ((a + b)*c + c^2)*sinh(x)^8 - 4*(a*c - c^2)*cosh(x)^6 + 4*(7*((a + b)*c + c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^6 + 8*(7*((a + b)*c + c^2)*cosh(x)^3 - 3*(a*c - c^2)*cosh(x))*sinh(x)^5 + 2*((3*a - b)*c + 3*c^2)*cosh(x)^4 + 2*(35*((a + b)*c + c^2)*cosh(x)^4 - 30*(a*c - c^2)*cosh(x)^2 + (3*a - b)*c + 3*c^2)*sinh(x)^4 + 8*(7*((a + b)*c + c^2)*cosh(x)^5 - 10*(a*c - c^2)*cosh(x)^3 + ((3*a - b)*c + 3*c^2)*cosh(x))*sinh(x)^3 - 4*(a*c - c^2)*cosh(x)^2 + 4*(7*((a + b)*c + c^2)*cosh(x)^6 - 15*(a*c - c^2)*cosh(x)^4 + 3*((3*a - b)*c + 3*c^2)*cosh(x)^2 - a*c + c^2)*sinh(x)^2 + (a + b)*c + c^2 + 8*(((a + b)*c + c^2)*cosh(x)^7 - 3*(a*c - c^2)*cosh(x)^5 + ((3*a - b)*c + 3*c^2)*cosh(x)^3 - (a*c - c^2)*cosh(x))*sinh(x))) + 2*sqrt(2)*c*sqrt(((a + b + c)*cosh(x)^4 + (a + b + c)*sinh(x)^4 - 4*(a - c)*cosh(x)^2 + 2*(3*(a + b + c)*cosh(x)^2 - 2*a + 2*c)*sinh(x)^2 + 3*a - b + 3*c)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(c*cosh(x)^4 + 4*c*cosh(x)*sinh(x)^3 + c*sinh(x)^4 - 2*c*cosh(x)^2 + 2*(3*c*cosh(x)^2 - c)*sinh(x)^2 + 4*(c*cosh(x)^3 - c*cosh(x))*sinh(x) + c)]","B",0
211,1,1617,0,0.440317," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)^2)^(5/2),x, algorithm=""fricas"")","\frac{24 \, \cosh\left(b c x + a c\right)^{9} + 216 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{8} + 24 \, \sinh\left(b c x + a c\right)^{9} + 6 \, {\left(144 \, \cosh\left(b c x + a c\right)^{2} - 41\right)} \sinh\left(b c x + a c\right)^{7} - 246 \, \cosh\left(b c x + a c\right)^{7} + 42 \, {\left(48 \, \cosh\left(b c x + a c\right)^{3} - 41 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{6} + 2 \, {\left(1512 \, \cosh\left(b c x + a c\right)^{4} - 2583 \, \cosh\left(b c x + a c\right)^{2} + 187\right)} \sinh\left(b c x + a c\right)^{5} + 374 \, \cosh\left(b c x + a c\right)^{5} + 2 \, {\left(1512 \, \cosh\left(b c x + a c\right)^{5} - 4305 \, \cosh\left(b c x + a c\right)^{3} + 935 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{4} + 2 \, {\left(1008 \, \cosh\left(b c x + a c\right)^{6} - 4305 \, \cosh\left(b c x + a c\right)^{4} + 1870 \, \cosh\left(b c x + a c\right)^{2} - 157\right)} \sinh\left(b c x + a c\right)^{3} - 314 \, \cosh\left(b c x + a c\right)^{3} + 2 \, {\left(432 \, \cosh\left(b c x + a c\right)^{7} - 2583 \, \cosh\left(b c x + a c\right)^{5} + 1870 \, \cosh\left(b c x + a c\right)^{3} - 471 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} - 45 \, {\left(\cosh\left(b c x + a c\right)^{8} + 8 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{7} + \sinh\left(b c x + a c\right)^{8} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{6} - 4 \, \cosh\left(b c x + a c\right)^{6} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{3} - 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{5} + 2 \, {\left(35 \, \cosh\left(b c x + a c\right)^{4} - 30 \, \cosh\left(b c x + a c\right)^{2} + 3\right)} \sinh\left(b c x + a c\right)^{4} + 6 \, \cosh\left(b c x + a c\right)^{4} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{5} - 10 \, \cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{6} - 15 \, \cosh\left(b c x + a c\right)^{4} + 9 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{2} - 4 \, \cosh\left(b c x + a c\right)^{2} + 8 \, {\left(\cosh\left(b c x + a c\right)^{7} - 3 \, \cosh\left(b c x + a c\right)^{5} + 3 \, \cosh\left(b c x + a c\right)^{3} - \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) + 1\right) + 45 \, {\left(\cosh\left(b c x + a c\right)^{8} + 8 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{7} + \sinh\left(b c x + a c\right)^{8} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{6} - 4 \, \cosh\left(b c x + a c\right)^{6} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{3} - 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{5} + 2 \, {\left(35 \, \cosh\left(b c x + a c\right)^{4} - 30 \, \cosh\left(b c x + a c\right)^{2} + 3\right)} \sinh\left(b c x + a c\right)^{4} + 6 \, \cosh\left(b c x + a c\right)^{4} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{5} - 10 \, \cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{6} - 15 \, \cosh\left(b c x + a c\right)^{4} + 9 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{2} - 4 \, \cosh\left(b c x + a c\right)^{2} + 8 \, {\left(\cosh\left(b c x + a c\right)^{7} - 3 \, \cosh\left(b c x + a c\right)^{5} + 3 \, \cosh\left(b c x + a c\right)^{3} - \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) - 1\right) + 2 \, {\left(108 \, \cosh\left(b c x + a c\right)^{8} - 861 \, \cosh\left(b c x + a c\right)^{6} + 935 \, \cosh\left(b c x + a c\right)^{4} - 471 \, \cosh\left(b c x + a c\right)^{2} + 33\right)} \sinh\left(b c x + a c\right) + 66 \, \cosh\left(b c x + a c\right)}{24 \, {\left(b c \cosh\left(b c x + a c\right)^{8} + 8 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{7} + b c \sinh\left(b c x + a c\right)^{8} - 4 \, b c \cosh\left(b c x + a c\right)^{6} + 4 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{2} - b c\right)} \sinh\left(b c x + a c\right)^{6} + 6 \, b c \cosh\left(b c x + a c\right)^{4} + 8 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{3} - 3 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{5} + 2 \, {\left(35 \, b c \cosh\left(b c x + a c\right)^{4} - 30 \, b c \cosh\left(b c x + a c\right)^{2} + 3 \, b c\right)} \sinh\left(b c x + a c\right)^{4} - 4 \, b c \cosh\left(b c x + a c\right)^{2} + 8 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{5} - 10 \, b c \cosh\left(b c x + a c\right)^{3} + 3 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + 4 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{6} - 15 \, b c \cosh\left(b c x + a c\right)^{4} + 9 \, b c \cosh\left(b c x + a c\right)^{2} - b c\right)} \sinh\left(b c x + a c\right)^{2} + b c + 8 \, {\left(b c \cosh\left(b c x + a c\right)^{7} - 3 \, b c \cosh\left(b c x + a c\right)^{5} + 3 \, b c \cosh\left(b c x + a c\right)^{3} - b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)\right)}}"," ",0,"1/24*(24*cosh(b*c*x + a*c)^9 + 216*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^8 + 24*sinh(b*c*x + a*c)^9 + 6*(144*cosh(b*c*x + a*c)^2 - 41)*sinh(b*c*x + a*c)^7 - 246*cosh(b*c*x + a*c)^7 + 42*(48*cosh(b*c*x + a*c)^3 - 41*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^6 + 2*(1512*cosh(b*c*x + a*c)^4 - 2583*cosh(b*c*x + a*c)^2 + 187)*sinh(b*c*x + a*c)^5 + 374*cosh(b*c*x + a*c)^5 + 2*(1512*cosh(b*c*x + a*c)^5 - 4305*cosh(b*c*x + a*c)^3 + 935*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^4 + 2*(1008*cosh(b*c*x + a*c)^6 - 4305*cosh(b*c*x + a*c)^4 + 1870*cosh(b*c*x + a*c)^2 - 157)*sinh(b*c*x + a*c)^3 - 314*cosh(b*c*x + a*c)^3 + 2*(432*cosh(b*c*x + a*c)^7 - 2583*cosh(b*c*x + a*c)^5 + 1870*cosh(b*c*x + a*c)^3 - 471*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 - 45*(cosh(b*c*x + a*c)^8 + 8*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^7 + sinh(b*c*x + a*c)^8 + 4*(7*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^6 - 4*cosh(b*c*x + a*c)^6 + 8*(7*cosh(b*c*x + a*c)^3 - 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^5 + 2*(35*cosh(b*c*x + a*c)^4 - 30*cosh(b*c*x + a*c)^2 + 3)*sinh(b*c*x + a*c)^4 + 6*cosh(b*c*x + a*c)^4 + 8*(7*cosh(b*c*x + a*c)^5 - 10*cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + 4*(7*cosh(b*c*x + a*c)^6 - 15*cosh(b*c*x + a*c)^4 + 9*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^2 - 4*cosh(b*c*x + a*c)^2 + 8*(cosh(b*c*x + a*c)^7 - 3*cosh(b*c*x + a*c)^5 + 3*cosh(b*c*x + a*c)^3 - cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) + 1) + 45*(cosh(b*c*x + a*c)^8 + 8*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^7 + sinh(b*c*x + a*c)^8 + 4*(7*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^6 - 4*cosh(b*c*x + a*c)^6 + 8*(7*cosh(b*c*x + a*c)^3 - 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^5 + 2*(35*cosh(b*c*x + a*c)^4 - 30*cosh(b*c*x + a*c)^2 + 3)*sinh(b*c*x + a*c)^4 + 6*cosh(b*c*x + a*c)^4 + 8*(7*cosh(b*c*x + a*c)^5 - 10*cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + 4*(7*cosh(b*c*x + a*c)^6 - 15*cosh(b*c*x + a*c)^4 + 9*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^2 - 4*cosh(b*c*x + a*c)^2 + 8*(cosh(b*c*x + a*c)^7 - 3*cosh(b*c*x + a*c)^5 + 3*cosh(b*c*x + a*c)^3 - cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) - 1) + 2*(108*cosh(b*c*x + a*c)^8 - 861*cosh(b*c*x + a*c)^6 + 935*cosh(b*c*x + a*c)^4 - 471*cosh(b*c*x + a*c)^2 + 33)*sinh(b*c*x + a*c) + 66*cosh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^8 + 8*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^7 + b*c*sinh(b*c*x + a*c)^8 - 4*b*c*cosh(b*c*x + a*c)^6 + 4*(7*b*c*cosh(b*c*x + a*c)^2 - b*c)*sinh(b*c*x + a*c)^6 + 6*b*c*cosh(b*c*x + a*c)^4 + 8*(7*b*c*cosh(b*c*x + a*c)^3 - 3*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^5 + 2*(35*b*c*cosh(b*c*x + a*c)^4 - 30*b*c*cosh(b*c*x + a*c)^2 + 3*b*c)*sinh(b*c*x + a*c)^4 - 4*b*c*cosh(b*c*x + a*c)^2 + 8*(7*b*c*cosh(b*c*x + a*c)^5 - 10*b*c*cosh(b*c*x + a*c)^3 + 3*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + 4*(7*b*c*cosh(b*c*x + a*c)^6 - 15*b*c*cosh(b*c*x + a*c)^4 + 9*b*c*cosh(b*c*x + a*c)^2 - b*c)*sinh(b*c*x + a*c)^2 + b*c + 8*(b*c*cosh(b*c*x + a*c)^7 - 3*b*c*cosh(b*c*x + a*c)^5 + 3*b*c*cosh(b*c*x + a*c)^3 - b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c))","B",0
212,1,613,0,0.406295," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \cosh\left(b c x + a c\right)^{5} + 10 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{4} + 2 \, \sinh\left(b c x + a c\right)^{5} + 10 \, {\left(2 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{3} - 10 \, \cosh\left(b c x + a c\right)^{3} + 10 \, {\left(2 \, \cosh\left(b c x + a c\right)^{3} - 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} - 3 \, {\left(\cosh\left(b c x + a c\right)^{4} + 4 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{3} + \sinh\left(b c x + a c\right)^{4} + 2 \, {\left(3 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right)^{2} + 4 \, {\left(\cosh\left(b c x + a c\right)^{3} - \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) + 1\right) + 3 \, {\left(\cosh\left(b c x + a c\right)^{4} + 4 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{3} + \sinh\left(b c x + a c\right)^{4} + 2 \, {\left(3 \, \cosh\left(b c x + a c\right)^{2} - 1\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right)^{2} + 4 \, {\left(\cosh\left(b c x + a c\right)^{3} - \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) - 1\right) + 2 \, {\left(5 \, \cosh\left(b c x + a c\right)^{4} - 15 \, \cosh\left(b c x + a c\right)^{2} + 2\right)} \sinh\left(b c x + a c\right) + 4 \, \cosh\left(b c x + a c\right)}{2 \, {\left(b c \cosh\left(b c x + a c\right)^{4} + 4 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{3} + b c \sinh\left(b c x + a c\right)^{4} - 2 \, b c \cosh\left(b c x + a c\right)^{2} + 2 \, {\left(3 \, b c \cosh\left(b c x + a c\right)^{2} - b c\right)} \sinh\left(b c x + a c\right)^{2} + b c + 4 \, {\left(b c \cosh\left(b c x + a c\right)^{3} - b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)\right)}}"," ",0,"1/2*(2*cosh(b*c*x + a*c)^5 + 10*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^4 + 2*sinh(b*c*x + a*c)^5 + 10*(2*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^3 - 10*cosh(b*c*x + a*c)^3 + 10*(2*cosh(b*c*x + a*c)^3 - 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 - 3*(cosh(b*c*x + a*c)^4 + 4*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^3 + sinh(b*c*x + a*c)^4 + 2*(3*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)^2 + 4*(cosh(b*c*x + a*c)^3 - cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) + 1) + 3*(cosh(b*c*x + a*c)^4 + 4*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^3 + sinh(b*c*x + a*c)^4 + 2*(3*cosh(b*c*x + a*c)^2 - 1)*sinh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)^2 + 4*(cosh(b*c*x + a*c)^3 - cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) - 1) + 2*(5*cosh(b*c*x + a*c)^4 - 15*cosh(b*c*x + a*c)^2 + 2)*sinh(b*c*x + a*c) + 4*cosh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^4 + 4*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^3 + b*c*sinh(b*c*x + a*c)^4 - 2*b*c*cosh(b*c*x + a*c)^2 + 2*(3*b*c*cosh(b*c*x + a*c)^2 - b*c)*sinh(b*c*x + a*c)^2 + b*c + 4*(b*c*cosh(b*c*x + a*c)^3 - b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c))","B",0
213,1,70,0,0.407798," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)^2)^(1/2),x, algorithm=""fricas"")","\frac{\cosh\left(b c x + a c\right) - \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) + 1\right) + \log\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right) - 1\right) + \sinh\left(b c x + a c\right)}{b c}"," ",0,"(cosh(b*c*x + a*c) - log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) + 1) + log(cosh(b*c*x + a*c) + sinh(b*c*x + a*c) - 1) + sinh(b*c*x + a*c))/(b*c)","A",0
214,1,53,0,0.391928," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right) - \cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}{b c}"," ",0,"-(2*arctan(cosh(b*c*x + a*c) + sinh(b*c*x + a*c)) - cosh(b*c*x + a*c) - sinh(b*c*x + a*c))/(b*c)","A",0
215,1,458,0,0.426398," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)^2)^(3/2),x, algorithm=""fricas"")","\frac{\cosh\left(b c x + a c\right)^{5} + 5 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{4} + \sinh\left(b c x + a c\right)^{5} + 5 \, {\left(2 \, \cosh\left(b c x + a c\right)^{2} + 1\right)} \sinh\left(b c x + a c\right)^{3} + 5 \, \cosh\left(b c x + a c\right)^{3} + 5 \, {\left(2 \, \cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} - 3 \, {\left(\cosh\left(b c x + a c\right)^{4} + 4 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{3} + \sinh\left(b c x + a c\right)^{4} + 2 \, {\left(3 \, \cosh\left(b c x + a c\right)^{2} + 1\right)} \sinh\left(b c x + a c\right)^{2} + 2 \, \cosh\left(b c x + a c\right)^{2} + 4 \, {\left(\cosh\left(b c x + a c\right)^{3} + \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \arctan\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right) + {\left(5 \, \cosh\left(b c x + a c\right)^{4} + 15 \, \cosh\left(b c x + a c\right)^{2} + 2\right)} \sinh\left(b c x + a c\right) + 2 \, \cosh\left(b c x + a c\right)}{b c \cosh\left(b c x + a c\right)^{4} + 4 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{3} + b c \sinh\left(b c x + a c\right)^{4} + 2 \, b c \cosh\left(b c x + a c\right)^{2} + 2 \, {\left(3 \, b c \cosh\left(b c x + a c\right)^{2} + b c\right)} \sinh\left(b c x + a c\right)^{2} + b c + 4 \, {\left(b c \cosh\left(b c x + a c\right)^{3} + b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)}"," ",0,"(cosh(b*c*x + a*c)^5 + 5*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^4 + sinh(b*c*x + a*c)^5 + 5*(2*cosh(b*c*x + a*c)^2 + 1)*sinh(b*c*x + a*c)^3 + 5*cosh(b*c*x + a*c)^3 + 5*(2*cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 - 3*(cosh(b*c*x + a*c)^4 + 4*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^3 + sinh(b*c*x + a*c)^4 + 2*(3*cosh(b*c*x + a*c)^2 + 1)*sinh(b*c*x + a*c)^2 + 2*cosh(b*c*x + a*c)^2 + 4*(cosh(b*c*x + a*c)^3 + cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*arctan(cosh(b*c*x + a*c) + sinh(b*c*x + a*c)) + (5*cosh(b*c*x + a*c)^4 + 15*cosh(b*c*x + a*c)^2 + 2)*sinh(b*c*x + a*c) + 2*cosh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^4 + 4*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^3 + b*c*sinh(b*c*x + a*c)^4 + 2*b*c*cosh(b*c*x + a*c)^2 + 2*(3*b*c*cosh(b*c*x + a*c)^2 + b*c)*sinh(b*c*x + a*c)^2 + b*c + 4*(b*c*cosh(b*c*x + a*c)^3 + b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c))","B",0
216,1,1226,0,0.491003," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, \cosh\left(b c x + a c\right)^{9} + 108 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{8} + 12 \, \sinh\left(b c x + a c\right)^{9} + 3 \, {\left(144 \, \cosh\left(b c x + a c\right)^{2} + 41\right)} \sinh\left(b c x + a c\right)^{7} + 123 \, \cosh\left(b c x + a c\right)^{7} + 21 \, {\left(48 \, \cosh\left(b c x + a c\right)^{3} + 41 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{6} + {\left(1512 \, \cosh\left(b c x + a c\right)^{4} + 2583 \, \cosh\left(b c x + a c\right)^{2} + 187\right)} \sinh\left(b c x + a c\right)^{5} + 187 \, \cosh\left(b c x + a c\right)^{5} + {\left(1512 \, \cosh\left(b c x + a c\right)^{5} + 4305 \, \cosh\left(b c x + a c\right)^{3} + 935 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{4} + {\left(1008 \, \cosh\left(b c x + a c\right)^{6} + 4305 \, \cosh\left(b c x + a c\right)^{4} + 1870 \, \cosh\left(b c x + a c\right)^{2} + 157\right)} \sinh\left(b c x + a c\right)^{3} + 157 \, \cosh\left(b c x + a c\right)^{3} + {\left(432 \, \cosh\left(b c x + a c\right)^{7} + 2583 \, \cosh\left(b c x + a c\right)^{5} + 1870 \, \cosh\left(b c x + a c\right)^{3} + 471 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} - 45 \, {\left(\cosh\left(b c x + a c\right)^{8} + 8 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{7} + \sinh\left(b c x + a c\right)^{8} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{2} + 1\right)} \sinh\left(b c x + a c\right)^{6} + 4 \, \cosh\left(b c x + a c\right)^{6} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{5} + 2 \, {\left(35 \, \cosh\left(b c x + a c\right)^{4} + 30 \, \cosh\left(b c x + a c\right)^{2} + 3\right)} \sinh\left(b c x + a c\right)^{4} + 6 \, \cosh\left(b c x + a c\right)^{4} + 8 \, {\left(7 \, \cosh\left(b c x + a c\right)^{5} + 10 \, \cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + 4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{6} + 15 \, \cosh\left(b c x + a c\right)^{4} + 9 \, \cosh\left(b c x + a c\right)^{2} + 1\right)} \sinh\left(b c x + a c\right)^{2} + 4 \, \cosh\left(b c x + a c\right)^{2} + 8 \, {\left(\cosh\left(b c x + a c\right)^{7} + 3 \, \cosh\left(b c x + a c\right)^{5} + 3 \, \cosh\left(b c x + a c\right)^{3} + \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right) + 1\right)} \arctan\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right) + {\left(108 \, \cosh\left(b c x + a c\right)^{8} + 861 \, \cosh\left(b c x + a c\right)^{6} + 935 \, \cosh\left(b c x + a c\right)^{4} + 471 \, \cosh\left(b c x + a c\right)^{2} + 33\right)} \sinh\left(b c x + a c\right) + 33 \, \cosh\left(b c x + a c\right)}{12 \, {\left(b c \cosh\left(b c x + a c\right)^{8} + 8 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{7} + b c \sinh\left(b c x + a c\right)^{8} + 4 \, b c \cosh\left(b c x + a c\right)^{6} + 4 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{2} + b c\right)} \sinh\left(b c x + a c\right)^{6} + 6 \, b c \cosh\left(b c x + a c\right)^{4} + 8 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{3} + 3 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{5} + 2 \, {\left(35 \, b c \cosh\left(b c x + a c\right)^{4} + 30 \, b c \cosh\left(b c x + a c\right)^{2} + 3 \, b c\right)} \sinh\left(b c x + a c\right)^{4} + 4 \, b c \cosh\left(b c x + a c\right)^{2} + 8 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{5} + 10 \, b c \cosh\left(b c x + a c\right)^{3} + 3 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + 4 \, {\left(7 \, b c \cosh\left(b c x + a c\right)^{6} + 15 \, b c \cosh\left(b c x + a c\right)^{4} + 9 \, b c \cosh\left(b c x + a c\right)^{2} + b c\right)} \sinh\left(b c x + a c\right)^{2} + b c + 8 \, {\left(b c \cosh\left(b c x + a c\right)^{7} + 3 \, b c \cosh\left(b c x + a c\right)^{5} + 3 \, b c \cosh\left(b c x + a c\right)^{3} + b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)\right)}}"," ",0,"1/12*(12*cosh(b*c*x + a*c)^9 + 108*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^8 + 12*sinh(b*c*x + a*c)^9 + 3*(144*cosh(b*c*x + a*c)^2 + 41)*sinh(b*c*x + a*c)^7 + 123*cosh(b*c*x + a*c)^7 + 21*(48*cosh(b*c*x + a*c)^3 + 41*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^6 + (1512*cosh(b*c*x + a*c)^4 + 2583*cosh(b*c*x + a*c)^2 + 187)*sinh(b*c*x + a*c)^5 + 187*cosh(b*c*x + a*c)^5 + (1512*cosh(b*c*x + a*c)^5 + 4305*cosh(b*c*x + a*c)^3 + 935*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^4 + (1008*cosh(b*c*x + a*c)^6 + 4305*cosh(b*c*x + a*c)^4 + 1870*cosh(b*c*x + a*c)^2 + 157)*sinh(b*c*x + a*c)^3 + 157*cosh(b*c*x + a*c)^3 + (432*cosh(b*c*x + a*c)^7 + 2583*cosh(b*c*x + a*c)^5 + 1870*cosh(b*c*x + a*c)^3 + 471*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 - 45*(cosh(b*c*x + a*c)^8 + 8*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^7 + sinh(b*c*x + a*c)^8 + 4*(7*cosh(b*c*x + a*c)^2 + 1)*sinh(b*c*x + a*c)^6 + 4*cosh(b*c*x + a*c)^6 + 8*(7*cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^5 + 2*(35*cosh(b*c*x + a*c)^4 + 30*cosh(b*c*x + a*c)^2 + 3)*sinh(b*c*x + a*c)^4 + 6*cosh(b*c*x + a*c)^4 + 8*(7*cosh(b*c*x + a*c)^5 + 10*cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + 4*(7*cosh(b*c*x + a*c)^6 + 15*cosh(b*c*x + a*c)^4 + 9*cosh(b*c*x + a*c)^2 + 1)*sinh(b*c*x + a*c)^2 + 4*cosh(b*c*x + a*c)^2 + 8*(cosh(b*c*x + a*c)^7 + 3*cosh(b*c*x + a*c)^5 + 3*cosh(b*c*x + a*c)^3 + cosh(b*c*x + a*c))*sinh(b*c*x + a*c) + 1)*arctan(cosh(b*c*x + a*c) + sinh(b*c*x + a*c)) + (108*cosh(b*c*x + a*c)^8 + 861*cosh(b*c*x + a*c)^6 + 935*cosh(b*c*x + a*c)^4 + 471*cosh(b*c*x + a*c)^2 + 33)*sinh(b*c*x + a*c) + 33*cosh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^8 + 8*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^7 + b*c*sinh(b*c*x + a*c)^8 + 4*b*c*cosh(b*c*x + a*c)^6 + 4*(7*b*c*cosh(b*c*x + a*c)^2 + b*c)*sinh(b*c*x + a*c)^6 + 6*b*c*cosh(b*c*x + a*c)^4 + 8*(7*b*c*cosh(b*c*x + a*c)^3 + 3*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^5 + 2*(35*b*c*cosh(b*c*x + a*c)^4 + 30*b*c*cosh(b*c*x + a*c)^2 + 3*b*c)*sinh(b*c*x + a*c)^4 + 4*b*c*cosh(b*c*x + a*c)^2 + 8*(7*b*c*cosh(b*c*x + a*c)^5 + 10*b*c*cosh(b*c*x + a*c)^3 + 3*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + 4*(7*b*c*cosh(b*c*x + a*c)^6 + 15*b*c*cosh(b*c*x + a*c)^4 + 9*b*c*cosh(b*c*x + a*c)^2 + b*c)*sinh(b*c*x + a*c)^2 + b*c + 8*(b*c*cosh(b*c*x + a*c)^7 + 3*b*c*cosh(b*c*x + a*c)^5 + 3*b*c*cosh(b*c*x + a*c)^3 + b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c))","B",0
217,1,296,0,0.437369," ","integrate(sin(coth(b*x+a))^3,x, algorithm=""fricas"")","\frac{\operatorname{Ci}\left(\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(3\right) + \operatorname{Ci}\left(-\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(3\right) + \operatorname{Ci}\left(\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(3\right) + \operatorname{Ci}\left(-\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(3\right) - 3 \, \operatorname{Ci}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) - 3 \, \operatorname{Ci}\left(-\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) - 3 \, \operatorname{Ci}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) - 3 \, \operatorname{Ci}\left(-\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) - 2 \, \cos\left(3\right) \operatorname{Si}\left(\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 6 \, \cos\left(1\right) \operatorname{Si}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \cos\left(3\right) \operatorname{Si}\left(\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - 6 \, \cos\left(1\right) \operatorname{Si}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{16 \, b}"," ",0,"1/16*(cos_integral(6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(3) + cos_integral(-6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(3) + cos_integral(6/(e^(2*b*x + 2*a) - 1))*sin(3) + cos_integral(-6/(e^(2*b*x + 2*a) - 1))*sin(3) - 3*cos_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(1) - 3*cos_integral(-2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(1) - 3*cos_integral(2/(e^(2*b*x + 2*a) - 1))*sin(1) - 3*cos_integral(-2/(e^(2*b*x + 2*a) - 1))*sin(1) - 2*cos(3)*sin_integral(6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 6*cos(1)*sin_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 2*cos(3)*sin_integral(6/(e^(2*b*x + 2*a) - 1)) - 6*cos(1)*sin_integral(2/(e^(2*b*x + 2*a) - 1)))/b","B",0
218,1,155,0,0.475727," ","integrate(sin(coth(b*x+a))^2,x, algorithm=""fricas"")","\frac{4 \, b x - \cos\left(2\right) \operatorname{Ci}\left(\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(2\right) \operatorname{Ci}\left(-\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + \cos\left(2\right) \operatorname{Ci}\left(\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + \cos\left(2\right) \operatorname{Ci}\left(-\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - 2 \, \sin\left(2\right) \operatorname{Si}\left(\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - 2 \, \sin\left(2\right) \operatorname{Si}\left(\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{8 \, b}"," ",0,"1/8*(4*b*x - cos(2)*cos_integral(4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) - cos(2)*cos_integral(-4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + cos(2)*cos_integral(4/(e^(2*b*x + 2*a) - 1)) + cos(2)*cos_integral(-4/(e^(2*b*x + 2*a) - 1)) - 2*sin(2)*sin_integral(4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) - 2*sin(2)*sin_integral(4/(e^(2*b*x + 2*a) - 1)))/b","A",0
219,1,149,0,0.438532," ","integrate(sin(coth(b*x+a)),x, algorithm=""fricas"")","-\frac{\operatorname{Ci}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) + \operatorname{Ci}\left(-\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) + \operatorname{Ci}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) + \operatorname{Ci}\left(-\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) \sin\left(1\right) - 2 \, \cos\left(1\right) \operatorname{Si}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \cos\left(1\right) \operatorname{Si}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{4 \, b}"," ",0,"-1/4*(cos_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(1) + cos_integral(-2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1))*sin(1) + cos_integral(2/(e^(2*b*x + 2*a) - 1))*sin(1) + cos_integral(-2/(e^(2*b*x + 2*a) - 1))*sin(1) - 2*cos(1)*sin_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 2*cos(1)*sin_integral(2/(e^(2*b*x + 2*a) - 1)))/b","B",0
220,0,0,0,0.443048," ","integrate(csc(coth(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(\coth\left(b x + a\right)\right), x\right)"," ",0,"integral(csc(coth(b*x + a)), x)","F",0
221,1,298,0,0.482456," ","integrate(cos(coth(b*x+a))^3,x, algorithm=""fricas"")","\frac{\cos\left(3\right) \operatorname{Ci}\left(\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 3 \, \cos\left(1\right) \operatorname{Ci}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 3 \, \cos\left(1\right) \operatorname{Ci}\left(-\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + \cos\left(3\right) \operatorname{Ci}\left(-\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(3\right) \operatorname{Ci}\left(\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - 3 \, \cos\left(1\right) \operatorname{Ci}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - 3 \, \cos\left(1\right) \operatorname{Ci}\left(-\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(3\right) \operatorname{Ci}\left(-\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(3\right) \operatorname{Si}\left(\frac{6 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 6 \, \sin\left(1\right) \operatorname{Si}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(3\right) \operatorname{Si}\left(\frac{6}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 6 \, \sin\left(1\right) \operatorname{Si}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{16 \, b}"," ",0,"1/16*(cos(3)*cos_integral(6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 3*cos(1)*cos_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 3*cos(1)*cos_integral(-2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + cos(3)*cos_integral(-6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) - cos(3)*cos_integral(6/(e^(2*b*x + 2*a) - 1)) - 3*cos(1)*cos_integral(2/(e^(2*b*x + 2*a) - 1)) - 3*cos(1)*cos_integral(-2/(e^(2*b*x + 2*a) - 1)) - cos(3)*cos_integral(-6/(e^(2*b*x + 2*a) - 1)) + 2*sin(3)*sin_integral(6*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 6*sin(1)*sin_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 2*sin(3)*sin_integral(6/(e^(2*b*x + 2*a) - 1)) + 6*sin(1)*sin_integral(2/(e^(2*b*x + 2*a) - 1)))/b","B",0
222,1,155,0,0.459212," ","integrate(cos(coth(b*x+a))^2,x, algorithm=""fricas"")","\frac{4 \, b x + \cos\left(2\right) \operatorname{Ci}\left(\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + \cos\left(2\right) \operatorname{Ci}\left(-\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(2\right) \operatorname{Ci}\left(\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(2\right) \operatorname{Ci}\left(-\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(2\right) \operatorname{Si}\left(\frac{4 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(2\right) \operatorname{Si}\left(\frac{4}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{8 \, b}"," ",0,"1/8*(4*b*x + cos(2)*cos_integral(4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + cos(2)*cos_integral(-4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) - cos(2)*cos_integral(4/(e^(2*b*x + 2*a) - 1)) - cos(2)*cos_integral(-4/(e^(2*b*x + 2*a) - 1)) + 2*sin(2)*sin_integral(4*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 2*sin(2)*sin_integral(4/(e^(2*b*x + 2*a) - 1)))/b","A",0
223,1,151,0,0.468354," ","integrate(cos(coth(b*x+a)),x, algorithm=""fricas"")","\frac{\cos\left(1\right) \operatorname{Ci}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + \cos\left(1\right) \operatorname{Ci}\left(-\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(1\right) \operatorname{Ci}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) - \cos\left(1\right) \operatorname{Ci}\left(-\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(1\right) \operatorname{Si}\left(\frac{2 \, e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right) + 2 \, \sin\left(1\right) \operatorname{Si}\left(\frac{2}{e^{\left(2 \, b x + 2 \, a\right)} - 1}\right)}{4 \, b}"," ",0,"1/4*(cos(1)*cos_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + cos(1)*cos_integral(-2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) - cos(1)*cos_integral(2/(e^(2*b*x + 2*a) - 1)) - cos(1)*cos_integral(-2/(e^(2*b*x + 2*a) - 1)) + 2*sin(1)*sin_integral(2*e^(2*b*x + 2*a)/(e^(2*b*x + 2*a) - 1)) + 2*sin(1)*sin_integral(2/(e^(2*b*x + 2*a) - 1)))/b","B",0
224,0,0,0,0.423310," ","integrate(sec(coth(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(\sec\left(\coth\left(b x + a\right)\right), x\right)"," ",0,"integral(sec(coth(b*x + a)), x)","F",0
