1,1,19,0,0.432787," ","integrate(sech(b*x+a),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}{b}"," ",0,"2*arctan(cosh(b*x + a) + sinh(b*x + a))/b","A",0
2,1,41,0,0.833042," ","integrate(sech(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2}{b \cosh\left(b x + a\right)^{2} + 2 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b \sinh\left(b x + a\right)^{2} + b}"," ",0,"-2/(b*cosh(b*x + a)^2 + 2*b*cosh(b*x + a)*sinh(b*x + a) + b*sinh(b*x + a)^2 + b)","B",0
3,1,267,0,1.128774," ","integrate(sech(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + \sinh\left(b x + a\right)^{3} + {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right) - \cosh\left(b x + a\right)}{b \cosh\left(b x + a\right)^{4} + 4 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b \sinh\left(b x + a\right)^{4} + 2 \, b \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b \cosh\left(b x + a\right)^{3} + b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b}"," ",0,"(cosh(b*x + a)^3 + 3*cosh(b*x + a)*sinh(b*x + a)^2 + sinh(b*x + a)^3 + (cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*arctan(cosh(b*x + a) + sinh(b*x + a)) + (3*cosh(b*x + a)^2 - 1)*sinh(b*x + a) - cosh(b*x + a))/(b*cosh(b*x + a)^4 + 4*b*cosh(b*x + a)*sinh(b*x + a)^3 + b*sinh(b*x + a)^4 + 2*b*cosh(b*x + a)^2 + 2*(3*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^2 + 4*(b*cosh(b*x + a)^3 + b*cosh(b*x + a))*sinh(b*x + a) + b)","B",0
4,1,164,0,1.355225," ","integrate(sech(b*x+a)^4,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}}{3 \, {\left(b \cosh\left(b x + a\right)^{5} + 5 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{4} + b \sinh\left(b x + a\right)^{5} + 3 \, b \cosh\left(b x + a\right)^{3} + {\left(10 \, b \cosh\left(b x + a\right)^{2} + 3 \, b\right)} \sinh\left(b x + a\right)^{3} + {\left(10 \, b \cosh\left(b x + a\right)^{3} + 9 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{2} + 4 \, b \cosh\left(b x + a\right) + {\left(5 \, b \cosh\left(b x + a\right)^{4} + 9 \, b \cosh\left(b x + a\right)^{2} + 2 \, b\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-8/3*(2*cosh(b*x + a) + sinh(b*x + a))/(b*cosh(b*x + a)^5 + 5*b*cosh(b*x + a)*sinh(b*x + a)^4 + b*sinh(b*x + a)^5 + 3*b*cosh(b*x + a)^3 + (10*b*cosh(b*x + a)^2 + 3*b)*sinh(b*x + a)^3 + (10*b*cosh(b*x + a)^3 + 9*b*cosh(b*x + a))*sinh(b*x + a)^2 + 4*b*cosh(b*x + a) + (5*b*cosh(b*x + a)^4 + 9*b*cosh(b*x + a)^2 + 2*b)*sinh(b*x + a))","B",0
5,1,812,0,1.024266," ","integrate(sech(b*x+a)^5,x, algorithm=""fricas"")","\frac{3 \, \cosh\left(b x + a\right)^{7} + 21 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{6} + 3 \, \sinh\left(b x + a\right)^{7} + {\left(63 \, \cosh\left(b x + a\right)^{2} + 11\right)} \sinh\left(b x + a\right)^{5} + 11 \, \cosh\left(b x + a\right)^{5} + 5 \, {\left(21 \, \cosh\left(b x + a\right)^{3} + 11 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{4} + {\left(105 \, \cosh\left(b x + a\right)^{4} + 110 \, \cosh\left(b x + a\right)^{2} - 11\right)} \sinh\left(b x + a\right)^{3} - 11 \, \cosh\left(b x + a\right)^{3} + {\left(63 \, \cosh\left(b x + a\right)^{5} + 110 \, \cosh\left(b x + a\right)^{3} - 33 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(\cosh\left(b x + a\right)^{8} + 8 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{7} + \sinh\left(b x + a\right)^{8} + 4 \, {\left(7 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{6} + 4 \, \cosh\left(b x + a\right)^{6} + 8 \, {\left(7 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 2 \, {\left(35 \, \cosh\left(b x + a\right)^{4} + 30 \, \cosh\left(b x + a\right)^{2} + 3\right)} \sinh\left(b x + a\right)^{4} + 6 \, \cosh\left(b x + a\right)^{4} + 8 \, {\left(7 \, \cosh\left(b x + a\right)^{5} + 10 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 4 \, {\left(7 \, \cosh\left(b x + a\right)^{6} + 15 \, \cosh\left(b x + a\right)^{4} + 9 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 4 \, \cosh\left(b x + a\right)^{2} + 8 \, {\left(\cosh\left(b x + a\right)^{7} + 3 \, \cosh\left(b x + a\right)^{5} + 3 \, \cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + {\left(21 \, \cosh\left(b x + a\right)^{6} + 55 \, \cosh\left(b x + a\right)^{4} - 33 \, \cosh\left(b x + a\right)^{2} - 3\right)} \sinh\left(b x + a\right) - 3 \, \cosh\left(b x + a\right)}{4 \, {\left(b \cosh\left(b x + a\right)^{8} + 8 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{7} + b \sinh\left(b x + a\right)^{8} + 4 \, b \cosh\left(b x + a\right)^{6} + 4 \, {\left(7 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{6} + 8 \, {\left(7 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 6 \, b \cosh\left(b x + a\right)^{4} + 2 \, {\left(35 \, b \cosh\left(b x + a\right)^{4} + 30 \, b \cosh\left(b x + a\right)^{2} + 3 \, b\right)} \sinh\left(b x + a\right)^{4} + 8 \, {\left(7 \, b \cosh\left(b x + a\right)^{5} + 10 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 4 \, b \cosh\left(b x + a\right)^{2} + 4 \, {\left(7 \, b \cosh\left(b x + a\right)^{6} + 15 \, b \cosh\left(b x + a\right)^{4} + 9 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{2} + 8 \, {\left(b \cosh\left(b x + a\right)^{7} + 3 \, b \cosh\left(b x + a\right)^{5} + 3 \, b \cosh\left(b x + a\right)^{3} + b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b\right)}}"," ",0,"1/4*(3*cosh(b*x + a)^7 + 21*cosh(b*x + a)*sinh(b*x + a)^6 + 3*sinh(b*x + a)^7 + (63*cosh(b*x + a)^2 + 11)*sinh(b*x + a)^5 + 11*cosh(b*x + a)^5 + 5*(21*cosh(b*x + a)^3 + 11*cosh(b*x + a))*sinh(b*x + a)^4 + (105*cosh(b*x + a)^4 + 110*cosh(b*x + a)^2 - 11)*sinh(b*x + a)^3 - 11*cosh(b*x + a)^3 + (63*cosh(b*x + a)^5 + 110*cosh(b*x + a)^3 - 33*cosh(b*x + a))*sinh(b*x + a)^2 + 3*(cosh(b*x + a)^8 + 8*cosh(b*x + a)*sinh(b*x + a)^7 + sinh(b*x + a)^8 + 4*(7*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^6 + 4*cosh(b*x + a)^6 + 8*(7*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^5 + 2*(35*cosh(b*x + a)^4 + 30*cosh(b*x + a)^2 + 3)*sinh(b*x + a)^4 + 6*cosh(b*x + a)^4 + 8*(7*cosh(b*x + a)^5 + 10*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^3 + 4*(7*cosh(b*x + a)^6 + 15*cosh(b*x + a)^4 + 9*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 4*cosh(b*x + a)^2 + 8*(cosh(b*x + a)^7 + 3*cosh(b*x + a)^5 + 3*cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*arctan(cosh(b*x + a) + sinh(b*x + a)) + (21*cosh(b*x + a)^6 + 55*cosh(b*x + a)^4 - 33*cosh(b*x + a)^2 - 3)*sinh(b*x + a) - 3*cosh(b*x + a))/(b*cosh(b*x + a)^8 + 8*b*cosh(b*x + a)*sinh(b*x + a)^7 + b*sinh(b*x + a)^8 + 4*b*cosh(b*x + a)^6 + 4*(7*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^6 + 8*(7*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^5 + 6*b*cosh(b*x + a)^4 + 2*(35*b*cosh(b*x + a)^4 + 30*b*cosh(b*x + a)^2 + 3*b)*sinh(b*x + a)^4 + 8*(7*b*cosh(b*x + a)^5 + 10*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^3 + 4*b*cosh(b*x + a)^2 + 4*(7*b*cosh(b*x + a)^6 + 15*b*cosh(b*x + a)^4 + 9*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^2 + 8*(b*cosh(b*x + a)^7 + 3*b*cosh(b*x + a)^5 + 3*b*cosh(b*x + a)^3 + b*cosh(b*x + a))*sinh(b*x + a) + b)","B",0
6,1,344,0,2.852977," ","integrate(sech(b*x+a)^6,x, algorithm=""fricas"")","-\frac{16 \, {\left(11 \, \cosh\left(b x + a\right)^{2} + 18 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 11 \, \sinh\left(b x + a\right)^{2} + 5\right)}}{15 \, {\left(b \cosh\left(b x + a\right)^{8} + 8 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{7} + b \sinh\left(b x + a\right)^{8} + 5 \, b \cosh\left(b x + a\right)^{6} + {\left(28 \, b \cosh\left(b x + a\right)^{2} + 5 \, b\right)} \sinh\left(b x + a\right)^{6} + 2 \, {\left(28 \, b \cosh\left(b x + a\right)^{3} + 15 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 10 \, b \cosh\left(b x + a\right)^{4} + 5 \, {\left(14 \, b \cosh\left(b x + a\right)^{4} + 15 \, b \cosh\left(b x + a\right)^{2} + 2 \, b\right)} \sinh\left(b x + a\right)^{4} + 4 \, {\left(14 \, b \cosh\left(b x + a\right)^{5} + 25 \, b \cosh\left(b x + a\right)^{3} + 10 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 11 \, b \cosh\left(b x + a\right)^{2} + {\left(28 \, b \cosh\left(b x + a\right)^{6} + 75 \, b \cosh\left(b x + a\right)^{4} + 60 \, b \cosh\left(b x + a\right)^{2} + 11 \, b\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b \cosh\left(b x + a\right)^{7} + 15 \, b \cosh\left(b x + a\right)^{5} + 20 \, b \cosh\left(b x + a\right)^{3} + 9 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 5 \, b\right)}}"," ",0,"-16/15*(11*cosh(b*x + a)^2 + 18*cosh(b*x + a)*sinh(b*x + a) + 11*sinh(b*x + a)^2 + 5)/(b*cosh(b*x + a)^8 + 8*b*cosh(b*x + a)*sinh(b*x + a)^7 + b*sinh(b*x + a)^8 + 5*b*cosh(b*x + a)^6 + (28*b*cosh(b*x + a)^2 + 5*b)*sinh(b*x + a)^6 + 2*(28*b*cosh(b*x + a)^3 + 15*b*cosh(b*x + a))*sinh(b*x + a)^5 + 10*b*cosh(b*x + a)^4 + 5*(14*b*cosh(b*x + a)^4 + 15*b*cosh(b*x + a)^2 + 2*b)*sinh(b*x + a)^4 + 4*(14*b*cosh(b*x + a)^5 + 25*b*cosh(b*x + a)^3 + 10*b*cosh(b*x + a))*sinh(b*x + a)^3 + 11*b*cosh(b*x + a)^2 + (28*b*cosh(b*x + a)^6 + 75*b*cosh(b*x + a)^4 + 60*b*cosh(b*x + a)^2 + 11*b)*sinh(b*x + a)^2 + 2*(4*b*cosh(b*x + a)^7 + 15*b*cosh(b*x + a)^5 + 20*b*cosh(b*x + a)^3 + 9*b*cosh(b*x + a))*sinh(b*x + a) + 5*b)","B",0
7,1,116,0,0.593174," ","integrate(sech(7*x)^4,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, \cosh\left(7 \, x\right) + \sinh\left(7 \, x\right)\right)}}{21 \, {\left(\cosh\left(7 \, x\right)^{5} + 5 \, \cosh\left(7 \, x\right) \sinh\left(7 \, x\right)^{4} + \sinh\left(7 \, x\right)^{5} + {\left(10 \, \cosh\left(7 \, x\right)^{2} + 3\right)} \sinh\left(7 \, x\right)^{3} + 3 \, \cosh\left(7 \, x\right)^{3} + {\left(10 \, \cosh\left(7 \, x\right)^{3} + 9 \, \cosh\left(7 \, x\right)\right)} \sinh\left(7 \, x\right)^{2} + {\left(5 \, \cosh\left(7 \, x\right)^{4} + 9 \, \cosh\left(7 \, x\right)^{2} + 2\right)} \sinh\left(7 \, x\right) + 4 \, \cosh\left(7 \, x\right)\right)}}"," ",0,"-8/21*(2*cosh(7*x) + sinh(7*x))/(cosh(7*x)^5 + 5*cosh(7*x)*sinh(7*x)^4 + sinh(7*x)^5 + (10*cosh(7*x)^2 + 3)*sinh(7*x)^3 + 3*cosh(7*x)^3 + (10*cosh(7*x)^3 + 9*cosh(7*x))*sinh(7*x)^2 + (5*cosh(7*x)^4 + 9*cosh(7*x)^2 + 2)*sinh(7*x) + 4*cosh(7*x))","B",0
8,1,280,0,0.472780," ","integrate(sech(pi*x)^6,x, algorithm=""fricas"")","-\frac{16 \, {\left(11 \, \cosh\left(\pi x\right)^{2} + 18 \, \cosh\left(\pi x\right) \sinh\left(\pi x\right) + 11 \, \sinh\left(\pi x\right)^{2} + 5\right)}}{15 \, {\left(5 \, \pi + \pi \cosh\left(\pi x\right)^{8} + 8 \, \pi \cosh\left(\pi x\right) \sinh\left(\pi x\right)^{7} + \pi \sinh\left(\pi x\right)^{8} + 5 \, \pi \cosh\left(\pi x\right)^{6} + {\left(5 \, \pi + 28 \, \pi \cosh\left(\pi x\right)^{2}\right)} \sinh\left(\pi x\right)^{6} + 2 \, {\left(28 \, \pi \cosh\left(\pi x\right)^{3} + 15 \, \pi \cosh\left(\pi x\right)\right)} \sinh\left(\pi x\right)^{5} + 10 \, \pi \cosh\left(\pi x\right)^{4} + 5 \, {\left(2 \, \pi + 14 \, \pi \cosh\left(\pi x\right)^{4} + 15 \, \pi \cosh\left(\pi x\right)^{2}\right)} \sinh\left(\pi x\right)^{4} + 4 \, {\left(14 \, \pi \cosh\left(\pi x\right)^{5} + 25 \, \pi \cosh\left(\pi x\right)^{3} + 10 \, \pi \cosh\left(\pi x\right)\right)} \sinh\left(\pi x\right)^{3} + 11 \, \pi \cosh\left(\pi x\right)^{2} + {\left(11 \, \pi + 28 \, \pi \cosh\left(\pi x\right)^{6} + 75 \, \pi \cosh\left(\pi x\right)^{4} + 60 \, \pi \cosh\left(\pi x\right)^{2}\right)} \sinh\left(\pi x\right)^{2} + 2 \, {\left(4 \, \pi \cosh\left(\pi x\right)^{7} + 15 \, \pi \cosh\left(\pi x\right)^{5} + 20 \, \pi \cosh\left(\pi x\right)^{3} + 9 \, \pi \cosh\left(\pi x\right)\right)} \sinh\left(\pi x\right)\right)}}"," ",0,"-16/15*(11*cosh(pi*x)^2 + 18*cosh(pi*x)*sinh(pi*x) + 11*sinh(pi*x)^2 + 5)/(5*pi + pi*cosh(pi*x)^8 + 8*pi*cosh(pi*x)*sinh(pi*x)^7 + pi*sinh(pi*x)^8 + 5*pi*cosh(pi*x)^6 + (5*pi + 28*pi*cosh(pi*x)^2)*sinh(pi*x)^6 + 2*(28*pi*cosh(pi*x)^3 + 15*pi*cosh(pi*x))*sinh(pi*x)^5 + 10*pi*cosh(pi*x)^4 + 5*(2*pi + 14*pi*cosh(pi*x)^4 + 15*pi*cosh(pi*x)^2)*sinh(pi*x)^4 + 4*(14*pi*cosh(pi*x)^5 + 25*pi*cosh(pi*x)^3 + 10*pi*cosh(pi*x))*sinh(pi*x)^3 + 11*pi*cosh(pi*x)^2 + (11*pi + 28*pi*cosh(pi*x)^6 + 75*pi*cosh(pi*x)^4 + 60*pi*cosh(pi*x)^2)*sinh(pi*x)^2 + 2*(4*pi*cosh(pi*x)^7 + 15*pi*cosh(pi*x)^5 + 20*pi*cosh(pi*x)^3 + 9*pi*cosh(pi*x))*sinh(pi*x))","B",0
9,0,0,0,0.657641," ","integrate(sech(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b x + a\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(sech(b*x + a)^(5/2), x)","F",0
10,0,0,0,0.561664," ","integrate(sech(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b x + a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sech(b*x + a)^(3/2), x)","F",0
11,0,0,0,0.478662," ","integrate(sech(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\operatorname{sech}\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(sech(b*x + a)), x)","F",0
12,0,0,0,1.137916," ","integrate(1/sech(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\operatorname{sech}\left(b x + a\right)}}, x\right)"," ",0,"integral(1/sqrt(sech(b*x + a)), x)","F",0
13,0,0,0,1.719155," ","integrate(1/sech(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\operatorname{sech}\left(b x + a\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sech(b*x + a)^(-3/2), x)","F",0
14,0,0,0,0.530469," ","integrate(1/sech(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\operatorname{sech}\left(b x + a\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sech(b*x + a)^(-5/2), x)","F",0
15,0,0,0,1.112407," ","integrate((b*sech(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right)} b^{3} \operatorname{sech}\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))*b^3*sech(d*x + c)^3, x)","F",0
16,0,0,0,0.396712," ","integrate((b*sech(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right)} b^{2} \operatorname{sech}\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))*b^2*sech(d*x + c)^2, x)","F",0
17,0,0,0,0.395396," ","integrate((b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right)} b \operatorname{sech}\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))*b*sech(d*x + c), x)","F",0
18,0,0,0,0.391098," ","integrate((b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c)), x)","F",0
19,0,0,0,0.392684," ","integrate(1/(b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right)}}{b \operatorname{sech}\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))/(b*sech(d*x + c)), x)","F",0
20,0,0,0,0.439569," ","integrate(1/(b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right)}}{b^{2} \operatorname{sech}\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))/(b^2*sech(d*x + c)^2), x)","F",0
21,0,0,0,0.416066," ","integrate(1/(b*sech(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right)}}{b^{3} \operatorname{sech}\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))/(b^3*sech(d*x + c)^3), x)","F",0
22,0,0,0,0.451394," ","integrate(1/(b*sech(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right)}}{b^{4} \operatorname{sech}\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c))/(b^4*sech(d*x + c)^4), x)","F",0
23,0,0,0,0.429862," ","integrate((b*sech(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \operatorname{sech}\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((b*sech(d*x + c))^n, x)","F",0
24,1,1604,0,0.424365," ","integrate((sech(b*x+a)^2)^(7/2),x, algorithm=""fricas"")","\frac{15 \, \cosh\left(b x + a\right)^{11} + 165 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{10} + 15 \, \sinh\left(b x + a\right)^{11} + 5 \, {\left(165 \, \cosh\left(b x + a\right)^{2} + 17\right)} \sinh\left(b x + a\right)^{9} + 85 \, \cosh\left(b x + a\right)^{9} + 45 \, {\left(55 \, \cosh\left(b x + a\right)^{3} + 17 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{8} + 18 \, {\left(275 \, \cosh\left(b x + a\right)^{4} + 170 \, \cosh\left(b x + a\right)^{2} + 11\right)} \sinh\left(b x + a\right)^{7} + 198 \, \cosh\left(b x + a\right)^{7} + 42 \, {\left(165 \, \cosh\left(b x + a\right)^{5} + 170 \, \cosh\left(b x + a\right)^{3} + 33 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{6} + 18 \, {\left(385 \, \cosh\left(b x + a\right)^{6} + 595 \, \cosh\left(b x + a\right)^{4} + 231 \, \cosh\left(b x + a\right)^{2} - 11\right)} \sinh\left(b x + a\right)^{5} - 198 \, \cosh\left(b x + a\right)^{5} + 90 \, {\left(55 \, \cosh\left(b x + a\right)^{7} + 119 \, \cosh\left(b x + a\right)^{5} + 77 \, \cosh\left(b x + a\right)^{3} - 11 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{4} + 5 \, {\left(495 \, \cosh\left(b x + a\right)^{8} + 1428 \, \cosh\left(b x + a\right)^{6} + 1386 \, \cosh\left(b x + a\right)^{4} - 396 \, \cosh\left(b x + a\right)^{2} - 17\right)} \sinh\left(b x + a\right)^{3} - 85 \, \cosh\left(b x + a\right)^{3} + 3 \, {\left(275 \, \cosh\left(b x + a\right)^{9} + 1020 \, \cosh\left(b x + a\right)^{7} + 1386 \, \cosh\left(b x + a\right)^{5} - 660 \, \cosh\left(b x + a\right)^{3} - 85 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{2} + 15 \, {\left(\cosh\left(b x + a\right)^{12} + 12 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{11} + \sinh\left(b x + a\right)^{12} + 6 \, {\left(11 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{10} + 6 \, \cosh\left(b x + a\right)^{10} + 20 \, {\left(11 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{9} + 15 \, {\left(33 \, \cosh\left(b x + a\right)^{4} + 18 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{8} + 15 \, \cosh\left(b x + a\right)^{8} + 24 \, {\left(33 \, \cosh\left(b x + a\right)^{5} + 30 \, \cosh\left(b x + a\right)^{3} + 5 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{7} + 4 \, {\left(231 \, \cosh\left(b x + a\right)^{6} + 315 \, \cosh\left(b x + a\right)^{4} + 105 \, \cosh\left(b x + a\right)^{2} + 5\right)} \sinh\left(b x + a\right)^{6} + 20 \, \cosh\left(b x + a\right)^{6} + 24 \, {\left(33 \, \cosh\left(b x + a\right)^{7} + 63 \, \cosh\left(b x + a\right)^{5} + 35 \, \cosh\left(b x + a\right)^{3} + 5 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 15 \, {\left(33 \, \cosh\left(b x + a\right)^{8} + 84 \, \cosh\left(b x + a\right)^{6} + 70 \, \cosh\left(b x + a\right)^{4} + 20 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{4} + 15 \, \cosh\left(b x + a\right)^{4} + 20 \, {\left(11 \, \cosh\left(b x + a\right)^{9} + 36 \, \cosh\left(b x + a\right)^{7} + 42 \, \cosh\left(b x + a\right)^{5} + 20 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 6 \, {\left(11 \, \cosh\left(b x + a\right)^{10} + 45 \, \cosh\left(b x + a\right)^{8} + 70 \, \cosh\left(b x + a\right)^{6} + 50 \, \cosh\left(b x + a\right)^{4} + 15 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 6 \, \cosh\left(b x + a\right)^{2} + 12 \, {\left(\cosh\left(b x + a\right)^{11} + 5 \, \cosh\left(b x + a\right)^{9} + 10 \, \cosh\left(b x + a\right)^{7} + 10 \, \cosh\left(b x + a\right)^{5} + 5 \, \cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 3 \, {\left(55 \, \cosh\left(b x + a\right)^{10} + 255 \, \cosh\left(b x + a\right)^{8} + 462 \, \cosh\left(b x + a\right)^{6} - 330 \, \cosh\left(b x + a\right)^{4} - 85 \, \cosh\left(b x + a\right)^{2} - 5\right)} \sinh\left(b x + a\right) - 15 \, \cosh\left(b x + a\right)}{24 \, {\left(b \cosh\left(b x + a\right)^{12} + 12 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{11} + b \sinh\left(b x + a\right)^{12} + 6 \, b \cosh\left(b x + a\right)^{10} + 6 \, {\left(11 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{10} + 20 \, {\left(11 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{9} + 15 \, b \cosh\left(b x + a\right)^{8} + 15 \, {\left(33 \, b \cosh\left(b x + a\right)^{4} + 18 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{8} + 24 \, {\left(33 \, b \cosh\left(b x + a\right)^{5} + 30 \, b \cosh\left(b x + a\right)^{3} + 5 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{7} + 20 \, b \cosh\left(b x + a\right)^{6} + 4 \, {\left(231 \, b \cosh\left(b x + a\right)^{6} + 315 \, b \cosh\left(b x + a\right)^{4} + 105 \, b \cosh\left(b x + a\right)^{2} + 5 \, b\right)} \sinh\left(b x + a\right)^{6} + 24 \, {\left(33 \, b \cosh\left(b x + a\right)^{7} + 63 \, b \cosh\left(b x + a\right)^{5} + 35 \, b \cosh\left(b x + a\right)^{3} + 5 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 15 \, b \cosh\left(b x + a\right)^{4} + 15 \, {\left(33 \, b \cosh\left(b x + a\right)^{8} + 84 \, b \cosh\left(b x + a\right)^{6} + 70 \, b \cosh\left(b x + a\right)^{4} + 20 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{4} + 20 \, {\left(11 \, b \cosh\left(b x + a\right)^{9} + 36 \, b \cosh\left(b x + a\right)^{7} + 42 \, b \cosh\left(b x + a\right)^{5} + 20 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 6 \, b \cosh\left(b x + a\right)^{2} + 6 \, {\left(11 \, b \cosh\left(b x + a\right)^{10} + 45 \, b \cosh\left(b x + a\right)^{8} + 70 \, b \cosh\left(b x + a\right)^{6} + 50 \, b \cosh\left(b x + a\right)^{4} + 15 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{2} + 12 \, {\left(b \cosh\left(b x + a\right)^{11} + 5 \, b \cosh\left(b x + a\right)^{9} + 10 \, b \cosh\left(b x + a\right)^{7} + 10 \, b \cosh\left(b x + a\right)^{5} + 5 \, b \cosh\left(b x + a\right)^{3} + b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b\right)}}"," ",0,"1/24*(15*cosh(b*x + a)^11 + 165*cosh(b*x + a)*sinh(b*x + a)^10 + 15*sinh(b*x + a)^11 + 5*(165*cosh(b*x + a)^2 + 17)*sinh(b*x + a)^9 + 85*cosh(b*x + a)^9 + 45*(55*cosh(b*x + a)^3 + 17*cosh(b*x + a))*sinh(b*x + a)^8 + 18*(275*cosh(b*x + a)^4 + 170*cosh(b*x + a)^2 + 11)*sinh(b*x + a)^7 + 198*cosh(b*x + a)^7 + 42*(165*cosh(b*x + a)^5 + 170*cosh(b*x + a)^3 + 33*cosh(b*x + a))*sinh(b*x + a)^6 + 18*(385*cosh(b*x + a)^6 + 595*cosh(b*x + a)^4 + 231*cosh(b*x + a)^2 - 11)*sinh(b*x + a)^5 - 198*cosh(b*x + a)^5 + 90*(55*cosh(b*x + a)^7 + 119*cosh(b*x + a)^5 + 77*cosh(b*x + a)^3 - 11*cosh(b*x + a))*sinh(b*x + a)^4 + 5*(495*cosh(b*x + a)^8 + 1428*cosh(b*x + a)^6 + 1386*cosh(b*x + a)^4 - 396*cosh(b*x + a)^2 - 17)*sinh(b*x + a)^3 - 85*cosh(b*x + a)^3 + 3*(275*cosh(b*x + a)^9 + 1020*cosh(b*x + a)^7 + 1386*cosh(b*x + a)^5 - 660*cosh(b*x + a)^3 - 85*cosh(b*x + a))*sinh(b*x + a)^2 + 15*(cosh(b*x + a)^12 + 12*cosh(b*x + a)*sinh(b*x + a)^11 + sinh(b*x + a)^12 + 6*(11*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^10 + 6*cosh(b*x + a)^10 + 20*(11*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^9 + 15*(33*cosh(b*x + a)^4 + 18*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^8 + 15*cosh(b*x + a)^8 + 24*(33*cosh(b*x + a)^5 + 30*cosh(b*x + a)^3 + 5*cosh(b*x + a))*sinh(b*x + a)^7 + 4*(231*cosh(b*x + a)^6 + 315*cosh(b*x + a)^4 + 105*cosh(b*x + a)^2 + 5)*sinh(b*x + a)^6 + 20*cosh(b*x + a)^6 + 24*(33*cosh(b*x + a)^7 + 63*cosh(b*x + a)^5 + 35*cosh(b*x + a)^3 + 5*cosh(b*x + a))*sinh(b*x + a)^5 + 15*(33*cosh(b*x + a)^8 + 84*cosh(b*x + a)^6 + 70*cosh(b*x + a)^4 + 20*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^4 + 15*cosh(b*x + a)^4 + 20*(11*cosh(b*x + a)^9 + 36*cosh(b*x + a)^7 + 42*cosh(b*x + a)^5 + 20*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^3 + 6*(11*cosh(b*x + a)^10 + 45*cosh(b*x + a)^8 + 70*cosh(b*x + a)^6 + 50*cosh(b*x + a)^4 + 15*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 6*cosh(b*x + a)^2 + 12*(cosh(b*x + a)^11 + 5*cosh(b*x + a)^9 + 10*cosh(b*x + a)^7 + 10*cosh(b*x + a)^5 + 5*cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*arctan(cosh(b*x + a) + sinh(b*x + a)) + 3*(55*cosh(b*x + a)^10 + 255*cosh(b*x + a)^8 + 462*cosh(b*x + a)^6 - 330*cosh(b*x + a)^4 - 85*cosh(b*x + a)^2 - 5)*sinh(b*x + a) - 15*cosh(b*x + a))/(b*cosh(b*x + a)^12 + 12*b*cosh(b*x + a)*sinh(b*x + a)^11 + b*sinh(b*x + a)^12 + 6*b*cosh(b*x + a)^10 + 6*(11*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^10 + 20*(11*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^9 + 15*b*cosh(b*x + a)^8 + 15*(33*b*cosh(b*x + a)^4 + 18*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^8 + 24*(33*b*cosh(b*x + a)^5 + 30*b*cosh(b*x + a)^3 + 5*b*cosh(b*x + a))*sinh(b*x + a)^7 + 20*b*cosh(b*x + a)^6 + 4*(231*b*cosh(b*x + a)^6 + 315*b*cosh(b*x + a)^4 + 105*b*cosh(b*x + a)^2 + 5*b)*sinh(b*x + a)^6 + 24*(33*b*cosh(b*x + a)^7 + 63*b*cosh(b*x + a)^5 + 35*b*cosh(b*x + a)^3 + 5*b*cosh(b*x + a))*sinh(b*x + a)^5 + 15*b*cosh(b*x + a)^4 + 15*(33*b*cosh(b*x + a)^8 + 84*b*cosh(b*x + a)^6 + 70*b*cosh(b*x + a)^4 + 20*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^4 + 20*(11*b*cosh(b*x + a)^9 + 36*b*cosh(b*x + a)^7 + 42*b*cosh(b*x + a)^5 + 20*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^3 + 6*b*cosh(b*x + a)^2 + 6*(11*b*cosh(b*x + a)^10 + 45*b*cosh(b*x + a)^8 + 70*b*cosh(b*x + a)^6 + 50*b*cosh(b*x + a)^4 + 15*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^2 + 12*(b*cosh(b*x + a)^11 + 5*b*cosh(b*x + a)^9 + 10*b*cosh(b*x + a)^7 + 10*b*cosh(b*x + a)^5 + 5*b*cosh(b*x + a)^3 + b*cosh(b*x + a))*sinh(b*x + a) + b)","B",0
25,1,812,0,0.444386," ","integrate((sech(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(b x + a\right)^{7} + 21 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{6} + 3 \, \sinh\left(b x + a\right)^{7} + {\left(63 \, \cosh\left(b x + a\right)^{2} + 11\right)} \sinh\left(b x + a\right)^{5} + 11 \, \cosh\left(b x + a\right)^{5} + 5 \, {\left(21 \, \cosh\left(b x + a\right)^{3} + 11 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{4} + {\left(105 \, \cosh\left(b x + a\right)^{4} + 110 \, \cosh\left(b x + a\right)^{2} - 11\right)} \sinh\left(b x + a\right)^{3} - 11 \, \cosh\left(b x + a\right)^{3} + {\left(63 \, \cosh\left(b x + a\right)^{5} + 110 \, \cosh\left(b x + a\right)^{3} - 33 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(\cosh\left(b x + a\right)^{8} + 8 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{7} + \sinh\left(b x + a\right)^{8} + 4 \, {\left(7 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{6} + 4 \, \cosh\left(b x + a\right)^{6} + 8 \, {\left(7 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 2 \, {\left(35 \, \cosh\left(b x + a\right)^{4} + 30 \, \cosh\left(b x + a\right)^{2} + 3\right)} \sinh\left(b x + a\right)^{4} + 6 \, \cosh\left(b x + a\right)^{4} + 8 \, {\left(7 \, \cosh\left(b x + a\right)^{5} + 10 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 4 \, {\left(7 \, \cosh\left(b x + a\right)^{6} + 15 \, \cosh\left(b x + a\right)^{4} + 9 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 4 \, \cosh\left(b x + a\right)^{2} + 8 \, {\left(\cosh\left(b x + a\right)^{7} + 3 \, \cosh\left(b x + a\right)^{5} + 3 \, \cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + {\left(21 \, \cosh\left(b x + a\right)^{6} + 55 \, \cosh\left(b x + a\right)^{4} - 33 \, \cosh\left(b x + a\right)^{2} - 3\right)} \sinh\left(b x + a\right) - 3 \, \cosh\left(b x + a\right)}{4 \, {\left(b \cosh\left(b x + a\right)^{8} + 8 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{7} + b \sinh\left(b x + a\right)^{8} + 4 \, b \cosh\left(b x + a\right)^{6} + 4 \, {\left(7 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{6} + 8 \, {\left(7 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{5} + 6 \, b \cosh\left(b x + a\right)^{4} + 2 \, {\left(35 \, b \cosh\left(b x + a\right)^{4} + 30 \, b \cosh\left(b x + a\right)^{2} + 3 \, b\right)} \sinh\left(b x + a\right)^{4} + 8 \, {\left(7 \, b \cosh\left(b x + a\right)^{5} + 10 \, b \cosh\left(b x + a\right)^{3} + 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 4 \, b \cosh\left(b x + a\right)^{2} + 4 \, {\left(7 \, b \cosh\left(b x + a\right)^{6} + 15 \, b \cosh\left(b x + a\right)^{4} + 9 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{2} + 8 \, {\left(b \cosh\left(b x + a\right)^{7} + 3 \, b \cosh\left(b x + a\right)^{5} + 3 \, b \cosh\left(b x + a\right)^{3} + b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b\right)}}"," ",0,"1/4*(3*cosh(b*x + a)^7 + 21*cosh(b*x + a)*sinh(b*x + a)^6 + 3*sinh(b*x + a)^7 + (63*cosh(b*x + a)^2 + 11)*sinh(b*x + a)^5 + 11*cosh(b*x + a)^5 + 5*(21*cosh(b*x + a)^3 + 11*cosh(b*x + a))*sinh(b*x + a)^4 + (105*cosh(b*x + a)^4 + 110*cosh(b*x + a)^2 - 11)*sinh(b*x + a)^3 - 11*cosh(b*x + a)^3 + (63*cosh(b*x + a)^5 + 110*cosh(b*x + a)^3 - 33*cosh(b*x + a))*sinh(b*x + a)^2 + 3*(cosh(b*x + a)^8 + 8*cosh(b*x + a)*sinh(b*x + a)^7 + sinh(b*x + a)^8 + 4*(7*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^6 + 4*cosh(b*x + a)^6 + 8*(7*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^5 + 2*(35*cosh(b*x + a)^4 + 30*cosh(b*x + a)^2 + 3)*sinh(b*x + a)^4 + 6*cosh(b*x + a)^4 + 8*(7*cosh(b*x + a)^5 + 10*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^3 + 4*(7*cosh(b*x + a)^6 + 15*cosh(b*x + a)^4 + 9*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 4*cosh(b*x + a)^2 + 8*(cosh(b*x + a)^7 + 3*cosh(b*x + a)^5 + 3*cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*arctan(cosh(b*x + a) + sinh(b*x + a)) + (21*cosh(b*x + a)^6 + 55*cosh(b*x + a)^4 - 33*cosh(b*x + a)^2 - 3)*sinh(b*x + a) - 3*cosh(b*x + a))/(b*cosh(b*x + a)^8 + 8*b*cosh(b*x + a)*sinh(b*x + a)^7 + b*sinh(b*x + a)^8 + 4*b*cosh(b*x + a)^6 + 4*(7*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^6 + 8*(7*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^5 + 6*b*cosh(b*x + a)^4 + 2*(35*b*cosh(b*x + a)^4 + 30*b*cosh(b*x + a)^2 + 3*b)*sinh(b*x + a)^4 + 8*(7*b*cosh(b*x + a)^5 + 10*b*cosh(b*x + a)^3 + 3*b*cosh(b*x + a))*sinh(b*x + a)^3 + 4*b*cosh(b*x + a)^2 + 4*(7*b*cosh(b*x + a)^6 + 15*b*cosh(b*x + a)^4 + 9*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^2 + 8*(b*cosh(b*x + a)^7 + 3*b*cosh(b*x + a)^5 + 3*b*cosh(b*x + a)^3 + b*cosh(b*x + a))*sinh(b*x + a) + b)","B",0
26,1,267,0,0.391699," ","integrate((sech(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{\cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + \sinh\left(b x + a\right)^{3} + {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right) - \cosh\left(b x + a\right)}{b \cosh\left(b x + a\right)^{4} + 4 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b \sinh\left(b x + a\right)^{4} + 2 \, b \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b \cosh\left(b x + a\right)^{2} + b\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b \cosh\left(b x + a\right)^{3} + b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b}"," ",0,"(cosh(b*x + a)^3 + 3*cosh(b*x + a)*sinh(b*x + a)^2 + sinh(b*x + a)^3 + (cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*arctan(cosh(b*x + a) + sinh(b*x + a)) + (3*cosh(b*x + a)^2 - 1)*sinh(b*x + a) - cosh(b*x + a))/(b*cosh(b*x + a)^4 + 4*b*cosh(b*x + a)*sinh(b*x + a)^3 + b*sinh(b*x + a)^4 + 2*b*cosh(b*x + a)^2 + 2*(3*b*cosh(b*x + a)^2 + b)*sinh(b*x + a)^2 + 4*(b*cosh(b*x + a)^3 + b*cosh(b*x + a))*sinh(b*x + a) + b)","B",0
27,1,19,0,0.380571," ","integrate((sech(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}{b}"," ",0,"2*arctan(cosh(b*x + a) + sinh(b*x + a))/b","A",0
28,1,10,0,0.380741," ","integrate(1/(sech(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sinh\left(b x + a\right)}{b}"," ",0,"sinh(b*x + a)/b","A",0
29,1,32,0,0.388364," ","integrate(1/(sech(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{\sinh\left(b x + a\right)^{3} + 3 \, {\left(\cosh\left(b x + a\right)^{2} + 3\right)} \sinh\left(b x + a\right)}{12 \, b}"," ",0,"1/12*(sinh(b*x + a)^3 + 3*(cosh(b*x + a)^2 + 3)*sinh(b*x + a))/b","A",0
30,1,66,0,0.455668," ","integrate(1/(sech(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sinh\left(b x + a\right)^{5} + 5 \, {\left(6 \, \cosh\left(b x + a\right)^{2} + 5\right)} \sinh\left(b x + a\right)^{3} + 15 \, {\left(\cosh\left(b x + a\right)^{4} + 5 \, \cosh\left(b x + a\right)^{2} + 10\right)} \sinh\left(b x + a\right)}{240 \, b}"," ",0,"1/240*(3*sinh(b*x + a)^5 + 5*(6*cosh(b*x + a)^2 + 5)*sinh(b*x + a)^3 + 15*(cosh(b*x + a)^4 + 5*cosh(b*x + a)^2 + 10)*sinh(b*x + a))/b","A",0
31,1,108,0,0.494030," ","integrate(1/(sech(b*x+a)^2)^(7/2),x, algorithm=""fricas"")","\frac{5 \, \sinh\left(b x + a\right)^{7} + 7 \, {\left(15 \, \cosh\left(b x + a\right)^{2} + 7\right)} \sinh\left(b x + a\right)^{5} + 35 \, {\left(5 \, \cosh\left(b x + a\right)^{4} + 14 \, \cosh\left(b x + a\right)^{2} + 7\right)} \sinh\left(b x + a\right)^{3} + 35 \, {\left(\cosh\left(b x + a\right)^{6} + 7 \, \cosh\left(b x + a\right)^{4} + 21 \, \cosh\left(b x + a\right)^{2} + 35\right)} \sinh\left(b x + a\right)}{2240 \, b}"," ",0,"1/2240*(5*sinh(b*x + a)^7 + 7*(15*cosh(b*x + a)^2 + 7)*sinh(b*x + a)^5 + 35*(5*cosh(b*x + a)^4 + 14*cosh(b*x + a)^2 + 7)*sinh(b*x + a)^3 + 35*(cosh(b*x + a)^6 + 7*cosh(b*x + a)^4 + 21*cosh(b*x + a)^2 + 35)*sinh(b*x + a))/b","A",0
32,1,1082,0,0.493515," ","integrate((a*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} e^{\left(2 \, x\right)} + a^{2}\right)} \sinh\left(x\right)^{7} + 11 \, a^{2} \cosh\left(x\right)^{5} + 21 \, {\left(a^{2} \cosh\left(x\right) e^{\left(2 \, x\right)} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} + {\left(63 \, a^{2} \cosh\left(x\right)^{2} + 11 \, a^{2} + {\left(63 \, a^{2} \cosh\left(x\right)^{2} + 11 \, a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{5} - 11 \, a^{2} \cosh\left(x\right)^{3} + 5 \, {\left(21 \, a^{2} \cosh\left(x\right)^{3} + 11 \, a^{2} \cosh\left(x\right) + {\left(21 \, a^{2} \cosh\left(x\right)^{3} + 11 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{4} + {\left(105 \, a^{2} \cosh\left(x\right)^{4} + 110 \, a^{2} \cosh\left(x\right)^{2} - 11 \, a^{2} + {\left(105 \, a^{2} \cosh\left(x\right)^{4} + 110 \, a^{2} \cosh\left(x\right)^{2} - 11 \, a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right) + {\left(63 \, a^{2} \cosh\left(x\right)^{5} + 110 \, a^{2} \cosh\left(x\right)^{3} - 33 \, a^{2} \cosh\left(x\right) + {\left(63 \, a^{2} \cosh\left(x\right)^{5} + 110 \, a^{2} \cosh\left(x\right)^{3} - 33 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{2} + 3 \, {\left(a^{2} \cosh\left(x\right)^{8} + {\left(a^{2} e^{\left(2 \, x\right)} + a^{2}\right)} \sinh\left(x\right)^{8} + 4 \, a^{2} \cosh\left(x\right)^{6} + 8 \, {\left(a^{2} \cosh\left(x\right) e^{\left(2 \, x\right)} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + {\left(7 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right) + {\left(7 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + {\left(35 \, a^{2} \cosh\left(x\right)^{4} + 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right) + {\left(7 \, a^{2} \cosh\left(x\right)^{5} + 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + {\left(7 \, a^{2} \cosh\left(x\right)^{6} + 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{2} + a^{2} + {\left(a^{2} \cosh\left(x\right)^{8} + 4 \, a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right) + {\left(a^{2} \cosh\left(x\right)^{7} + 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + {\left(3 \, a^{2} \cosh\left(x\right)^{7} + 11 \, a^{2} \cosh\left(x\right)^{5} - 11 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + {\left(21 \, a^{2} \cosh\left(x\right)^{6} + 55 \, a^{2} \cosh\left(x\right)^{4} - 33 \, a^{2} \cosh\left(x\right)^{2} - 3 \, a^{2} + {\left(21 \, a^{2} \cosh\left(x\right)^{6} + 55 \, a^{2} \cosh\left(x\right)^{4} - 33 \, a^{2} \cosh\left(x\right)^{2} - 3 \, a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{4 \, {\left(8 \, \cosh\left(x\right) e^{x} \sinh\left(x\right)^{7} + e^{x} \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} e^{x} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{x} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} e^{x} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{x} \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)} e^{x} \sinh\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)} e^{x} \sinh\left(x\right) + {\left(\cosh\left(x\right)^{8} + 4 \, \cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{2} + 1\right)} e^{x}\right)}}"," ",0,"1/4*(3*a^2*cosh(x)^7 + 3*(a^2*e^(2*x) + a^2)*sinh(x)^7 + 11*a^2*cosh(x)^5 + 21*(a^2*cosh(x)*e^(2*x) + a^2*cosh(x))*sinh(x)^6 + (63*a^2*cosh(x)^2 + 11*a^2 + (63*a^2*cosh(x)^2 + 11*a^2)*e^(2*x))*sinh(x)^5 - 11*a^2*cosh(x)^3 + 5*(21*a^2*cosh(x)^3 + 11*a^2*cosh(x) + (21*a^2*cosh(x)^3 + 11*a^2*cosh(x))*e^(2*x))*sinh(x)^4 + (105*a^2*cosh(x)^4 + 110*a^2*cosh(x)^2 - 11*a^2 + (105*a^2*cosh(x)^4 + 110*a^2*cosh(x)^2 - 11*a^2)*e^(2*x))*sinh(x)^3 - 3*a^2*cosh(x) + (63*a^2*cosh(x)^5 + 110*a^2*cosh(x)^3 - 33*a^2*cosh(x) + (63*a^2*cosh(x)^5 + 110*a^2*cosh(x)^3 - 33*a^2*cosh(x))*e^(2*x))*sinh(x)^2 + 3*(a^2*cosh(x)^8 + (a^2*e^(2*x) + a^2)*sinh(x)^8 + 4*a^2*cosh(x)^6 + 8*(a^2*cosh(x)*e^(2*x) + a^2*cosh(x))*sinh(x)^7 + 4*(7*a^2*cosh(x)^2 + a^2 + (7*a^2*cosh(x)^2 + a^2)*e^(2*x))*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 + 3*a^2*cosh(x) + (7*a^2*cosh(x)^3 + 3*a^2*cosh(x))*e^(2*x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 + 30*a^2*cosh(x)^2 + 3*a^2 + (35*a^2*cosh(x)^4 + 30*a^2*cosh(x)^2 + 3*a^2)*e^(2*x))*sinh(x)^4 + 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 + 10*a^2*cosh(x)^3 + 3*a^2*cosh(x) + (7*a^2*cosh(x)^5 + 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*e^(2*x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 + 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 + a^2 + (7*a^2*cosh(x)^6 + 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 + a^2)*e^(2*x))*sinh(x)^2 + a^2 + (a^2*cosh(x)^8 + 4*a^2*cosh(x)^6 + 6*a^2*cosh(x)^4 + 4*a^2*cosh(x)^2 + a^2)*e^(2*x) + 8*(a^2*cosh(x)^7 + 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 + a^2*cosh(x) + (a^2*cosh(x)^7 + 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 + a^2*cosh(x))*e^(2*x))*sinh(x))*arctan(cosh(x) + sinh(x)) + (3*a^2*cosh(x)^7 + 11*a^2*cosh(x)^5 - 11*a^2*cosh(x)^3 - 3*a^2*cosh(x))*e^(2*x) + (21*a^2*cosh(x)^6 + 55*a^2*cosh(x)^4 - 33*a^2*cosh(x)^2 - 3*a^2 + (21*a^2*cosh(x)^6 + 55*a^2*cosh(x)^4 - 33*a^2*cosh(x)^2 - 3*a^2)*e^(2*x))*sinh(x))*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(8*cosh(x)*e^x*sinh(x)^7 + e^x*sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*e^x*sinh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*e^x*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*e^x*sinh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*e^x*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*e^x*sinh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*e^x*sinh(x) + (cosh(x)^8 + 4*cosh(x)^6 + 6*cosh(x)^4 + 4*cosh(x)^2 + 1)*e^x)","B",0
33,1,310,0,0.458394," ","integrate((a*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a \cosh\left(x\right)^{3} + {\left(a e^{\left(2 \, x\right)} + a\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a \cosh\left(x\right) e^{\left(2 \, x\right)} + a \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + {\left(a \cosh\left(x\right)^{4} + {\left(a e^{\left(2 \, x\right)} + a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a \cosh\left(x\right) e^{\left(2 \, x\right)} + a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(2 \, x\right)} + a\right)} \sinh\left(x\right)^{2} + {\left(a \cosh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(2 \, x\right)} + 4 \, {\left(a \cosh\left(x\right)^{3} + a \cosh\left(x\right) + {\left(a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right) + a\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - a \cosh\left(x\right) + {\left(a \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + {\left(3 \, a \cosh\left(x\right)^{2} + {\left(3 \, a \cosh\left(x\right)^{2} - a\right)} e^{\left(2 \, x\right)} - a\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{4 \, \cosh\left(x\right) e^{x} \sinh\left(x\right)^{3} + e^{x} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} e^{x} \sinh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{x} \sinh\left(x\right) + {\left(\cosh\left(x\right)^{4} + 2 \, \cosh\left(x\right)^{2} + 1\right)} e^{x}}"," ",0,"(a*cosh(x)^3 + (a*e^(2*x) + a)*sinh(x)^3 + 3*(a*cosh(x)*e^(2*x) + a*cosh(x))*sinh(x)^2 + (a*cosh(x)^4 + (a*e^(2*x) + a)*sinh(x)^4 + 4*(a*cosh(x)*e^(2*x) + a*cosh(x))*sinh(x)^3 + 2*a*cosh(x)^2 + 2*(3*a*cosh(x)^2 + (3*a*cosh(x)^2 + a)*e^(2*x) + a)*sinh(x)^2 + (a*cosh(x)^4 + 2*a*cosh(x)^2 + a)*e^(2*x) + 4*(a*cosh(x)^3 + a*cosh(x) + (a*cosh(x)^3 + a*cosh(x))*e^(2*x))*sinh(x) + a)*arctan(cosh(x) + sinh(x)) - a*cosh(x) + (a*cosh(x)^3 - a*cosh(x))*e^(2*x) + (3*a*cosh(x)^2 + (3*a*cosh(x)^2 - a)*e^(2*x) - a)*sinh(x))*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(4*cosh(x)*e^x*sinh(x)^3 + e^x*sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*e^x*sinh(x)^2 + 4*(cosh(x)^3 + cosh(x))*e^x*sinh(x) + (cosh(x)^4 + 2*cosh(x)^2 + 1)*e^x)","B",0
34,1,145,0,0.441694," ","integrate((a*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\sqrt{-a} \log\left(\frac{2 \, a \cosh\left(x\right) e^{x} \sinh\left(x\right) + a e^{x} \sinh\left(x\right)^{2} + 2 \, {\left(\cosh\left(x\right) e^{\left(2 \, x\right)} + {\left(e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right) + \cosh\left(x\right)\right)} \sqrt{-a} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x} + {\left(a \cosh\left(x\right)^{2} - a\right)} e^{x}}{2 \, \cosh\left(x\right) e^{x} \sinh\left(x\right) + e^{x} \sinh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{2} + 1\right)} e^{x}}\right), 2 \, \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} {\left(e^{\left(2 \, x\right)} + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)\right]"," ",0,"[sqrt(-a)*log((2*a*cosh(x)*e^x*sinh(x) + a*e^x*sinh(x)^2 + 2*(cosh(x)*e^(2*x) + (e^(2*x) + 1)*sinh(x) + cosh(x))*sqrt(-a)*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x + (a*cosh(x)^2 - a)*e^x)/(2*cosh(x)*e^x*sinh(x) + e^x*sinh(x)^2 + (cosh(x)^2 + 1)*e^x)), 2*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*(e^(2*x) + 1)*arctan(cosh(x) + sinh(x))]","A",0
35,1,79,0,0.436147," ","integrate(1/(a*sech(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{2} - 1\right)} e^{\left(2 \, x\right)} + 2 \, {\left(\cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{2 \, {\left(a \cosh\left(x\right) e^{x} + a e^{x} \sinh\left(x\right)\right)}}"," ",0,"1/2*((e^(2*x) + 1)*sinh(x)^2 + cosh(x)^2 + (cosh(x)^2 - 1)*e^(2*x) + 2*(cosh(x)*e^(2*x) + cosh(x))*sinh(x) - 1)*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(a*cosh(x)*e^x + a*e^x*sinh(x))","B",0
36,1,277,0,0.629004," ","integrate(1/(a*sech(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{6} + \cosh\left(x\right)^{6} + 6 \, {\left(\cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, {\left(5 \, \cosh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{2} + 3\right)} e^{\left(2 \, x\right)} + 3\right)} \sinh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + {\left(5 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \cosh\left(x\right)^{4} + 18 \, \cosh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{4} + 18 \, \cosh\left(x\right)^{2} - 3\right)} e^{\left(2 \, x\right)} - 3\right)} \sinh\left(x\right)^{2} - 9 \, \cosh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{6} + 9 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} - 1\right)} e^{\left(2 \, x\right)} + 6 \, {\left(\cosh\left(x\right)^{5} + 6 \, \cosh\left(x\right)^{3} + {\left(\cosh\left(x\right)^{5} + 6 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{24 \, {\left(a^{2} \cosh\left(x\right)^{3} e^{x} + 3 \, a^{2} \cosh\left(x\right)^{2} e^{x} \sinh\left(x\right) + 3 \, a^{2} \cosh\left(x\right) e^{x} \sinh\left(x\right)^{2} + a^{2} e^{x} \sinh\left(x\right)^{3}\right)}}"," ",0,"1/24*((e^(2*x) + 1)*sinh(x)^6 + cosh(x)^6 + 6*(cosh(x)*e^(2*x) + cosh(x))*sinh(x)^5 + 3*(5*cosh(x)^2 + (5*cosh(x)^2 + 3)*e^(2*x) + 3)*sinh(x)^4 + 9*cosh(x)^4 + 4*(5*cosh(x)^3 + (5*cosh(x)^3 + 9*cosh(x))*e^(2*x) + 9*cosh(x))*sinh(x)^3 + 3*(5*cosh(x)^4 + 18*cosh(x)^2 + (5*cosh(x)^4 + 18*cosh(x)^2 - 3)*e^(2*x) - 3)*sinh(x)^2 - 9*cosh(x)^2 + (cosh(x)^6 + 9*cosh(x)^4 - 9*cosh(x)^2 - 1)*e^(2*x) + 6*(cosh(x)^5 + 6*cosh(x)^3 + (cosh(x)^5 + 6*cosh(x)^3 - 3*cosh(x))*e^(2*x) - 3*cosh(x))*sinh(x) - 1)*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(a^2*cosh(x)^3*e^x + 3*a^2*cosh(x)^2*e^x*sinh(x) + 3*a^2*cosh(x)*e^x*sinh(x)^2 + a^2*e^x*sinh(x)^3)","B",0
37,1,580,0,0.579891," ","integrate(1/(a*sech(x)^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{10} + 3 \, \cosh\left(x\right)^{10} + 30 \, {\left(\cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{9} + 5 \, {\left(27 \, \cosh\left(x\right)^{2} + {\left(27 \, \cosh\left(x\right)^{2} + 5\right)} e^{\left(2 \, x\right)} + 5\right)} \sinh\left(x\right)^{8} + 25 \, \cosh\left(x\right)^{8} + 40 \, {\left(9 \, \cosh\left(x\right)^{3} + {\left(9 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(63 \, \cosh\left(x\right)^{4} + 70 \, \cosh\left(x\right)^{2} + {\left(63 \, \cosh\left(x\right)^{4} + 70 \, \cosh\left(x\right)^{2} + 15\right)} e^{\left(2 \, x\right)} + 15\right)} \sinh\left(x\right)^{6} + 150 \, \cosh\left(x\right)^{6} + 4 \, {\left(189 \, \cosh\left(x\right)^{5} + 350 \, \cosh\left(x\right)^{3} + {\left(189 \, \cosh\left(x\right)^{5} + 350 \, \cosh\left(x\right)^{3} + 225 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 225 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(63 \, \cosh\left(x\right)^{6} + 175 \, \cosh\left(x\right)^{4} + 225 \, \cosh\left(x\right)^{2} + {\left(63 \, \cosh\left(x\right)^{6} + 175 \, \cosh\left(x\right)^{4} + 225 \, \cosh\left(x\right)^{2} - 15\right)} e^{\left(2 \, x\right)} - 15\right)} \sinh\left(x\right)^{4} - 150 \, \cosh\left(x\right)^{4} + 40 \, {\left(9 \, \cosh\left(x\right)^{7} + 35 \, \cosh\left(x\right)^{5} + 75 \, \cosh\left(x\right)^{3} + {\left(9 \, \cosh\left(x\right)^{7} + 35 \, \cosh\left(x\right)^{5} + 75 \, \cosh\left(x\right)^{3} - 15 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 15 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(27 \, \cosh\left(x\right)^{8} + 140 \, \cosh\left(x\right)^{6} + 450 \, \cosh\left(x\right)^{4} - 180 \, \cosh\left(x\right)^{2} + {\left(27 \, \cosh\left(x\right)^{8} + 140 \, \cosh\left(x\right)^{6} + 450 \, \cosh\left(x\right)^{4} - 180 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(2 \, x\right)} - 5\right)} \sinh\left(x\right)^{2} - 25 \, \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{10} + 25 \, \cosh\left(x\right)^{8} + 150 \, \cosh\left(x\right)^{6} - 150 \, \cosh\left(x\right)^{4} - 25 \, \cosh\left(x\right)^{2} - 3\right)} e^{\left(2 \, x\right)} + 10 \, {\left(3 \, \cosh\left(x\right)^{9} + 20 \, \cosh\left(x\right)^{7} + 90 \, \cosh\left(x\right)^{5} - 60 \, \cosh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{9} + 20 \, \cosh\left(x\right)^{7} + 90 \, \cosh\left(x\right)^{5} - 60 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 3\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{480 \, {\left(a^{3} \cosh\left(x\right)^{5} e^{x} + 5 \, a^{3} \cosh\left(x\right)^{4} e^{x} \sinh\left(x\right) + 10 \, a^{3} \cosh\left(x\right)^{3} e^{x} \sinh\left(x\right)^{2} + 10 \, a^{3} \cosh\left(x\right)^{2} e^{x} \sinh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right) e^{x} \sinh\left(x\right)^{4} + a^{3} e^{x} \sinh\left(x\right)^{5}\right)}}"," ",0,"1/480*(3*(e^(2*x) + 1)*sinh(x)^10 + 3*cosh(x)^10 + 30*(cosh(x)*e^(2*x) + cosh(x))*sinh(x)^9 + 5*(27*cosh(x)^2 + (27*cosh(x)^2 + 5)*e^(2*x) + 5)*sinh(x)^8 + 25*cosh(x)^8 + 40*(9*cosh(x)^3 + (9*cosh(x)^3 + 5*cosh(x))*e^(2*x) + 5*cosh(x))*sinh(x)^7 + 10*(63*cosh(x)^4 + 70*cosh(x)^2 + (63*cosh(x)^4 + 70*cosh(x)^2 + 15)*e^(2*x) + 15)*sinh(x)^6 + 150*cosh(x)^6 + 4*(189*cosh(x)^5 + 350*cosh(x)^3 + (189*cosh(x)^5 + 350*cosh(x)^3 + 225*cosh(x))*e^(2*x) + 225*cosh(x))*sinh(x)^5 + 10*(63*cosh(x)^6 + 175*cosh(x)^4 + 225*cosh(x)^2 + (63*cosh(x)^6 + 175*cosh(x)^4 + 225*cosh(x)^2 - 15)*e^(2*x) - 15)*sinh(x)^4 - 150*cosh(x)^4 + 40*(9*cosh(x)^7 + 35*cosh(x)^5 + 75*cosh(x)^3 + (9*cosh(x)^7 + 35*cosh(x)^5 + 75*cosh(x)^3 - 15*cosh(x))*e^(2*x) - 15*cosh(x))*sinh(x)^3 + 5*(27*cosh(x)^8 + 140*cosh(x)^6 + 450*cosh(x)^4 - 180*cosh(x)^2 + (27*cosh(x)^8 + 140*cosh(x)^6 + 450*cosh(x)^4 - 180*cosh(x)^2 - 5)*e^(2*x) - 5)*sinh(x)^2 - 25*cosh(x)^2 + (3*cosh(x)^10 + 25*cosh(x)^8 + 150*cosh(x)^6 - 150*cosh(x)^4 - 25*cosh(x)^2 - 3)*e^(2*x) + 10*(3*cosh(x)^9 + 20*cosh(x)^7 + 90*cosh(x)^5 - 60*cosh(x)^3 + (3*cosh(x)^9 + 20*cosh(x)^7 + 90*cosh(x)^5 - 60*cosh(x)^3 - 5*cosh(x))*e^(2*x) - 5*cosh(x))*sinh(x) - 3)*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(a^3*cosh(x)^5*e^x + 5*a^3*cosh(x)^4*e^x*sinh(x) + 10*a^3*cosh(x)^3*e^x*sinh(x)^2 + 10*a^3*cosh(x)^2*e^x*sinh(x)^3 + 5*a^3*cosh(x)*e^x*sinh(x)^4 + a^3*e^x*sinh(x)^5)","B",0
38,1,970,0,0.738216," ","integrate(1/(a*sech(x)^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(5 \, {\left(e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{14} + 5 \, \cosh\left(x\right)^{14} + 70 \, {\left(\cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{13} + 7 \, {\left(65 \, \cosh\left(x\right)^{2} + {\left(65 \, \cosh\left(x\right)^{2} + 7\right)} e^{\left(2 \, x\right)} + 7\right)} \sinh\left(x\right)^{12} + 49 \, \cosh\left(x\right)^{12} + 28 \, {\left(65 \, \cosh\left(x\right)^{3} + {\left(65 \, \cosh\left(x\right)^{3} + 21 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 21 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{11} + 7 \, {\left(715 \, \cosh\left(x\right)^{4} + 462 \, \cosh\left(x\right)^{2} + {\left(715 \, \cosh\left(x\right)^{4} + 462 \, \cosh\left(x\right)^{2} + 35\right)} e^{\left(2 \, x\right)} + 35\right)} \sinh\left(x\right)^{10} + 245 \, \cosh\left(x\right)^{10} + 70 \, {\left(143 \, \cosh\left(x\right)^{5} + 154 \, \cosh\left(x\right)^{3} + {\left(143 \, \cosh\left(x\right)^{5} + 154 \, \cosh\left(x\right)^{3} + 35 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 35 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{9} + 35 \, {\left(429 \, \cosh\left(x\right)^{6} + 693 \, \cosh\left(x\right)^{4} + 315 \, \cosh\left(x\right)^{2} + {\left(429 \, \cosh\left(x\right)^{6} + 693 \, \cosh\left(x\right)^{4} + 315 \, \cosh\left(x\right)^{2} + 35\right)} e^{\left(2 \, x\right)} + 35\right)} \sinh\left(x\right)^{8} + 1225 \, \cosh\left(x\right)^{8} + 8 \, {\left(2145 \, \cosh\left(x\right)^{7} + 4851 \, \cosh\left(x\right)^{5} + 3675 \, \cosh\left(x\right)^{3} + {\left(2145 \, \cosh\left(x\right)^{7} + 4851 \, \cosh\left(x\right)^{5} + 3675 \, \cosh\left(x\right)^{3} + 1225 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 1225 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 7 \, {\left(2145 \, \cosh\left(x\right)^{8} + 6468 \, \cosh\left(x\right)^{6} + 7350 \, \cosh\left(x\right)^{4} + 4900 \, \cosh\left(x\right)^{2} + {\left(2145 \, \cosh\left(x\right)^{8} + 6468 \, \cosh\left(x\right)^{6} + 7350 \, \cosh\left(x\right)^{4} + 4900 \, \cosh\left(x\right)^{2} - 175\right)} e^{\left(2 \, x\right)} - 175\right)} \sinh\left(x\right)^{6} - 1225 \, \cosh\left(x\right)^{6} + 14 \, {\left(715 \, \cosh\left(x\right)^{9} + 2772 \, \cosh\left(x\right)^{7} + 4410 \, \cosh\left(x\right)^{5} + 4900 \, \cosh\left(x\right)^{3} + {\left(715 \, \cosh\left(x\right)^{9} + 2772 \, \cosh\left(x\right)^{7} + 4410 \, \cosh\left(x\right)^{5} + 4900 \, \cosh\left(x\right)^{3} - 525 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 525 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 35 \, {\left(143 \, \cosh\left(x\right)^{10} + 693 \, \cosh\left(x\right)^{8} + 1470 \, \cosh\left(x\right)^{6} + 2450 \, \cosh\left(x\right)^{4} - 525 \, \cosh\left(x\right)^{2} + {\left(143 \, \cosh\left(x\right)^{10} + 693 \, \cosh\left(x\right)^{8} + 1470 \, \cosh\left(x\right)^{6} + 2450 \, \cosh\left(x\right)^{4} - 525 \, \cosh\left(x\right)^{2} - 7\right)} e^{\left(2 \, x\right)} - 7\right)} \sinh\left(x\right)^{4} - 245 \, \cosh\left(x\right)^{4} + 140 \, {\left(13 \, \cosh\left(x\right)^{11} + 77 \, \cosh\left(x\right)^{9} + 210 \, \cosh\left(x\right)^{7} + 490 \, \cosh\left(x\right)^{5} - 175 \, \cosh\left(x\right)^{3} + {\left(13 \, \cosh\left(x\right)^{11} + 77 \, \cosh\left(x\right)^{9} + 210 \, \cosh\left(x\right)^{7} + 490 \, \cosh\left(x\right)^{5} - 175 \, \cosh\left(x\right)^{3} - 7 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 7 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 7 \, {\left(65 \, \cosh\left(x\right)^{12} + 462 \, \cosh\left(x\right)^{10} + 1575 \, \cosh\left(x\right)^{8} + 4900 \, \cosh\left(x\right)^{6} - 2625 \, \cosh\left(x\right)^{4} - 210 \, \cosh\left(x\right)^{2} + {\left(65 \, \cosh\left(x\right)^{12} + 462 \, \cosh\left(x\right)^{10} + 1575 \, \cosh\left(x\right)^{8} + 4900 \, \cosh\left(x\right)^{6} - 2625 \, \cosh\left(x\right)^{4} - 210 \, \cosh\left(x\right)^{2} - 7\right)} e^{\left(2 \, x\right)} - 7\right)} \sinh\left(x\right)^{2} - 49 \, \cosh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{14} + 49 \, \cosh\left(x\right)^{12} + 245 \, \cosh\left(x\right)^{10} + 1225 \, \cosh\left(x\right)^{8} - 1225 \, \cosh\left(x\right)^{6} - 245 \, \cosh\left(x\right)^{4} - 49 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(2 \, x\right)} + 14 \, {\left(5 \, \cosh\left(x\right)^{13} + 42 \, \cosh\left(x\right)^{11} + 175 \, \cosh\left(x\right)^{9} + 700 \, \cosh\left(x\right)^{7} - 525 \, \cosh\left(x\right)^{5} - 70 \, \cosh\left(x\right)^{3} + {\left(5 \, \cosh\left(x\right)^{13} + 42 \, \cosh\left(x\right)^{11} + 175 \, \cosh\left(x\right)^{9} + 700 \, \cosh\left(x\right)^{7} - 525 \, \cosh\left(x\right)^{5} - 70 \, \cosh\left(x\right)^{3} - 7 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 7 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 5\right)} \sqrt{\frac{a}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1}} e^{x}}{4480 \, {\left(a^{4} \cosh\left(x\right)^{7} e^{x} + 7 \, a^{4} \cosh\left(x\right)^{6} e^{x} \sinh\left(x\right) + 21 \, a^{4} \cosh\left(x\right)^{5} e^{x} \sinh\left(x\right)^{2} + 35 \, a^{4} \cosh\left(x\right)^{4} e^{x} \sinh\left(x\right)^{3} + 35 \, a^{4} \cosh\left(x\right)^{3} e^{x} \sinh\left(x\right)^{4} + 21 \, a^{4} \cosh\left(x\right)^{2} e^{x} \sinh\left(x\right)^{5} + 7 \, a^{4} \cosh\left(x\right) e^{x} \sinh\left(x\right)^{6} + a^{4} e^{x} \sinh\left(x\right)^{7}\right)}}"," ",0,"1/4480*(5*(e^(2*x) + 1)*sinh(x)^14 + 5*cosh(x)^14 + 70*(cosh(x)*e^(2*x) + cosh(x))*sinh(x)^13 + 7*(65*cosh(x)^2 + (65*cosh(x)^2 + 7)*e^(2*x) + 7)*sinh(x)^12 + 49*cosh(x)^12 + 28*(65*cosh(x)^3 + (65*cosh(x)^3 + 21*cosh(x))*e^(2*x) + 21*cosh(x))*sinh(x)^11 + 7*(715*cosh(x)^4 + 462*cosh(x)^2 + (715*cosh(x)^4 + 462*cosh(x)^2 + 35)*e^(2*x) + 35)*sinh(x)^10 + 245*cosh(x)^10 + 70*(143*cosh(x)^5 + 154*cosh(x)^3 + (143*cosh(x)^5 + 154*cosh(x)^3 + 35*cosh(x))*e^(2*x) + 35*cosh(x))*sinh(x)^9 + 35*(429*cosh(x)^6 + 693*cosh(x)^4 + 315*cosh(x)^2 + (429*cosh(x)^6 + 693*cosh(x)^4 + 315*cosh(x)^2 + 35)*e^(2*x) + 35)*sinh(x)^8 + 1225*cosh(x)^8 + 8*(2145*cosh(x)^7 + 4851*cosh(x)^5 + 3675*cosh(x)^3 + (2145*cosh(x)^7 + 4851*cosh(x)^5 + 3675*cosh(x)^3 + 1225*cosh(x))*e^(2*x) + 1225*cosh(x))*sinh(x)^7 + 7*(2145*cosh(x)^8 + 6468*cosh(x)^6 + 7350*cosh(x)^4 + 4900*cosh(x)^2 + (2145*cosh(x)^8 + 6468*cosh(x)^6 + 7350*cosh(x)^4 + 4900*cosh(x)^2 - 175)*e^(2*x) - 175)*sinh(x)^6 - 1225*cosh(x)^6 + 14*(715*cosh(x)^9 + 2772*cosh(x)^7 + 4410*cosh(x)^5 + 4900*cosh(x)^3 + (715*cosh(x)^9 + 2772*cosh(x)^7 + 4410*cosh(x)^5 + 4900*cosh(x)^3 - 525*cosh(x))*e^(2*x) - 525*cosh(x))*sinh(x)^5 + 35*(143*cosh(x)^10 + 693*cosh(x)^8 + 1470*cosh(x)^6 + 2450*cosh(x)^4 - 525*cosh(x)^2 + (143*cosh(x)^10 + 693*cosh(x)^8 + 1470*cosh(x)^6 + 2450*cosh(x)^4 - 525*cosh(x)^2 - 7)*e^(2*x) - 7)*sinh(x)^4 - 245*cosh(x)^4 + 140*(13*cosh(x)^11 + 77*cosh(x)^9 + 210*cosh(x)^7 + 490*cosh(x)^5 - 175*cosh(x)^3 + (13*cosh(x)^11 + 77*cosh(x)^9 + 210*cosh(x)^7 + 490*cosh(x)^5 - 175*cosh(x)^3 - 7*cosh(x))*e^(2*x) - 7*cosh(x))*sinh(x)^3 + 7*(65*cosh(x)^12 + 462*cosh(x)^10 + 1575*cosh(x)^8 + 4900*cosh(x)^6 - 2625*cosh(x)^4 - 210*cosh(x)^2 + (65*cosh(x)^12 + 462*cosh(x)^10 + 1575*cosh(x)^8 + 4900*cosh(x)^6 - 2625*cosh(x)^4 - 210*cosh(x)^2 - 7)*e^(2*x) - 7)*sinh(x)^2 - 49*cosh(x)^2 + (5*cosh(x)^14 + 49*cosh(x)^12 + 245*cosh(x)^10 + 1225*cosh(x)^8 - 1225*cosh(x)^6 - 245*cosh(x)^4 - 49*cosh(x)^2 - 5)*e^(2*x) + 14*(5*cosh(x)^13 + 42*cosh(x)^11 + 175*cosh(x)^9 + 700*cosh(x)^7 - 525*cosh(x)^5 - 70*cosh(x)^3 + (5*cosh(x)^13 + 42*cosh(x)^11 + 175*cosh(x)^9 + 700*cosh(x)^7 - 525*cosh(x)^5 - 70*cosh(x)^3 - 7*cosh(x))*e^(2*x) - 7*cosh(x))*sinh(x) - 5)*sqrt(a/(e^(4*x) + 2*e^(2*x) + 1))*e^x/(a^4*cosh(x)^7*e^x + 7*a^4*cosh(x)^6*e^x*sinh(x) + 21*a^4*cosh(x)^5*e^x*sinh(x)^2 + 35*a^4*cosh(x)^4*e^x*sinh(x)^3 + 35*a^4*cosh(x)^3*e^x*sinh(x)^4 + 21*a^4*cosh(x)^2*e^x*sinh(x)^5 + 7*a^4*cosh(x)*e^x*sinh(x)^6 + a^4*e^x*sinh(x)^7)","B",0
39,0,0,0,0.499995," ","integrate((a*sech(x)^3)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \operatorname{sech}\left(x\right)^{3}} a^{2} \operatorname{sech}\left(x\right)^{6}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3)*a^2*sech(x)^6, x)","F",0
40,0,0,0,0.714568," ","integrate((a*sech(x)^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \operatorname{sech}\left(x\right)^{3}} a \operatorname{sech}\left(x\right)^{3}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3)*a*sech(x)^3, x)","F",0
41,0,0,0,1.044057," ","integrate((a*sech(x)^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \operatorname{sech}\left(x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3), x)","F",0
42,0,0,0,0.525007," ","integrate(1/(a*sech(x)^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \operatorname{sech}\left(x\right)^{3}}}{a \operatorname{sech}\left(x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3)/(a*sech(x)^3), x)","F",0
43,0,0,0,1.589120," ","integrate(1/(a*sech(x)^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \operatorname{sech}\left(x\right)^{3}}}{a^{2} \operatorname{sech}\left(x\right)^{6}}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3)/(a^2*sech(x)^6), x)","F",0
44,0,0,0,0.410920," ","integrate(1/(a*sech(x)^3)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \operatorname{sech}\left(x\right)^{3}}}{a^{3} \operatorname{sech}\left(x\right)^{9}}, x\right)"," ",0,"integral(sqrt(a*sech(x)^3)/(a^3*sech(x)^9), x)","F",0
45,1,2804,0,0.531552," ","integrate((a*sech(x)^4)^(7/2),x, algorithm=""fricas"")","-\frac{2048 \, {\left(1716 \, a^{3} \cosh\left(x\right)^{12} + 1287 \, a^{3} \cosh\left(x\right)^{10} + 1716 \, {\left(a^{3} e^{\left(4 \, x\right)} + 2 \, a^{3} e^{\left(2 \, x\right)} + a^{3}\right)} \sinh\left(x\right)^{12} + 20592 \, {\left(a^{3} \cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, a^{3} \cosh\left(x\right) e^{\left(2 \, x\right)} + a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{11} + 715 \, a^{3} \cosh\left(x\right)^{8} + 1287 \, {\left(88 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + {\left(88 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(88 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{10} + 4290 \, {\left(88 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right) + {\left(88 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(88 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{9} + 286 \, a^{3} \cosh\left(x\right)^{6} + 715 \, {\left(1188 \, a^{3} \cosh\left(x\right)^{4} + 81 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + {\left(1188 \, a^{3} \cosh\left(x\right)^{4} + 81 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1188 \, a^{3} \cosh\left(x\right)^{4} + 81 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{8} + 1144 \, {\left(1188 \, a^{3} \cosh\left(x\right)^{5} + 135 \, a^{3} \cosh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right) + {\left(1188 \, a^{3} \cosh\left(x\right)^{5} + 135 \, a^{3} \cosh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1188 \, a^{3} \cosh\left(x\right)^{5} + 135 \, a^{3} \cosh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{7} + 78 \, a^{3} \cosh\left(x\right)^{4} + 286 \, {\left(5544 \, a^{3} \cosh\left(x\right)^{6} + 945 \, a^{3} \cosh\left(x\right)^{4} + 70 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + {\left(5544 \, a^{3} \cosh\left(x\right)^{6} + 945 \, a^{3} \cosh\left(x\right)^{4} + 70 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(5544 \, a^{3} \cosh\left(x\right)^{6} + 945 \, a^{3} \cosh\left(x\right)^{4} + 70 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{6} + 572 \, {\left(2376 \, a^{3} \cosh\left(x\right)^{7} + 567 \, a^{3} \cosh\left(x\right)^{5} + 70 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right) + {\left(2376 \, a^{3} \cosh\left(x\right)^{7} + 567 \, a^{3} \cosh\left(x\right)^{5} + 70 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(2376 \, a^{3} \cosh\left(x\right)^{7} + 567 \, a^{3} \cosh\left(x\right)^{5} + 70 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{5} + 13 \, a^{3} \cosh\left(x\right)^{2} + 26 \, {\left(32670 \, a^{3} \cosh\left(x\right)^{8} + 10395 \, a^{3} \cosh\left(x\right)^{6} + 1925 \, a^{3} \cosh\left(x\right)^{4} + 165 \, a^{3} \cosh\left(x\right)^{2} + 3 \, a^{3} + {\left(32670 \, a^{3} \cosh\left(x\right)^{8} + 10395 \, a^{3} \cosh\left(x\right)^{6} + 1925 \, a^{3} \cosh\left(x\right)^{4} + 165 \, a^{3} \cosh\left(x\right)^{2} + 3 \, a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(32670 \, a^{3} \cosh\left(x\right)^{8} + 10395 \, a^{3} \cosh\left(x\right)^{6} + 1925 \, a^{3} \cosh\left(x\right)^{4} + 165 \, a^{3} \cosh\left(x\right)^{2} + 3 \, a^{3}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{4} + 104 \, {\left(3630 \, a^{3} \cosh\left(x\right)^{9} + 1485 \, a^{3} \cosh\left(x\right)^{7} + 385 \, a^{3} \cosh\left(x\right)^{5} + 55 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right) + {\left(3630 \, a^{3} \cosh\left(x\right)^{9} + 1485 \, a^{3} \cosh\left(x\right)^{7} + 385 \, a^{3} \cosh\left(x\right)^{5} + 55 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(3630 \, a^{3} \cosh\left(x\right)^{9} + 1485 \, a^{3} \cosh\left(x\right)^{7} + 385 \, a^{3} \cosh\left(x\right)^{5} + 55 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{3} + a^{3} + 13 \, {\left(8712 \, a^{3} \cosh\left(x\right)^{10} + 4455 \, a^{3} \cosh\left(x\right)^{8} + 1540 \, a^{3} \cosh\left(x\right)^{6} + 330 \, a^{3} \cosh\left(x\right)^{4} + 36 \, a^{3} \cosh\left(x\right)^{2} + a^{3} + {\left(8712 \, a^{3} \cosh\left(x\right)^{10} + 4455 \, a^{3} \cosh\left(x\right)^{8} + 1540 \, a^{3} \cosh\left(x\right)^{6} + 330 \, a^{3} \cosh\left(x\right)^{4} + 36 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(8712 \, a^{3} \cosh\left(x\right)^{10} + 4455 \, a^{3} \cosh\left(x\right)^{8} + 1540 \, a^{3} \cosh\left(x\right)^{6} + 330 \, a^{3} \cosh\left(x\right)^{4} + 36 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{2} + {\left(1716 \, a^{3} \cosh\left(x\right)^{12} + 1287 \, a^{3} \cosh\left(x\right)^{10} + 715 \, a^{3} \cosh\left(x\right)^{8} + 286 \, a^{3} \cosh\left(x\right)^{6} + 78 \, a^{3} \cosh\left(x\right)^{4} + 13 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1716 \, a^{3} \cosh\left(x\right)^{12} + 1287 \, a^{3} \cosh\left(x\right)^{10} + 715 \, a^{3} \cosh\left(x\right)^{8} + 286 \, a^{3} \cosh\left(x\right)^{6} + 78 \, a^{3} \cosh\left(x\right)^{4} + 13 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} e^{\left(2 \, x\right)} + 26 \, {\left(792 \, a^{3} \cosh\left(x\right)^{11} + 495 \, a^{3} \cosh\left(x\right)^{9} + 220 \, a^{3} \cosh\left(x\right)^{7} + 66 \, a^{3} \cosh\left(x\right)^{5} + 12 \, a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right) + {\left(792 \, a^{3} \cosh\left(x\right)^{11} + 495 \, a^{3} \cosh\left(x\right)^{9} + 220 \, a^{3} \cosh\left(x\right)^{7} + 66 \, a^{3} \cosh\left(x\right)^{5} + 12 \, a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(792 \, a^{3} \cosh\left(x\right)^{11} + 495 \, a^{3} \cosh\left(x\right)^{9} + 220 \, a^{3} \cosh\left(x\right)^{7} + 66 \, a^{3} \cosh\left(x\right)^{5} + 12 \, a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{3003 \, {\left(26 \, \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right)^{25} + e^{\left(2 \, x\right)} \sinh\left(x\right)^{26} + 13 \, {\left(25 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{24} + 104 \, {\left(25 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{23} + 26 \, {\left(575 \, \cosh\left(x\right)^{4} + 138 \, \cosh\left(x\right)^{2} + 3\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{22} + 572 \, {\left(115 \, \cosh\left(x\right)^{5} + 46 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{21} + 286 \, {\left(805 \, \cosh\left(x\right)^{6} + 483 \, \cosh\left(x\right)^{4} + 63 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{20} + 1144 \, {\left(575 \, \cosh\left(x\right)^{7} + 483 \, \cosh\left(x\right)^{5} + 105 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{19} + 143 \, {\left(10925 \, \cosh\left(x\right)^{8} + 12236 \, \cosh\left(x\right)^{6} + 3990 \, \cosh\left(x\right)^{4} + 380 \, \cosh\left(x\right)^{2} + 5\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{18} + 286 \, {\left(10925 \, \cosh\left(x\right)^{9} + 15732 \, \cosh\left(x\right)^{7} + 7182 \, \cosh\left(x\right)^{5} + 1140 \, \cosh\left(x\right)^{3} + 45 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{17} + 143 \, {\left(37145 \, \cosh\left(x\right)^{10} + 66861 \, \cosh\left(x\right)^{8} + 40698 \, \cosh\left(x\right)^{6} + 9690 \, \cosh\left(x\right)^{4} + 765 \, \cosh\left(x\right)^{2} + 9\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{16} + 208 \, {\left(37145 \, \cosh\left(x\right)^{11} + 81719 \, \cosh\left(x\right)^{9} + 63954 \, \cosh\left(x\right)^{7} + 21318 \, \cosh\left(x\right)^{5} + 2805 \, \cosh\left(x\right)^{3} + 99 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{15} + 52 \, {\left(185725 \, \cosh\left(x\right)^{12} + 490314 \, \cosh\left(x\right)^{10} + 479655 \, \cosh\left(x\right)^{8} + 213180 \, \cosh\left(x\right)^{6} + 42075 \, \cosh\left(x\right)^{4} + 2970 \, \cosh\left(x\right)^{2} + 33\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{14} + 8 \, {\left(1300075 \, \cosh\left(x\right)^{13} + 4056234 \, \cosh\left(x\right)^{11} + 4849845 \, \cosh\left(x\right)^{9} + 2771340 \, \cosh\left(x\right)^{7} + 765765 \, \cosh\left(x\right)^{5} + 90090 \, \cosh\left(x\right)^{3} + 3003 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{13} + 52 \, {\left(185725 \, \cosh\left(x\right)^{14} + 676039 \, \cosh\left(x\right)^{12} + 969969 \, \cosh\left(x\right)^{10} + 692835 \, \cosh\left(x\right)^{8} + 255255 \, \cosh\left(x\right)^{6} + 45045 \, \cosh\left(x\right)^{4} + 3003 \, \cosh\left(x\right)^{2} + 33\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{12} + 208 \, {\left(37145 \, \cosh\left(x\right)^{15} + 156009 \, \cosh\left(x\right)^{13} + 264537 \, \cosh\left(x\right)^{11} + 230945 \, \cosh\left(x\right)^{9} + 109395 \, \cosh\left(x\right)^{7} + 27027 \, \cosh\left(x\right)^{5} + 3003 \, \cosh\left(x\right)^{3} + 99 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{11} + 143 \, {\left(37145 \, \cosh\left(x\right)^{16} + 178296 \, \cosh\left(x\right)^{14} + 352716 \, \cosh\left(x\right)^{12} + 369512 \, \cosh\left(x\right)^{10} + 218790 \, \cosh\left(x\right)^{8} + 72072 \, \cosh\left(x\right)^{6} + 12012 \, \cosh\left(x\right)^{4} + 792 \, \cosh\left(x\right)^{2} + 9\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{10} + 286 \, {\left(10925 \, \cosh\left(x\right)^{17} + 59432 \, \cosh\left(x\right)^{15} + 135660 \, \cosh\left(x\right)^{13} + 167960 \, \cosh\left(x\right)^{11} + 121550 \, \cosh\left(x\right)^{9} + 51480 \, \cosh\left(x\right)^{7} + 12012 \, \cosh\left(x\right)^{5} + 1320 \, \cosh\left(x\right)^{3} + 45 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{9} + 143 \, {\left(10925 \, \cosh\left(x\right)^{18} + 66861 \, \cosh\left(x\right)^{16} + 174420 \, \cosh\left(x\right)^{14} + 251940 \, \cosh\left(x\right)^{12} + 218790 \, \cosh\left(x\right)^{10} + 115830 \, \cosh\left(x\right)^{8} + 36036 \, \cosh\left(x\right)^{6} + 5940 \, \cosh\left(x\right)^{4} + 405 \, \cosh\left(x\right)^{2} + 5\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{8} + 1144 \, {\left(575 \, \cosh\left(x\right)^{19} + 3933 \, \cosh\left(x\right)^{17} + 11628 \, \cosh\left(x\right)^{15} + 19380 \, \cosh\left(x\right)^{13} + 19890 \, \cosh\left(x\right)^{11} + 12870 \, \cosh\left(x\right)^{9} + 5148 \, \cosh\left(x\right)^{7} + 1188 \, \cosh\left(x\right)^{5} + 135 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{7} + 286 \, {\left(805 \, \cosh\left(x\right)^{20} + 6118 \, \cosh\left(x\right)^{18} + 20349 \, \cosh\left(x\right)^{16} + 38760 \, \cosh\left(x\right)^{14} + 46410 \, \cosh\left(x\right)^{12} + 36036 \, \cosh\left(x\right)^{10} + 18018 \, \cosh\left(x\right)^{8} + 5544 \, \cosh\left(x\right)^{6} + 945 \, \cosh\left(x\right)^{4} + 70 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{6} + 572 \, {\left(115 \, \cosh\left(x\right)^{21} + 966 \, \cosh\left(x\right)^{19} + 3591 \, \cosh\left(x\right)^{17} + 7752 \, \cosh\left(x\right)^{15} + 10710 \, \cosh\left(x\right)^{13} + 9828 \, \cosh\left(x\right)^{11} + 6006 \, \cosh\left(x\right)^{9} + 2376 \, \cosh\left(x\right)^{7} + 567 \, \cosh\left(x\right)^{5} + 70 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{5} + 26 \, {\left(575 \, \cosh\left(x\right)^{22} + 5313 \, \cosh\left(x\right)^{20} + 21945 \, \cosh\left(x\right)^{18} + 53295 \, \cosh\left(x\right)^{16} + 84150 \, \cosh\left(x\right)^{14} + 90090 \, \cosh\left(x\right)^{12} + 66066 \, \cosh\left(x\right)^{10} + 32670 \, \cosh\left(x\right)^{8} + 10395 \, \cosh\left(x\right)^{6} + 1925 \, \cosh\left(x\right)^{4} + 165 \, \cosh\left(x\right)^{2} + 3\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{4} + 104 \, {\left(25 \, \cosh\left(x\right)^{23} + 253 \, \cosh\left(x\right)^{21} + 1155 \, \cosh\left(x\right)^{19} + 3135 \, \cosh\left(x\right)^{17} + 5610 \, \cosh\left(x\right)^{15} + 6930 \, \cosh\left(x\right)^{13} + 6006 \, \cosh\left(x\right)^{11} + 3630 \, \cosh\left(x\right)^{9} + 1485 \, \cosh\left(x\right)^{7} + 385 \, \cosh\left(x\right)^{5} + 55 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{3} + 13 \, {\left(25 \, \cosh\left(x\right)^{24} + 276 \, \cosh\left(x\right)^{22} + 1386 \, \cosh\left(x\right)^{20} + 4180 \, \cosh\left(x\right)^{18} + 8415 \, \cosh\left(x\right)^{16} + 11880 \, \cosh\left(x\right)^{14} + 12012 \, \cosh\left(x\right)^{12} + 8712 \, \cosh\left(x\right)^{10} + 4455 \, \cosh\left(x\right)^{8} + 1540 \, \cosh\left(x\right)^{6} + 330 \, \cosh\left(x\right)^{4} + 36 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + 26 \, {\left(\cosh\left(x\right)^{25} + 12 \, \cosh\left(x\right)^{23} + 66 \, \cosh\left(x\right)^{21} + 220 \, \cosh\left(x\right)^{19} + 495 \, \cosh\left(x\right)^{17} + 792 \, \cosh\left(x\right)^{15} + 924 \, \cosh\left(x\right)^{13} + 792 \, \cosh\left(x\right)^{11} + 495 \, \cosh\left(x\right)^{9} + 220 \, \cosh\left(x\right)^{7} + 66 \, \cosh\left(x\right)^{5} + 12 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right) + {\left(\cosh\left(x\right)^{26} + 13 \, \cosh\left(x\right)^{24} + 78 \, \cosh\left(x\right)^{22} + 286 \, \cosh\left(x\right)^{20} + 715 \, \cosh\left(x\right)^{18} + 1287 \, \cosh\left(x\right)^{16} + 1716 \, \cosh\left(x\right)^{14} + 1716 \, \cosh\left(x\right)^{12} + 1287 \, \cosh\left(x\right)^{10} + 715 \, \cosh\left(x\right)^{8} + 286 \, \cosh\left(x\right)^{6} + 78 \, \cosh\left(x\right)^{4} + 13 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)}\right)}}"," ",0,"-2048/3003*(1716*a^3*cosh(x)^12 + 1287*a^3*cosh(x)^10 + 1716*(a^3*e^(4*x) + 2*a^3*e^(2*x) + a^3)*sinh(x)^12 + 20592*(a^3*cosh(x)*e^(4*x) + 2*a^3*cosh(x)*e^(2*x) + a^3*cosh(x))*sinh(x)^11 + 715*a^3*cosh(x)^8 + 1287*(88*a^3*cosh(x)^2 + a^3 + (88*a^3*cosh(x)^2 + a^3)*e^(4*x) + 2*(88*a^3*cosh(x)^2 + a^3)*e^(2*x))*sinh(x)^10 + 4290*(88*a^3*cosh(x)^3 + 3*a^3*cosh(x) + (88*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(4*x) + 2*(88*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(2*x))*sinh(x)^9 + 286*a^3*cosh(x)^6 + 715*(1188*a^3*cosh(x)^4 + 81*a^3*cosh(x)^2 + a^3 + (1188*a^3*cosh(x)^4 + 81*a^3*cosh(x)^2 + a^3)*e^(4*x) + 2*(1188*a^3*cosh(x)^4 + 81*a^3*cosh(x)^2 + a^3)*e^(2*x))*sinh(x)^8 + 1144*(1188*a^3*cosh(x)^5 + 135*a^3*cosh(x)^3 + 5*a^3*cosh(x) + (1188*a^3*cosh(x)^5 + 135*a^3*cosh(x)^3 + 5*a^3*cosh(x))*e^(4*x) + 2*(1188*a^3*cosh(x)^5 + 135*a^3*cosh(x)^3 + 5*a^3*cosh(x))*e^(2*x))*sinh(x)^7 + 78*a^3*cosh(x)^4 + 286*(5544*a^3*cosh(x)^6 + 945*a^3*cosh(x)^4 + 70*a^3*cosh(x)^2 + a^3 + (5544*a^3*cosh(x)^6 + 945*a^3*cosh(x)^4 + 70*a^3*cosh(x)^2 + a^3)*e^(4*x) + 2*(5544*a^3*cosh(x)^6 + 945*a^3*cosh(x)^4 + 70*a^3*cosh(x)^2 + a^3)*e^(2*x))*sinh(x)^6 + 572*(2376*a^3*cosh(x)^7 + 567*a^3*cosh(x)^5 + 70*a^3*cosh(x)^3 + 3*a^3*cosh(x) + (2376*a^3*cosh(x)^7 + 567*a^3*cosh(x)^5 + 70*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(4*x) + 2*(2376*a^3*cosh(x)^7 + 567*a^3*cosh(x)^5 + 70*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(2*x))*sinh(x)^5 + 13*a^3*cosh(x)^2 + 26*(32670*a^3*cosh(x)^8 + 10395*a^3*cosh(x)^6 + 1925*a^3*cosh(x)^4 + 165*a^3*cosh(x)^2 + 3*a^3 + (32670*a^3*cosh(x)^8 + 10395*a^3*cosh(x)^6 + 1925*a^3*cosh(x)^4 + 165*a^3*cosh(x)^2 + 3*a^3)*e^(4*x) + 2*(32670*a^3*cosh(x)^8 + 10395*a^3*cosh(x)^6 + 1925*a^3*cosh(x)^4 + 165*a^3*cosh(x)^2 + 3*a^3)*e^(2*x))*sinh(x)^4 + 104*(3630*a^3*cosh(x)^9 + 1485*a^3*cosh(x)^7 + 385*a^3*cosh(x)^5 + 55*a^3*cosh(x)^3 + 3*a^3*cosh(x) + (3630*a^3*cosh(x)^9 + 1485*a^3*cosh(x)^7 + 385*a^3*cosh(x)^5 + 55*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(4*x) + 2*(3630*a^3*cosh(x)^9 + 1485*a^3*cosh(x)^7 + 385*a^3*cosh(x)^5 + 55*a^3*cosh(x)^3 + 3*a^3*cosh(x))*e^(2*x))*sinh(x)^3 + a^3 + 13*(8712*a^3*cosh(x)^10 + 4455*a^3*cosh(x)^8 + 1540*a^3*cosh(x)^6 + 330*a^3*cosh(x)^4 + 36*a^3*cosh(x)^2 + a^3 + (8712*a^3*cosh(x)^10 + 4455*a^3*cosh(x)^8 + 1540*a^3*cosh(x)^6 + 330*a^3*cosh(x)^4 + 36*a^3*cosh(x)^2 + a^3)*e^(4*x) + 2*(8712*a^3*cosh(x)^10 + 4455*a^3*cosh(x)^8 + 1540*a^3*cosh(x)^6 + 330*a^3*cosh(x)^4 + 36*a^3*cosh(x)^2 + a^3)*e^(2*x))*sinh(x)^2 + (1716*a^3*cosh(x)^12 + 1287*a^3*cosh(x)^10 + 715*a^3*cosh(x)^8 + 286*a^3*cosh(x)^6 + 78*a^3*cosh(x)^4 + 13*a^3*cosh(x)^2 + a^3)*e^(4*x) + 2*(1716*a^3*cosh(x)^12 + 1287*a^3*cosh(x)^10 + 715*a^3*cosh(x)^8 + 286*a^3*cosh(x)^6 + 78*a^3*cosh(x)^4 + 13*a^3*cosh(x)^2 + a^3)*e^(2*x) + 26*(792*a^3*cosh(x)^11 + 495*a^3*cosh(x)^9 + 220*a^3*cosh(x)^7 + 66*a^3*cosh(x)^5 + 12*a^3*cosh(x)^3 + a^3*cosh(x) + (792*a^3*cosh(x)^11 + 495*a^3*cosh(x)^9 + 220*a^3*cosh(x)^7 + 66*a^3*cosh(x)^5 + 12*a^3*cosh(x)^3 + a^3*cosh(x))*e^(4*x) + 2*(792*a^3*cosh(x)^11 + 495*a^3*cosh(x)^9 + 220*a^3*cosh(x)^7 + 66*a^3*cosh(x)^5 + 12*a^3*cosh(x)^3 + a^3*cosh(x))*e^(2*x))*sinh(x))*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(26*cosh(x)*e^(2*x)*sinh(x)^25 + e^(2*x)*sinh(x)^26 + 13*(25*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^24 + 104*(25*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^23 + 26*(575*cosh(x)^4 + 138*cosh(x)^2 + 3)*e^(2*x)*sinh(x)^22 + 572*(115*cosh(x)^5 + 46*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^21 + 286*(805*cosh(x)^6 + 483*cosh(x)^4 + 63*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^20 + 1144*(575*cosh(x)^7 + 483*cosh(x)^5 + 105*cosh(x)^3 + 5*cosh(x))*e^(2*x)*sinh(x)^19 + 143*(10925*cosh(x)^8 + 12236*cosh(x)^6 + 3990*cosh(x)^4 + 380*cosh(x)^2 + 5)*e^(2*x)*sinh(x)^18 + 286*(10925*cosh(x)^9 + 15732*cosh(x)^7 + 7182*cosh(x)^5 + 1140*cosh(x)^3 + 45*cosh(x))*e^(2*x)*sinh(x)^17 + 143*(37145*cosh(x)^10 + 66861*cosh(x)^8 + 40698*cosh(x)^6 + 9690*cosh(x)^4 + 765*cosh(x)^2 + 9)*e^(2*x)*sinh(x)^16 + 208*(37145*cosh(x)^11 + 81719*cosh(x)^9 + 63954*cosh(x)^7 + 21318*cosh(x)^5 + 2805*cosh(x)^3 + 99*cosh(x))*e^(2*x)*sinh(x)^15 + 52*(185725*cosh(x)^12 + 490314*cosh(x)^10 + 479655*cosh(x)^8 + 213180*cosh(x)^6 + 42075*cosh(x)^4 + 2970*cosh(x)^2 + 33)*e^(2*x)*sinh(x)^14 + 8*(1300075*cosh(x)^13 + 4056234*cosh(x)^11 + 4849845*cosh(x)^9 + 2771340*cosh(x)^7 + 765765*cosh(x)^5 + 90090*cosh(x)^3 + 3003*cosh(x))*e^(2*x)*sinh(x)^13 + 52*(185725*cosh(x)^14 + 676039*cosh(x)^12 + 969969*cosh(x)^10 + 692835*cosh(x)^8 + 255255*cosh(x)^6 + 45045*cosh(x)^4 + 3003*cosh(x)^2 + 33)*e^(2*x)*sinh(x)^12 + 208*(37145*cosh(x)^15 + 156009*cosh(x)^13 + 264537*cosh(x)^11 + 230945*cosh(x)^9 + 109395*cosh(x)^7 + 27027*cosh(x)^5 + 3003*cosh(x)^3 + 99*cosh(x))*e^(2*x)*sinh(x)^11 + 143*(37145*cosh(x)^16 + 178296*cosh(x)^14 + 352716*cosh(x)^12 + 369512*cosh(x)^10 + 218790*cosh(x)^8 + 72072*cosh(x)^6 + 12012*cosh(x)^4 + 792*cosh(x)^2 + 9)*e^(2*x)*sinh(x)^10 + 286*(10925*cosh(x)^17 + 59432*cosh(x)^15 + 135660*cosh(x)^13 + 167960*cosh(x)^11 + 121550*cosh(x)^9 + 51480*cosh(x)^7 + 12012*cosh(x)^5 + 1320*cosh(x)^3 + 45*cosh(x))*e^(2*x)*sinh(x)^9 + 143*(10925*cosh(x)^18 + 66861*cosh(x)^16 + 174420*cosh(x)^14 + 251940*cosh(x)^12 + 218790*cosh(x)^10 + 115830*cosh(x)^8 + 36036*cosh(x)^6 + 5940*cosh(x)^4 + 405*cosh(x)^2 + 5)*e^(2*x)*sinh(x)^8 + 1144*(575*cosh(x)^19 + 3933*cosh(x)^17 + 11628*cosh(x)^15 + 19380*cosh(x)^13 + 19890*cosh(x)^11 + 12870*cosh(x)^9 + 5148*cosh(x)^7 + 1188*cosh(x)^5 + 135*cosh(x)^3 + 5*cosh(x))*e^(2*x)*sinh(x)^7 + 286*(805*cosh(x)^20 + 6118*cosh(x)^18 + 20349*cosh(x)^16 + 38760*cosh(x)^14 + 46410*cosh(x)^12 + 36036*cosh(x)^10 + 18018*cosh(x)^8 + 5544*cosh(x)^6 + 945*cosh(x)^4 + 70*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^6 + 572*(115*cosh(x)^21 + 966*cosh(x)^19 + 3591*cosh(x)^17 + 7752*cosh(x)^15 + 10710*cosh(x)^13 + 9828*cosh(x)^11 + 6006*cosh(x)^9 + 2376*cosh(x)^7 + 567*cosh(x)^5 + 70*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^5 + 26*(575*cosh(x)^22 + 5313*cosh(x)^20 + 21945*cosh(x)^18 + 53295*cosh(x)^16 + 84150*cosh(x)^14 + 90090*cosh(x)^12 + 66066*cosh(x)^10 + 32670*cosh(x)^8 + 10395*cosh(x)^6 + 1925*cosh(x)^4 + 165*cosh(x)^2 + 3)*e^(2*x)*sinh(x)^4 + 104*(25*cosh(x)^23 + 253*cosh(x)^21 + 1155*cosh(x)^19 + 3135*cosh(x)^17 + 5610*cosh(x)^15 + 6930*cosh(x)^13 + 6006*cosh(x)^11 + 3630*cosh(x)^9 + 1485*cosh(x)^7 + 385*cosh(x)^5 + 55*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^3 + 13*(25*cosh(x)^24 + 276*cosh(x)^22 + 1386*cosh(x)^20 + 4180*cosh(x)^18 + 8415*cosh(x)^16 + 11880*cosh(x)^14 + 12012*cosh(x)^12 + 8712*cosh(x)^10 + 4455*cosh(x)^8 + 1540*cosh(x)^6 + 330*cosh(x)^4 + 36*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^2 + 26*(cosh(x)^25 + 12*cosh(x)^23 + 66*cosh(x)^21 + 220*cosh(x)^19 + 495*cosh(x)^17 + 792*cosh(x)^15 + 924*cosh(x)^13 + 792*cosh(x)^11 + 495*cosh(x)^9 + 220*cosh(x)^7 + 66*cosh(x)^5 + 12*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x) + (cosh(x)^26 + 13*cosh(x)^24 + 78*cosh(x)^22 + 286*cosh(x)^20 + 715*cosh(x)^18 + 1287*cosh(x)^16 + 1716*cosh(x)^14 + 1716*cosh(x)^12 + 1287*cosh(x)^10 + 715*cosh(x)^8 + 286*cosh(x)^6 + 78*cosh(x)^4 + 13*cosh(x)^2 + 1)*e^(2*x))","B",0
46,1,1475,0,0.472518," ","integrate((a*sech(x)^4)^(5/2),x, algorithm=""fricas"")","-\frac{256 \, {\left(126 \, a^{2} \cosh\left(x\right)^{8} + 126 \, {\left(a^{2} e^{\left(4 \, x\right)} + 2 \, a^{2} e^{\left(2 \, x\right)} + a^{2}\right)} \sinh\left(x\right)^{8} + 84 \, a^{2} \cosh\left(x\right)^{6} + 1008 \, {\left(a^{2} \cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, a^{2} \cosh\left(x\right) e^{\left(2 \, x\right)} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 84 \, {\left(42 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + {\left(42 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(42 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{6} + 36 \, a^{2} \cosh\left(x\right)^{4} + 504 \, {\left(14 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right) + {\left(14 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(14 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{5} + 36 \, {\left(245 \, a^{2} \cosh\left(x\right)^{4} + 35 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + {\left(245 \, a^{2} \cosh\left(x\right)^{4} + 35 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(245 \, a^{2} \cosh\left(x\right)^{4} + 35 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} + 48 \, {\left(147 \, a^{2} \cosh\left(x\right)^{5} + 35 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right) + {\left(147 \, a^{2} \cosh\left(x\right)^{5} + 35 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(147 \, a^{2} \cosh\left(x\right)^{5} + 35 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{3} + 9 \, {\left(392 \, a^{2} \cosh\left(x\right)^{6} + 140 \, a^{2} \cosh\left(x\right)^{4} + 24 \, a^{2} \cosh\left(x\right)^{2} + a^{2} + {\left(392 \, a^{2} \cosh\left(x\right)^{6} + 140 \, a^{2} \cosh\left(x\right)^{4} + 24 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(392 \, a^{2} \cosh\left(x\right)^{6} + 140 \, a^{2} \cosh\left(x\right)^{4} + 24 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{2} + a^{2} + {\left(126 \, a^{2} \cosh\left(x\right)^{8} + 84 \, a^{2} \cosh\left(x\right)^{6} + 36 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(4 \, x\right)} + 2 \, {\left(126 \, a^{2} \cosh\left(x\right)^{8} + 84 \, a^{2} \cosh\left(x\right)^{6} + 36 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} e^{\left(2 \, x\right)} + 18 \, {\left(56 \, a^{2} \cosh\left(x\right)^{7} + 28 \, a^{2} \cosh\left(x\right)^{5} + 8 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right) + {\left(56 \, a^{2} \cosh\left(x\right)^{7} + 28 \, a^{2} \cosh\left(x\right)^{5} + 8 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(56 \, a^{2} \cosh\left(x\right)^{7} + 28 \, a^{2} \cosh\left(x\right)^{5} + 8 \, a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{315 \, {\left(18 \, \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right)^{17} + e^{\left(2 \, x\right)} \sinh\left(x\right)^{18} + 9 \, {\left(17 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{16} + 48 \, {\left(17 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{15} + 36 \, {\left(85 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{14} + 504 \, {\left(17 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{13} + 84 \, {\left(221 \, \cosh\left(x\right)^{6} + 195 \, \cosh\left(x\right)^{4} + 39 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{12} + 144 \, {\left(221 \, \cosh\left(x\right)^{7} + 273 \, \cosh\left(x\right)^{5} + 91 \, \cosh\left(x\right)^{3} + 7 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{11} + 18 \, {\left(2431 \, \cosh\left(x\right)^{8} + 4004 \, \cosh\left(x\right)^{6} + 2002 \, \cosh\left(x\right)^{4} + 308 \, \cosh\left(x\right)^{2} + 7\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{10} + 4 \, {\left(12155 \, \cosh\left(x\right)^{9} + 25740 \, \cosh\left(x\right)^{7} + 18018 \, \cosh\left(x\right)^{5} + 4620 \, \cosh\left(x\right)^{3} + 315 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{9} + 18 \, {\left(2431 \, \cosh\left(x\right)^{10} + 6435 \, \cosh\left(x\right)^{8} + 6006 \, \cosh\left(x\right)^{6} + 2310 \, \cosh\left(x\right)^{4} + 315 \, \cosh\left(x\right)^{2} + 7\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{8} + 144 \, {\left(221 \, \cosh\left(x\right)^{11} + 715 \, \cosh\left(x\right)^{9} + 858 \, \cosh\left(x\right)^{7} + 462 \, \cosh\left(x\right)^{5} + 105 \, \cosh\left(x\right)^{3} + 7 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{7} + 84 \, {\left(221 \, \cosh\left(x\right)^{12} + 858 \, \cosh\left(x\right)^{10} + 1287 \, \cosh\left(x\right)^{8} + 924 \, \cosh\left(x\right)^{6} + 315 \, \cosh\left(x\right)^{4} + 42 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{6} + 504 \, {\left(17 \, \cosh\left(x\right)^{13} + 78 \, \cosh\left(x\right)^{11} + 143 \, \cosh\left(x\right)^{9} + 132 \, \cosh\left(x\right)^{7} + 63 \, \cosh\left(x\right)^{5} + 14 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{5} + 36 \, {\left(85 \, \cosh\left(x\right)^{14} + 455 \, \cosh\left(x\right)^{12} + 1001 \, \cosh\left(x\right)^{10} + 1155 \, \cosh\left(x\right)^{8} + 735 \, \cosh\left(x\right)^{6} + 245 \, \cosh\left(x\right)^{4} + 35 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{4} + 48 \, {\left(17 \, \cosh\left(x\right)^{15} + 105 \, \cosh\left(x\right)^{13} + 273 \, \cosh\left(x\right)^{11} + 385 \, \cosh\left(x\right)^{9} + 315 \, \cosh\left(x\right)^{7} + 147 \, \cosh\left(x\right)^{5} + 35 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{3} + 9 \, {\left(17 \, \cosh\left(x\right)^{16} + 120 \, \cosh\left(x\right)^{14} + 364 \, \cosh\left(x\right)^{12} + 616 \, \cosh\left(x\right)^{10} + 630 \, \cosh\left(x\right)^{8} + 392 \, \cosh\left(x\right)^{6} + 140 \, \cosh\left(x\right)^{4} + 24 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + 18 \, {\left(\cosh\left(x\right)^{17} + 8 \, \cosh\left(x\right)^{15} + 28 \, \cosh\left(x\right)^{13} + 56 \, \cosh\left(x\right)^{11} + 70 \, \cosh\left(x\right)^{9} + 56 \, \cosh\left(x\right)^{7} + 28 \, \cosh\left(x\right)^{5} + 8 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right) + {\left(\cosh\left(x\right)^{18} + 9 \, \cosh\left(x\right)^{16} + 36 \, \cosh\left(x\right)^{14} + 84 \, \cosh\left(x\right)^{12} + 126 \, \cosh\left(x\right)^{10} + 126 \, \cosh\left(x\right)^{8} + 84 \, \cosh\left(x\right)^{6} + 36 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)}\right)}}"," ",0,"-256/315*(126*a^2*cosh(x)^8 + 126*(a^2*e^(4*x) + 2*a^2*e^(2*x) + a^2)*sinh(x)^8 + 84*a^2*cosh(x)^6 + 1008*(a^2*cosh(x)*e^(4*x) + 2*a^2*cosh(x)*e^(2*x) + a^2*cosh(x))*sinh(x)^7 + 84*(42*a^2*cosh(x)^2 + a^2 + (42*a^2*cosh(x)^2 + a^2)*e^(4*x) + 2*(42*a^2*cosh(x)^2 + a^2)*e^(2*x))*sinh(x)^6 + 36*a^2*cosh(x)^4 + 504*(14*a^2*cosh(x)^3 + a^2*cosh(x) + (14*a^2*cosh(x)^3 + a^2*cosh(x))*e^(4*x) + 2*(14*a^2*cosh(x)^3 + a^2*cosh(x))*e^(2*x))*sinh(x)^5 + 36*(245*a^2*cosh(x)^4 + 35*a^2*cosh(x)^2 + a^2 + (245*a^2*cosh(x)^4 + 35*a^2*cosh(x)^2 + a^2)*e^(4*x) + 2*(245*a^2*cosh(x)^4 + 35*a^2*cosh(x)^2 + a^2)*e^(2*x))*sinh(x)^4 + 9*a^2*cosh(x)^2 + 48*(147*a^2*cosh(x)^5 + 35*a^2*cosh(x)^3 + 3*a^2*cosh(x) + (147*a^2*cosh(x)^5 + 35*a^2*cosh(x)^3 + 3*a^2*cosh(x))*e^(4*x) + 2*(147*a^2*cosh(x)^5 + 35*a^2*cosh(x)^3 + 3*a^2*cosh(x))*e^(2*x))*sinh(x)^3 + 9*(392*a^2*cosh(x)^6 + 140*a^2*cosh(x)^4 + 24*a^2*cosh(x)^2 + a^2 + (392*a^2*cosh(x)^6 + 140*a^2*cosh(x)^4 + 24*a^2*cosh(x)^2 + a^2)*e^(4*x) + 2*(392*a^2*cosh(x)^6 + 140*a^2*cosh(x)^4 + 24*a^2*cosh(x)^2 + a^2)*e^(2*x))*sinh(x)^2 + a^2 + (126*a^2*cosh(x)^8 + 84*a^2*cosh(x)^6 + 36*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 + a^2)*e^(4*x) + 2*(126*a^2*cosh(x)^8 + 84*a^2*cosh(x)^6 + 36*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 + a^2)*e^(2*x) + 18*(56*a^2*cosh(x)^7 + 28*a^2*cosh(x)^5 + 8*a^2*cosh(x)^3 + a^2*cosh(x) + (56*a^2*cosh(x)^7 + 28*a^2*cosh(x)^5 + 8*a^2*cosh(x)^3 + a^2*cosh(x))*e^(4*x) + 2*(56*a^2*cosh(x)^7 + 28*a^2*cosh(x)^5 + 8*a^2*cosh(x)^3 + a^2*cosh(x))*e^(2*x))*sinh(x))*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(18*cosh(x)*e^(2*x)*sinh(x)^17 + e^(2*x)*sinh(x)^18 + 9*(17*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^16 + 48*(17*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^15 + 36*(85*cosh(x)^4 + 30*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^14 + 504*(17*cosh(x)^5 + 10*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x)^13 + 84*(221*cosh(x)^6 + 195*cosh(x)^4 + 39*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^12 + 144*(221*cosh(x)^7 + 273*cosh(x)^5 + 91*cosh(x)^3 + 7*cosh(x))*e^(2*x)*sinh(x)^11 + 18*(2431*cosh(x)^8 + 4004*cosh(x)^6 + 2002*cosh(x)^4 + 308*cosh(x)^2 + 7)*e^(2*x)*sinh(x)^10 + 4*(12155*cosh(x)^9 + 25740*cosh(x)^7 + 18018*cosh(x)^5 + 4620*cosh(x)^3 + 315*cosh(x))*e^(2*x)*sinh(x)^9 + 18*(2431*cosh(x)^10 + 6435*cosh(x)^8 + 6006*cosh(x)^6 + 2310*cosh(x)^4 + 315*cosh(x)^2 + 7)*e^(2*x)*sinh(x)^8 + 144*(221*cosh(x)^11 + 715*cosh(x)^9 + 858*cosh(x)^7 + 462*cosh(x)^5 + 105*cosh(x)^3 + 7*cosh(x))*e^(2*x)*sinh(x)^7 + 84*(221*cosh(x)^12 + 858*cosh(x)^10 + 1287*cosh(x)^8 + 924*cosh(x)^6 + 315*cosh(x)^4 + 42*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^6 + 504*(17*cosh(x)^13 + 78*cosh(x)^11 + 143*cosh(x)^9 + 132*cosh(x)^7 + 63*cosh(x)^5 + 14*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x)^5 + 36*(85*cosh(x)^14 + 455*cosh(x)^12 + 1001*cosh(x)^10 + 1155*cosh(x)^8 + 735*cosh(x)^6 + 245*cosh(x)^4 + 35*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^4 + 48*(17*cosh(x)^15 + 105*cosh(x)^13 + 273*cosh(x)^11 + 385*cosh(x)^9 + 315*cosh(x)^7 + 147*cosh(x)^5 + 35*cosh(x)^3 + 3*cosh(x))*e^(2*x)*sinh(x)^3 + 9*(17*cosh(x)^16 + 120*cosh(x)^14 + 364*cosh(x)^12 + 616*cosh(x)^10 + 630*cosh(x)^8 + 392*cosh(x)^6 + 140*cosh(x)^4 + 24*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^2 + 18*(cosh(x)^17 + 8*cosh(x)^15 + 28*cosh(x)^13 + 56*cosh(x)^11 + 70*cosh(x)^9 + 56*cosh(x)^7 + 28*cosh(x)^5 + 8*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x) + (cosh(x)^18 + 9*cosh(x)^16 + 36*cosh(x)^14 + 84*cosh(x)^12 + 126*cosh(x)^10 + 126*cosh(x)^8 + 84*cosh(x)^6 + 36*cosh(x)^4 + 9*cosh(x)^2 + 1)*e^(2*x))","B",0
47,1,516,0,0.427509," ","integrate((a*sech(x)^4)^(3/2),x, algorithm=""fricas"")","-\frac{16 \, {\left(10 \, a \cosh\left(x\right)^{4} + 10 \, {\left(a e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} + a\right)} \sinh\left(x\right)^{4} + 40 \, {\left(a \cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, a \cosh\left(x\right) e^{\left(2 \, x\right)} + a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, a \cosh\left(x\right)^{2} + 5 \, {\left(12 \, a \cosh\left(x\right)^{2} + {\left(12 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(4 \, x\right)} + 2 \, {\left(12 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(2 \, x\right)} + a\right)} \sinh\left(x\right)^{2} + {\left(10 \, a \cosh\left(x\right)^{4} + 5 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(4 \, x\right)} + 2 \, {\left(10 \, a \cosh\left(x\right)^{4} + 5 \, a \cosh\left(x\right)^{2} + a\right)} e^{\left(2 \, x\right)} + 10 \, {\left(4 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right) + {\left(4 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(4 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right) + a\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{15 \, {\left(10 \, \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right)^{9} + e^{\left(2 \, x\right)} \sinh\left(x\right)^{10} + 5 \, {\left(9 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, \cosh\left(x\right)^{4} + 14 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, \cosh\left(x\right)^{5} + 70 \, \cosh\left(x\right)^{3} + 15 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, \cosh\left(x\right)^{6} + 35 \, \cosh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, \cosh\left(x\right)^{7} + 7 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, \cosh\left(x\right)^{8} + 28 \, \cosh\left(x\right)^{6} + 30 \, \cosh\left(x\right)^{4} + 12 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + 10 \, {\left(\cosh\left(x\right)^{9} + 4 \, \cosh\left(x\right)^{7} + 6 \, \cosh\left(x\right)^{5} + 4 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} \sinh\left(x\right) + {\left(\cosh\left(x\right)^{10} + 5 \, \cosh\left(x\right)^{8} + 10 \, \cosh\left(x\right)^{6} + 10 \, \cosh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)}\right)}}"," ",0,"-16/15*(10*a*cosh(x)^4 + 10*(a*e^(4*x) + 2*a*e^(2*x) + a)*sinh(x)^4 + 40*(a*cosh(x)*e^(4*x) + 2*a*cosh(x)*e^(2*x) + a*cosh(x))*sinh(x)^3 + 5*a*cosh(x)^2 + 5*(12*a*cosh(x)^2 + (12*a*cosh(x)^2 + a)*e^(4*x) + 2*(12*a*cosh(x)^2 + a)*e^(2*x) + a)*sinh(x)^2 + (10*a*cosh(x)^4 + 5*a*cosh(x)^2 + a)*e^(4*x) + 2*(10*a*cosh(x)^4 + 5*a*cosh(x)^2 + a)*e^(2*x) + 10*(4*a*cosh(x)^3 + a*cosh(x) + (4*a*cosh(x)^3 + a*cosh(x))*e^(4*x) + 2*(4*a*cosh(x)^3 + a*cosh(x))*e^(2*x))*sinh(x) + a)*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(10*cosh(x)*e^(2*x)*sinh(x)^9 + e^(2*x)*sinh(x)^10 + 5*(9*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^8 + 40*(3*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x)^7 + 10*(21*cosh(x)^4 + 14*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^6 + 4*(63*cosh(x)^5 + 70*cosh(x)^3 + 15*cosh(x))*e^(2*x)*sinh(x)^5 + 10*(21*cosh(x)^6 + 35*cosh(x)^4 + 15*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^4 + 40*(3*cosh(x)^7 + 7*cosh(x)^5 + 5*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x)^3 + 5*(9*cosh(x)^8 + 28*cosh(x)^6 + 30*cosh(x)^4 + 12*cosh(x)^2 + 1)*e^(2*x)*sinh(x)^2 + 10*(cosh(x)^9 + 4*cosh(x)^7 + 6*cosh(x)^5 + 4*cosh(x)^3 + cosh(x))*e^(2*x)*sinh(x) + (cosh(x)^10 + 5*cosh(x)^8 + 10*cosh(x)^6 + 10*cosh(x)^4 + 5*cosh(x)^2 + 1)*e^(2*x))","B",0
48,1,81,0,0.429877," ","integrate((a*sech(x)^4)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} {\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)} e^{\left(2 \, x\right)}}{2 \, \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right) + e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)}}"," ",0,"-2*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*(e^(4*x) + 2*e^(2*x) + 1)*e^(2*x)/(2*cosh(x)*e^(2*x)*sinh(x) + e^(2*x)*sinh(x)^2 + (cosh(x)^2 + 1)*e^(2*x))","B",0
49,1,253,0,0.440574," ","integrate(1/(a*sech(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{4} + \cosh\left(x\right)^{4} + 4 \, {\left(\cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, \cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{2} + 2 \, x\right)} e^{\left(4 \, x\right)} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 2 \, x\right)} e^{\left(2 \, x\right)} + 2 \, x\right)} \sinh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{4} + 4 \, x \cosh\left(x\right)^{2} - 1\right)} e^{\left(4 \, x\right)} + 2 \, {\left(\cosh\left(x\right)^{4} + 4 \, x \cosh\left(x\right)^{2} - 1\right)} e^{\left(2 \, x\right)} + 4 \, {\left(\cosh\left(x\right)^{3} + 2 \, x \cosh\left(x\right) + {\left(\cosh\left(x\right)^{3} + 2 \, x \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(\cosh\left(x\right)^{3} + 2 \, x \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right) - 1\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{8 \, {\left(a \cosh\left(x\right)^{2} e^{\left(2 \, x\right)} + 2 \, a \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right) + a e^{\left(2 \, x\right)} \sinh\left(x\right)^{2}\right)}}"," ",0,"1/8*((e^(4*x) + 2*e^(2*x) + 1)*sinh(x)^4 + cosh(x)^4 + 4*(cosh(x)*e^(4*x) + 2*cosh(x)*e^(2*x) + cosh(x))*sinh(x)^3 + 4*x*cosh(x)^2 + 2*(3*cosh(x)^2 + (3*cosh(x)^2 + 2*x)*e^(4*x) + 2*(3*cosh(x)^2 + 2*x)*e^(2*x) + 2*x)*sinh(x)^2 + (cosh(x)^4 + 4*x*cosh(x)^2 - 1)*e^(4*x) + 2*(cosh(x)^4 + 4*x*cosh(x)^2 - 1)*e^(2*x) + 4*(cosh(x)^3 + 2*x*cosh(x) + (cosh(x)^3 + 2*x*cosh(x))*e^(4*x) + 2*(cosh(x)^3 + 2*x*cosh(x))*e^(2*x))*sinh(x) - 1)*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(a*cosh(x)^2*e^(2*x) + 2*a*cosh(x)*e^(2*x)*sinh(x) + a*e^(2*x)*sinh(x)^2)","B",0
50,1,1141,0,0.446578," ","integrate(1/(a*sech(x)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{12} + \cosh\left(x\right)^{12} + 12 \, {\left(\cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, \cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{11} + 3 \, {\left(22 \, \cosh\left(x\right)^{2} + {\left(22 \, \cosh\left(x\right)^{2} + 3\right)} e^{\left(4 \, x\right)} + 2 \, {\left(22 \, \cosh\left(x\right)^{2} + 3\right)} e^{\left(2 \, x\right)} + 3\right)} \sinh\left(x\right)^{10} + 9 \, \cosh\left(x\right)^{10} + 10 \, {\left(22 \, \cosh\left(x\right)^{3} + {\left(22 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(22 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{9} + 45 \, {\left(11 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + {\left(11 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(4 \, x\right)} + 2 \, {\left(11 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{8} + 45 \, \cosh\left(x\right)^{8} + 72 \, {\left(11 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + {\left(11 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(11 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 120 \, x \cosh\left(x\right)^{6} + 6 \, {\left(154 \, \cosh\left(x\right)^{6} + 315 \, \cosh\left(x\right)^{4} + 210 \, \cosh\left(x\right)^{2} + {\left(154 \, \cosh\left(x\right)^{6} + 315 \, \cosh\left(x\right)^{4} + 210 \, \cosh\left(x\right)^{2} + 20 \, x\right)} e^{\left(4 \, x\right)} + 2 \, {\left(154 \, \cosh\left(x\right)^{6} + 315 \, \cosh\left(x\right)^{4} + 210 \, \cosh\left(x\right)^{2} + 20 \, x\right)} e^{\left(2 \, x\right)} + 20 \, x\right)} \sinh\left(x\right)^{6} + 36 \, {\left(22 \, \cosh\left(x\right)^{7} + 63 \, \cosh\left(x\right)^{5} + 70 \, \cosh\left(x\right)^{3} + 20 \, x \cosh\left(x\right) + {\left(22 \, \cosh\left(x\right)^{7} + 63 \, \cosh\left(x\right)^{5} + 70 \, \cosh\left(x\right)^{3} + 20 \, x \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(22 \, \cosh\left(x\right)^{7} + 63 \, \cosh\left(x\right)^{5} + 70 \, \cosh\left(x\right)^{3} + 20 \, x \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{5} + 45 \, {\left(11 \, \cosh\left(x\right)^{8} + 42 \, \cosh\left(x\right)^{6} + 70 \, \cosh\left(x\right)^{4} + 40 \, x \cosh\left(x\right)^{2} + {\left(11 \, \cosh\left(x\right)^{8} + 42 \, \cosh\left(x\right)^{6} + 70 \, \cosh\left(x\right)^{4} + 40 \, x \cosh\left(x\right)^{2} - 1\right)} e^{\left(4 \, x\right)} + 2 \, {\left(11 \, \cosh\left(x\right)^{8} + 42 \, \cosh\left(x\right)^{6} + 70 \, \cosh\left(x\right)^{4} + 40 \, x \cosh\left(x\right)^{2} - 1\right)} e^{\left(2 \, x\right)} - 1\right)} \sinh\left(x\right)^{4} - 45 \, \cosh\left(x\right)^{4} + 20 \, {\left(11 \, \cosh\left(x\right)^{9} + 54 \, \cosh\left(x\right)^{7} + 126 \, \cosh\left(x\right)^{5} + 120 \, x \cosh\left(x\right)^{3} + {\left(11 \, \cosh\left(x\right)^{9} + 54 \, \cosh\left(x\right)^{7} + 126 \, \cosh\left(x\right)^{5} + 120 \, x \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(11 \, \cosh\left(x\right)^{9} + 54 \, \cosh\left(x\right)^{7} + 126 \, \cosh\left(x\right)^{5} + 120 \, x \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(22 \, \cosh\left(x\right)^{10} + 135 \, \cosh\left(x\right)^{8} + 420 \, \cosh\left(x\right)^{6} + 600 \, x \cosh\left(x\right)^{4} - 90 \, \cosh\left(x\right)^{2} + {\left(22 \, \cosh\left(x\right)^{10} + 135 \, \cosh\left(x\right)^{8} + 420 \, \cosh\left(x\right)^{6} + 600 \, x \cosh\left(x\right)^{4} - 90 \, \cosh\left(x\right)^{2} - 3\right)} e^{\left(4 \, x\right)} + 2 \, {\left(22 \, \cosh\left(x\right)^{10} + 135 \, \cosh\left(x\right)^{8} + 420 \, \cosh\left(x\right)^{6} + 600 \, x \cosh\left(x\right)^{4} - 90 \, \cosh\left(x\right)^{2} - 3\right)} e^{\left(2 \, x\right)} - 3\right)} \sinh\left(x\right)^{2} - 9 \, \cosh\left(x\right)^{2} + {\left(\cosh\left(x\right)^{12} + 9 \, \cosh\left(x\right)^{10} + 45 \, \cosh\left(x\right)^{8} + 120 \, x \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} - 1\right)} e^{\left(4 \, x\right)} + 2 \, {\left(\cosh\left(x\right)^{12} + 9 \, \cosh\left(x\right)^{10} + 45 \, \cosh\left(x\right)^{8} + 120 \, x \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} - 1\right)} e^{\left(2 \, x\right)} + 6 \, {\left(2 \, \cosh\left(x\right)^{11} + 15 \, \cosh\left(x\right)^{9} + 60 \, \cosh\left(x\right)^{7} + 120 \, x \cosh\left(x\right)^{5} - 30 \, \cosh\left(x\right)^{3} + {\left(2 \, \cosh\left(x\right)^{11} + 15 \, \cosh\left(x\right)^{9} + 60 \, \cosh\left(x\right)^{7} + 120 \, x \cosh\left(x\right)^{5} - 30 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(2 \, \cosh\left(x\right)^{11} + 15 \, \cosh\left(x\right)^{9} + 60 \, \cosh\left(x\right)^{7} + 120 \, x \cosh\left(x\right)^{5} - 30 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{384 \, {\left(a^{2} \cosh\left(x\right)^{6} e^{\left(2 \, x\right)} + 6 \, a^{2} \cosh\left(x\right)^{5} e^{\left(2 \, x\right)} \sinh\left(x\right) + 15 \, a^{2} \cosh\left(x\right)^{4} e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + 20 \, a^{2} \cosh\left(x\right)^{3} e^{\left(2 \, x\right)} \sinh\left(x\right)^{3} + 15 \, a^{2} \cosh\left(x\right)^{2} e^{\left(2 \, x\right)} \sinh\left(x\right)^{4} + 6 \, a^{2} \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right)^{5} + a^{2} e^{\left(2 \, x\right)} \sinh\left(x\right)^{6}\right)}}"," ",0,"1/384*((e^(4*x) + 2*e^(2*x) + 1)*sinh(x)^12 + cosh(x)^12 + 12*(cosh(x)*e^(4*x) + 2*cosh(x)*e^(2*x) + cosh(x))*sinh(x)^11 + 3*(22*cosh(x)^2 + (22*cosh(x)^2 + 3)*e^(4*x) + 2*(22*cosh(x)^2 + 3)*e^(2*x) + 3)*sinh(x)^10 + 9*cosh(x)^10 + 10*(22*cosh(x)^3 + (22*cosh(x)^3 + 9*cosh(x))*e^(4*x) + 2*(22*cosh(x)^3 + 9*cosh(x))*e^(2*x) + 9*cosh(x))*sinh(x)^9 + 45*(11*cosh(x)^4 + 9*cosh(x)^2 + (11*cosh(x)^4 + 9*cosh(x)^2 + 1)*e^(4*x) + 2*(11*cosh(x)^4 + 9*cosh(x)^2 + 1)*e^(2*x) + 1)*sinh(x)^8 + 45*cosh(x)^8 + 72*(11*cosh(x)^5 + 15*cosh(x)^3 + (11*cosh(x)^5 + 15*cosh(x)^3 + 5*cosh(x))*e^(4*x) + 2*(11*cosh(x)^5 + 15*cosh(x)^3 + 5*cosh(x))*e^(2*x) + 5*cosh(x))*sinh(x)^7 + 120*x*cosh(x)^6 + 6*(154*cosh(x)^6 + 315*cosh(x)^4 + 210*cosh(x)^2 + (154*cosh(x)^6 + 315*cosh(x)^4 + 210*cosh(x)^2 + 20*x)*e^(4*x) + 2*(154*cosh(x)^6 + 315*cosh(x)^4 + 210*cosh(x)^2 + 20*x)*e^(2*x) + 20*x)*sinh(x)^6 + 36*(22*cosh(x)^7 + 63*cosh(x)^5 + 70*cosh(x)^3 + 20*x*cosh(x) + (22*cosh(x)^7 + 63*cosh(x)^5 + 70*cosh(x)^3 + 20*x*cosh(x))*e^(4*x) + 2*(22*cosh(x)^7 + 63*cosh(x)^5 + 70*cosh(x)^3 + 20*x*cosh(x))*e^(2*x))*sinh(x)^5 + 45*(11*cosh(x)^8 + 42*cosh(x)^6 + 70*cosh(x)^4 + 40*x*cosh(x)^2 + (11*cosh(x)^8 + 42*cosh(x)^6 + 70*cosh(x)^4 + 40*x*cosh(x)^2 - 1)*e^(4*x) + 2*(11*cosh(x)^8 + 42*cosh(x)^6 + 70*cosh(x)^4 + 40*x*cosh(x)^2 - 1)*e^(2*x) - 1)*sinh(x)^4 - 45*cosh(x)^4 + 20*(11*cosh(x)^9 + 54*cosh(x)^7 + 126*cosh(x)^5 + 120*x*cosh(x)^3 + (11*cosh(x)^9 + 54*cosh(x)^7 + 126*cosh(x)^5 + 120*x*cosh(x)^3 - 9*cosh(x))*e^(4*x) + 2*(11*cosh(x)^9 + 54*cosh(x)^7 + 126*cosh(x)^5 + 120*x*cosh(x)^3 - 9*cosh(x))*e^(2*x) - 9*cosh(x))*sinh(x)^3 + 3*(22*cosh(x)^10 + 135*cosh(x)^8 + 420*cosh(x)^6 + 600*x*cosh(x)^4 - 90*cosh(x)^2 + (22*cosh(x)^10 + 135*cosh(x)^8 + 420*cosh(x)^6 + 600*x*cosh(x)^4 - 90*cosh(x)^2 - 3)*e^(4*x) + 2*(22*cosh(x)^10 + 135*cosh(x)^8 + 420*cosh(x)^6 + 600*x*cosh(x)^4 - 90*cosh(x)^2 - 3)*e^(2*x) - 3)*sinh(x)^2 - 9*cosh(x)^2 + (cosh(x)^12 + 9*cosh(x)^10 + 45*cosh(x)^8 + 120*x*cosh(x)^6 - 45*cosh(x)^4 - 9*cosh(x)^2 - 1)*e^(4*x) + 2*(cosh(x)^12 + 9*cosh(x)^10 + 45*cosh(x)^8 + 120*x*cosh(x)^6 - 45*cosh(x)^4 - 9*cosh(x)^2 - 1)*e^(2*x) + 6*(2*cosh(x)^11 + 15*cosh(x)^9 + 60*cosh(x)^7 + 120*x*cosh(x)^5 - 30*cosh(x)^3 + (2*cosh(x)^11 + 15*cosh(x)^9 + 60*cosh(x)^7 + 120*x*cosh(x)^5 - 30*cosh(x)^3 - 3*cosh(x))*e^(4*x) + 2*(2*cosh(x)^11 + 15*cosh(x)^9 + 60*cosh(x)^7 + 120*x*cosh(x)^5 - 30*cosh(x)^3 - 3*cosh(x))*e^(2*x) - 3*cosh(x))*sinh(x) - 1)*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(a^2*cosh(x)^6*e^(2*x) + 6*a^2*cosh(x)^5*e^(2*x)*sinh(x) + 15*a^2*cosh(x)^4*e^(2*x)*sinh(x)^2 + 20*a^2*cosh(x)^3*e^(2*x)*sinh(x)^3 + 15*a^2*cosh(x)^2*e^(2*x)*sinh(x)^4 + 6*a^2*cosh(x)*e^(2*x)*sinh(x)^5 + a^2*e^(2*x)*sinh(x)^6)","B",0
51,1,2600,0,0.462449," ","integrate(1/(a*sech(x)^4)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)} \sinh\left(x\right)^{20} + 2 \, \cosh\left(x\right)^{20} + 40 \, {\left(\cosh\left(x\right) e^{\left(4 \, x\right)} + 2 \, \cosh\left(x\right) e^{\left(2 \, x\right)} + \cosh\left(x\right)\right)} \sinh\left(x\right)^{19} + 5 \, {\left(76 \, \cosh\left(x\right)^{2} + {\left(76 \, \cosh\left(x\right)^{2} + 5\right)} e^{\left(4 \, x\right)} + 2 \, {\left(76 \, \cosh\left(x\right)^{2} + 5\right)} e^{\left(2 \, x\right)} + 5\right)} \sinh\left(x\right)^{18} + 25 \, \cosh\left(x\right)^{18} + 30 \, {\left(76 \, \cosh\left(x\right)^{3} + {\left(76 \, \cosh\left(x\right)^{3} + 15 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(76 \, \cosh\left(x\right)^{3} + 15 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 15 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{17} + 15 \, {\left(646 \, \cosh\left(x\right)^{4} + 255 \, \cosh\left(x\right)^{2} + {\left(646 \, \cosh\left(x\right)^{4} + 255 \, \cosh\left(x\right)^{2} + 10\right)} e^{\left(4 \, x\right)} + 2 \, {\left(646 \, \cosh\left(x\right)^{4} + 255 \, \cosh\left(x\right)^{2} + 10\right)} e^{\left(2 \, x\right)} + 10\right)} \sinh\left(x\right)^{16} + 150 \, \cosh\left(x\right)^{16} + 48 \, {\left(646 \, \cosh\left(x\right)^{5} + 425 \, \cosh\left(x\right)^{3} + {\left(646 \, \cosh\left(x\right)^{5} + 425 \, \cosh\left(x\right)^{3} + 50 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(646 \, \cosh\left(x\right)^{5} + 425 \, \cosh\left(x\right)^{3} + 50 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 50 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{15} + 60 \, {\left(1292 \, \cosh\left(x\right)^{6} + 1275 \, \cosh\left(x\right)^{4} + 300 \, \cosh\left(x\right)^{2} + {\left(1292 \, \cosh\left(x\right)^{6} + 1275 \, \cosh\left(x\right)^{4} + 300 \, \cosh\left(x\right)^{2} + 10\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1292 \, \cosh\left(x\right)^{6} + 1275 \, \cosh\left(x\right)^{4} + 300 \, \cosh\left(x\right)^{2} + 10\right)} e^{\left(2 \, x\right)} + 10\right)} \sinh\left(x\right)^{14} + 600 \, \cosh\left(x\right)^{14} + 120 \, {\left(1292 \, \cosh\left(x\right)^{7} + 1785 \, \cosh\left(x\right)^{5} + 700 \, \cosh\left(x\right)^{3} + {\left(1292 \, \cosh\left(x\right)^{7} + 1785 \, \cosh\left(x\right)^{5} + 700 \, \cosh\left(x\right)^{3} + 70 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1292 \, \cosh\left(x\right)^{7} + 1785 \, \cosh\left(x\right)^{5} + 700 \, \cosh\left(x\right)^{3} + 70 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 70 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{13} + 60 \, {\left(4199 \, \cosh\left(x\right)^{8} + 7735 \, \cosh\left(x\right)^{6} + 4550 \, \cosh\left(x\right)^{4} + 910 \, \cosh\left(x\right)^{2} + {\left(4199 \, \cosh\left(x\right)^{8} + 7735 \, \cosh\left(x\right)^{6} + 4550 \, \cosh\left(x\right)^{4} + 910 \, \cosh\left(x\right)^{2} + 35\right)} e^{\left(4 \, x\right)} + 2 \, {\left(4199 \, \cosh\left(x\right)^{8} + 7735 \, \cosh\left(x\right)^{6} + 4550 \, \cosh\left(x\right)^{4} + 910 \, \cosh\left(x\right)^{2} + 35\right)} e^{\left(2 \, x\right)} + 35\right)} \sinh\left(x\right)^{12} + 2100 \, \cosh\left(x\right)^{12} + 80 \, {\left(4199 \, \cosh\left(x\right)^{9} + 9945 \, \cosh\left(x\right)^{7} + 8190 \, \cosh\left(x\right)^{5} + 2730 \, \cosh\left(x\right)^{3} + {\left(4199 \, \cosh\left(x\right)^{9} + 9945 \, \cosh\left(x\right)^{7} + 8190 \, \cosh\left(x\right)^{5} + 2730 \, \cosh\left(x\right)^{3} + 315 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(4199 \, \cosh\left(x\right)^{9} + 9945 \, \cosh\left(x\right)^{7} + 8190 \, \cosh\left(x\right)^{5} + 2730 \, \cosh\left(x\right)^{3} + 315 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} + 315 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{11} + 5040 \, x \cosh\left(x\right)^{10} + 2 \, {\left(184756 \, \cosh\left(x\right)^{10} + 546975 \, \cosh\left(x\right)^{8} + 600600 \, \cosh\left(x\right)^{6} + 300300 \, \cosh\left(x\right)^{4} + 69300 \, \cosh\left(x\right)^{2} + {\left(184756 \, \cosh\left(x\right)^{10} + 546975 \, \cosh\left(x\right)^{8} + 600600 \, \cosh\left(x\right)^{6} + 300300 \, \cosh\left(x\right)^{4} + 69300 \, \cosh\left(x\right)^{2} + 2520 \, x\right)} e^{\left(4 \, x\right)} + 2 \, {\left(184756 \, \cosh\left(x\right)^{10} + 546975 \, \cosh\left(x\right)^{8} + 600600 \, \cosh\left(x\right)^{6} + 300300 \, \cosh\left(x\right)^{4} + 69300 \, \cosh\left(x\right)^{2} + 2520 \, x\right)} e^{\left(2 \, x\right)} + 2520 \, x\right)} \sinh\left(x\right)^{10} + 20 \, {\left(16796 \, \cosh\left(x\right)^{11} + 60775 \, \cosh\left(x\right)^{9} + 85800 \, \cosh\left(x\right)^{7} + 60060 \, \cosh\left(x\right)^{5} + 23100 \, \cosh\left(x\right)^{3} + 2520 \, x \cosh\left(x\right) + {\left(16796 \, \cosh\left(x\right)^{11} + 60775 \, \cosh\left(x\right)^{9} + 85800 \, \cosh\left(x\right)^{7} + 60060 \, \cosh\left(x\right)^{5} + 23100 \, \cosh\left(x\right)^{3} + 2520 \, x \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(16796 \, \cosh\left(x\right)^{11} + 60775 \, \cosh\left(x\right)^{9} + 85800 \, \cosh\left(x\right)^{7} + 60060 \, \cosh\left(x\right)^{5} + 23100 \, \cosh\left(x\right)^{3} + 2520 \, x \cosh\left(x\right)\right)} e^{\left(2 \, x\right)}\right)} \sinh\left(x\right)^{9} + 30 \, {\left(8398 \, \cosh\left(x\right)^{12} + 36465 \, \cosh\left(x\right)^{10} + 64350 \, \cosh\left(x\right)^{8} + 60060 \, \cosh\left(x\right)^{6} + 34650 \, \cosh\left(x\right)^{4} + 7560 \, x \cosh\left(x\right)^{2} + {\left(8398 \, \cosh\left(x\right)^{12} + 36465 \, \cosh\left(x\right)^{10} + 64350 \, \cosh\left(x\right)^{8} + 60060 \, \cosh\left(x\right)^{6} + 34650 \, \cosh\left(x\right)^{4} + 7560 \, x \cosh\left(x\right)^{2} - 70\right)} e^{\left(4 \, x\right)} + 2 \, {\left(8398 \, \cosh\left(x\right)^{12} + 36465 \, \cosh\left(x\right)^{10} + 64350 \, \cosh\left(x\right)^{8} + 60060 \, \cosh\left(x\right)^{6} + 34650 \, \cosh\left(x\right)^{4} + 7560 \, x \cosh\left(x\right)^{2} - 70\right)} e^{\left(2 \, x\right)} - 70\right)} \sinh\left(x\right)^{8} - 2100 \, \cosh\left(x\right)^{8} + 240 \, {\left(646 \, \cosh\left(x\right)^{13} + 3315 \, \cosh\left(x\right)^{11} + 7150 \, \cosh\left(x\right)^{9} + 8580 \, \cosh\left(x\right)^{7} + 6930 \, \cosh\left(x\right)^{5} + 2520 \, x \cosh\left(x\right)^{3} + {\left(646 \, \cosh\left(x\right)^{13} + 3315 \, \cosh\left(x\right)^{11} + 7150 \, \cosh\left(x\right)^{9} + 8580 \, \cosh\left(x\right)^{7} + 6930 \, \cosh\left(x\right)^{5} + 2520 \, x \cosh\left(x\right)^{3} - 70 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(646 \, \cosh\left(x\right)^{13} + 3315 \, \cosh\left(x\right)^{11} + 7150 \, \cosh\left(x\right)^{9} + 8580 \, \cosh\left(x\right)^{7} + 6930 \, \cosh\left(x\right)^{5} + 2520 \, x \cosh\left(x\right)^{3} - 70 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 70 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 60 \, {\left(1292 \, \cosh\left(x\right)^{14} + 7735 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 30030 \, \cosh\left(x\right)^{8} + 32340 \, \cosh\left(x\right)^{6} + 17640 \, x \cosh\left(x\right)^{4} - 980 \, \cosh\left(x\right)^{2} + {\left(1292 \, \cosh\left(x\right)^{14} + 7735 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 30030 \, \cosh\left(x\right)^{8} + 32340 \, \cosh\left(x\right)^{6} + 17640 \, x \cosh\left(x\right)^{4} - 980 \, \cosh\left(x\right)^{2} - 10\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1292 \, \cosh\left(x\right)^{14} + 7735 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 30030 \, \cosh\left(x\right)^{8} + 32340 \, \cosh\left(x\right)^{6} + 17640 \, x \cosh\left(x\right)^{4} - 980 \, \cosh\left(x\right)^{2} - 10\right)} e^{\left(2 \, x\right)} - 10\right)} \sinh\left(x\right)^{6} - 600 \, \cosh\left(x\right)^{6} + 24 \, {\left(1292 \, \cosh\left(x\right)^{15} + 8925 \, \cosh\left(x\right)^{13} + 27300 \, \cosh\left(x\right)^{11} + 50050 \, \cosh\left(x\right)^{9} + 69300 \, \cosh\left(x\right)^{7} + 52920 \, x \cosh\left(x\right)^{5} - 4900 \, \cosh\left(x\right)^{3} + {\left(1292 \, \cosh\left(x\right)^{15} + 8925 \, \cosh\left(x\right)^{13} + 27300 \, \cosh\left(x\right)^{11} + 50050 \, \cosh\left(x\right)^{9} + 69300 \, \cosh\left(x\right)^{7} + 52920 \, x \cosh\left(x\right)^{5} - 4900 \, \cosh\left(x\right)^{3} - 150 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(1292 \, \cosh\left(x\right)^{15} + 8925 \, \cosh\left(x\right)^{13} + 27300 \, \cosh\left(x\right)^{11} + 50050 \, \cosh\left(x\right)^{9} + 69300 \, \cosh\left(x\right)^{7} + 52920 \, x \cosh\left(x\right)^{5} - 4900 \, \cosh\left(x\right)^{3} - 150 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 150 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 30 \, {\left(323 \, \cosh\left(x\right)^{16} + 2550 \, \cosh\left(x\right)^{14} + 9100 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 34650 \, \cosh\left(x\right)^{8} + 35280 \, x \cosh\left(x\right)^{6} - 4900 \, \cosh\left(x\right)^{4} - 300 \, \cosh\left(x\right)^{2} + {\left(323 \, \cosh\left(x\right)^{16} + 2550 \, \cosh\left(x\right)^{14} + 9100 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 34650 \, \cosh\left(x\right)^{8} + 35280 \, x \cosh\left(x\right)^{6} - 4900 \, \cosh\left(x\right)^{4} - 300 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(4 \, x\right)} + 2 \, {\left(323 \, \cosh\left(x\right)^{16} + 2550 \, \cosh\left(x\right)^{14} + 9100 \, \cosh\left(x\right)^{12} + 20020 \, \cosh\left(x\right)^{10} + 34650 \, \cosh\left(x\right)^{8} + 35280 \, x \cosh\left(x\right)^{6} - 4900 \, \cosh\left(x\right)^{4} - 300 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(2 \, x\right)} - 5\right)} \sinh\left(x\right)^{4} - 150 \, \cosh\left(x\right)^{4} + 120 \, {\left(19 \, \cosh\left(x\right)^{17} + 170 \, \cosh\left(x\right)^{15} + 700 \, \cosh\left(x\right)^{13} + 1820 \, \cosh\left(x\right)^{11} + 3850 \, \cosh\left(x\right)^{9} + 5040 \, x \cosh\left(x\right)^{7} - 980 \, \cosh\left(x\right)^{5} - 100 \, \cosh\left(x\right)^{3} + {\left(19 \, \cosh\left(x\right)^{17} + 170 \, \cosh\left(x\right)^{15} + 700 \, \cosh\left(x\right)^{13} + 1820 \, \cosh\left(x\right)^{11} + 3850 \, \cosh\left(x\right)^{9} + 5040 \, x \cosh\left(x\right)^{7} - 980 \, \cosh\left(x\right)^{5} - 100 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(19 \, \cosh\left(x\right)^{17} + 170 \, \cosh\left(x\right)^{15} + 700 \, \cosh\left(x\right)^{13} + 1820 \, \cosh\left(x\right)^{11} + 3850 \, \cosh\left(x\right)^{9} + 5040 \, x \cosh\left(x\right)^{7} - 980 \, \cosh\left(x\right)^{5} - 100 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(76 \, \cosh\left(x\right)^{18} + 765 \, \cosh\left(x\right)^{16} + 3600 \, \cosh\left(x\right)^{14} + 10920 \, \cosh\left(x\right)^{12} + 27720 \, \cosh\left(x\right)^{10} + 45360 \, x \cosh\left(x\right)^{8} - 11760 \, \cosh\left(x\right)^{6} - 1800 \, \cosh\left(x\right)^{4} - 180 \, \cosh\left(x\right)^{2} + {\left(76 \, \cosh\left(x\right)^{18} + 765 \, \cosh\left(x\right)^{16} + 3600 \, \cosh\left(x\right)^{14} + 10920 \, \cosh\left(x\right)^{12} + 27720 \, \cosh\left(x\right)^{10} + 45360 \, x \cosh\left(x\right)^{8} - 11760 \, \cosh\left(x\right)^{6} - 1800 \, \cosh\left(x\right)^{4} - 180 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(4 \, x\right)} + 2 \, {\left(76 \, \cosh\left(x\right)^{18} + 765 \, \cosh\left(x\right)^{16} + 3600 \, \cosh\left(x\right)^{14} + 10920 \, \cosh\left(x\right)^{12} + 27720 \, \cosh\left(x\right)^{10} + 45360 \, x \cosh\left(x\right)^{8} - 11760 \, \cosh\left(x\right)^{6} - 1800 \, \cosh\left(x\right)^{4} - 180 \, \cosh\left(x\right)^{2} - 5\right)} e^{\left(2 \, x\right)} - 5\right)} \sinh\left(x\right)^{2} - 25 \, \cosh\left(x\right)^{2} + {\left(2 \, \cosh\left(x\right)^{20} + 25 \, \cosh\left(x\right)^{18} + 150 \, \cosh\left(x\right)^{16} + 600 \, \cosh\left(x\right)^{14} + 2100 \, \cosh\left(x\right)^{12} + 5040 \, x \cosh\left(x\right)^{10} - 2100 \, \cosh\left(x\right)^{8} - 600 \, \cosh\left(x\right)^{6} - 150 \, \cosh\left(x\right)^{4} - 25 \, \cosh\left(x\right)^{2} - 2\right)} e^{\left(4 \, x\right)} + 2 \, {\left(2 \, \cosh\left(x\right)^{20} + 25 \, \cosh\left(x\right)^{18} + 150 \, \cosh\left(x\right)^{16} + 600 \, \cosh\left(x\right)^{14} + 2100 \, \cosh\left(x\right)^{12} + 5040 \, x \cosh\left(x\right)^{10} - 2100 \, \cosh\left(x\right)^{8} - 600 \, \cosh\left(x\right)^{6} - 150 \, \cosh\left(x\right)^{4} - 25 \, \cosh\left(x\right)^{2} - 2\right)} e^{\left(2 \, x\right)} + 10 \, {\left(4 \, \cosh\left(x\right)^{19} + 45 \, \cosh\left(x\right)^{17} + 240 \, \cosh\left(x\right)^{15} + 840 \, \cosh\left(x\right)^{13} + 2520 \, \cosh\left(x\right)^{11} + 5040 \, x \cosh\left(x\right)^{9} - 1680 \, \cosh\left(x\right)^{7} - 360 \, \cosh\left(x\right)^{5} - 60 \, \cosh\left(x\right)^{3} + {\left(4 \, \cosh\left(x\right)^{19} + 45 \, \cosh\left(x\right)^{17} + 240 \, \cosh\left(x\right)^{15} + 840 \, \cosh\left(x\right)^{13} + 2520 \, \cosh\left(x\right)^{11} + 5040 \, x \cosh\left(x\right)^{9} - 1680 \, \cosh\left(x\right)^{7} - 360 \, \cosh\left(x\right)^{5} - 60 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} e^{\left(4 \, x\right)} + 2 \, {\left(4 \, \cosh\left(x\right)^{19} + 45 \, \cosh\left(x\right)^{17} + 240 \, \cosh\left(x\right)^{15} + 840 \, \cosh\left(x\right)^{13} + 2520 \, \cosh\left(x\right)^{11} + 5040 \, x \cosh\left(x\right)^{9} - 1680 \, \cosh\left(x\right)^{7} - 360 \, \cosh\left(x\right)^{5} - 60 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} e^{\left(2 \, x\right)} - 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 2\right)} \sqrt{\frac{a}{e^{\left(8 \, x\right)} + 4 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 4 \, e^{\left(2 \, x\right)} + 1}} e^{\left(2 \, x\right)}}{20480 \, {\left(a^{3} \cosh\left(x\right)^{10} e^{\left(2 \, x\right)} + 10 \, a^{3} \cosh\left(x\right)^{9} e^{\left(2 \, x\right)} \sinh\left(x\right) + 45 \, a^{3} \cosh\left(x\right)^{8} e^{\left(2 \, x\right)} \sinh\left(x\right)^{2} + 120 \, a^{3} \cosh\left(x\right)^{7} e^{\left(2 \, x\right)} \sinh\left(x\right)^{3} + 210 \, a^{3} \cosh\left(x\right)^{6} e^{\left(2 \, x\right)} \sinh\left(x\right)^{4} + 252 \, a^{3} \cosh\left(x\right)^{5} e^{\left(2 \, x\right)} \sinh\left(x\right)^{5} + 210 \, a^{3} \cosh\left(x\right)^{4} e^{\left(2 \, x\right)} \sinh\left(x\right)^{6} + 120 \, a^{3} \cosh\left(x\right)^{3} e^{\left(2 \, x\right)} \sinh\left(x\right)^{7} + 45 \, a^{3} \cosh\left(x\right)^{2} e^{\left(2 \, x\right)} \sinh\left(x\right)^{8} + 10 \, a^{3} \cosh\left(x\right) e^{\left(2 \, x\right)} \sinh\left(x\right)^{9} + a^{3} e^{\left(2 \, x\right)} \sinh\left(x\right)^{10}\right)}}"," ",0,"1/20480*(2*(e^(4*x) + 2*e^(2*x) + 1)*sinh(x)^20 + 2*cosh(x)^20 + 40*(cosh(x)*e^(4*x) + 2*cosh(x)*e^(2*x) + cosh(x))*sinh(x)^19 + 5*(76*cosh(x)^2 + (76*cosh(x)^2 + 5)*e^(4*x) + 2*(76*cosh(x)^2 + 5)*e^(2*x) + 5)*sinh(x)^18 + 25*cosh(x)^18 + 30*(76*cosh(x)^3 + (76*cosh(x)^3 + 15*cosh(x))*e^(4*x) + 2*(76*cosh(x)^3 + 15*cosh(x))*e^(2*x) + 15*cosh(x))*sinh(x)^17 + 15*(646*cosh(x)^4 + 255*cosh(x)^2 + (646*cosh(x)^4 + 255*cosh(x)^2 + 10)*e^(4*x) + 2*(646*cosh(x)^4 + 255*cosh(x)^2 + 10)*e^(2*x) + 10)*sinh(x)^16 + 150*cosh(x)^16 + 48*(646*cosh(x)^5 + 425*cosh(x)^3 + (646*cosh(x)^5 + 425*cosh(x)^3 + 50*cosh(x))*e^(4*x) + 2*(646*cosh(x)^5 + 425*cosh(x)^3 + 50*cosh(x))*e^(2*x) + 50*cosh(x))*sinh(x)^15 + 60*(1292*cosh(x)^6 + 1275*cosh(x)^4 + 300*cosh(x)^2 + (1292*cosh(x)^6 + 1275*cosh(x)^4 + 300*cosh(x)^2 + 10)*e^(4*x) + 2*(1292*cosh(x)^6 + 1275*cosh(x)^4 + 300*cosh(x)^2 + 10)*e^(2*x) + 10)*sinh(x)^14 + 600*cosh(x)^14 + 120*(1292*cosh(x)^7 + 1785*cosh(x)^5 + 700*cosh(x)^3 + (1292*cosh(x)^7 + 1785*cosh(x)^5 + 700*cosh(x)^3 + 70*cosh(x))*e^(4*x) + 2*(1292*cosh(x)^7 + 1785*cosh(x)^5 + 700*cosh(x)^3 + 70*cosh(x))*e^(2*x) + 70*cosh(x))*sinh(x)^13 + 60*(4199*cosh(x)^8 + 7735*cosh(x)^6 + 4550*cosh(x)^4 + 910*cosh(x)^2 + (4199*cosh(x)^8 + 7735*cosh(x)^6 + 4550*cosh(x)^4 + 910*cosh(x)^2 + 35)*e^(4*x) + 2*(4199*cosh(x)^8 + 7735*cosh(x)^6 + 4550*cosh(x)^4 + 910*cosh(x)^2 + 35)*e^(2*x) + 35)*sinh(x)^12 + 2100*cosh(x)^12 + 80*(4199*cosh(x)^9 + 9945*cosh(x)^7 + 8190*cosh(x)^5 + 2730*cosh(x)^3 + (4199*cosh(x)^9 + 9945*cosh(x)^7 + 8190*cosh(x)^5 + 2730*cosh(x)^3 + 315*cosh(x))*e^(4*x) + 2*(4199*cosh(x)^9 + 9945*cosh(x)^7 + 8190*cosh(x)^5 + 2730*cosh(x)^3 + 315*cosh(x))*e^(2*x) + 315*cosh(x))*sinh(x)^11 + 5040*x*cosh(x)^10 + 2*(184756*cosh(x)^10 + 546975*cosh(x)^8 + 600600*cosh(x)^6 + 300300*cosh(x)^4 + 69300*cosh(x)^2 + (184756*cosh(x)^10 + 546975*cosh(x)^8 + 600600*cosh(x)^6 + 300300*cosh(x)^4 + 69300*cosh(x)^2 + 2520*x)*e^(4*x) + 2*(184756*cosh(x)^10 + 546975*cosh(x)^8 + 600600*cosh(x)^6 + 300300*cosh(x)^4 + 69300*cosh(x)^2 + 2520*x)*e^(2*x) + 2520*x)*sinh(x)^10 + 20*(16796*cosh(x)^11 + 60775*cosh(x)^9 + 85800*cosh(x)^7 + 60060*cosh(x)^5 + 23100*cosh(x)^3 + 2520*x*cosh(x) + (16796*cosh(x)^11 + 60775*cosh(x)^9 + 85800*cosh(x)^7 + 60060*cosh(x)^5 + 23100*cosh(x)^3 + 2520*x*cosh(x))*e^(4*x) + 2*(16796*cosh(x)^11 + 60775*cosh(x)^9 + 85800*cosh(x)^7 + 60060*cosh(x)^5 + 23100*cosh(x)^3 + 2520*x*cosh(x))*e^(2*x))*sinh(x)^9 + 30*(8398*cosh(x)^12 + 36465*cosh(x)^10 + 64350*cosh(x)^8 + 60060*cosh(x)^6 + 34650*cosh(x)^4 + 7560*x*cosh(x)^2 + (8398*cosh(x)^12 + 36465*cosh(x)^10 + 64350*cosh(x)^8 + 60060*cosh(x)^6 + 34650*cosh(x)^4 + 7560*x*cosh(x)^2 - 70)*e^(4*x) + 2*(8398*cosh(x)^12 + 36465*cosh(x)^10 + 64350*cosh(x)^8 + 60060*cosh(x)^6 + 34650*cosh(x)^4 + 7560*x*cosh(x)^2 - 70)*e^(2*x) - 70)*sinh(x)^8 - 2100*cosh(x)^8 + 240*(646*cosh(x)^13 + 3315*cosh(x)^11 + 7150*cosh(x)^9 + 8580*cosh(x)^7 + 6930*cosh(x)^5 + 2520*x*cosh(x)^3 + (646*cosh(x)^13 + 3315*cosh(x)^11 + 7150*cosh(x)^9 + 8580*cosh(x)^7 + 6930*cosh(x)^5 + 2520*x*cosh(x)^3 - 70*cosh(x))*e^(4*x) + 2*(646*cosh(x)^13 + 3315*cosh(x)^11 + 7150*cosh(x)^9 + 8580*cosh(x)^7 + 6930*cosh(x)^5 + 2520*x*cosh(x)^3 - 70*cosh(x))*e^(2*x) - 70*cosh(x))*sinh(x)^7 + 60*(1292*cosh(x)^14 + 7735*cosh(x)^12 + 20020*cosh(x)^10 + 30030*cosh(x)^8 + 32340*cosh(x)^6 + 17640*x*cosh(x)^4 - 980*cosh(x)^2 + (1292*cosh(x)^14 + 7735*cosh(x)^12 + 20020*cosh(x)^10 + 30030*cosh(x)^8 + 32340*cosh(x)^6 + 17640*x*cosh(x)^4 - 980*cosh(x)^2 - 10)*e^(4*x) + 2*(1292*cosh(x)^14 + 7735*cosh(x)^12 + 20020*cosh(x)^10 + 30030*cosh(x)^8 + 32340*cosh(x)^6 + 17640*x*cosh(x)^4 - 980*cosh(x)^2 - 10)*e^(2*x) - 10)*sinh(x)^6 - 600*cosh(x)^6 + 24*(1292*cosh(x)^15 + 8925*cosh(x)^13 + 27300*cosh(x)^11 + 50050*cosh(x)^9 + 69300*cosh(x)^7 + 52920*x*cosh(x)^5 - 4900*cosh(x)^3 + (1292*cosh(x)^15 + 8925*cosh(x)^13 + 27300*cosh(x)^11 + 50050*cosh(x)^9 + 69300*cosh(x)^7 + 52920*x*cosh(x)^5 - 4900*cosh(x)^3 - 150*cosh(x))*e^(4*x) + 2*(1292*cosh(x)^15 + 8925*cosh(x)^13 + 27300*cosh(x)^11 + 50050*cosh(x)^9 + 69300*cosh(x)^7 + 52920*x*cosh(x)^5 - 4900*cosh(x)^3 - 150*cosh(x))*e^(2*x) - 150*cosh(x))*sinh(x)^5 + 30*(323*cosh(x)^16 + 2550*cosh(x)^14 + 9100*cosh(x)^12 + 20020*cosh(x)^10 + 34650*cosh(x)^8 + 35280*x*cosh(x)^6 - 4900*cosh(x)^4 - 300*cosh(x)^2 + (323*cosh(x)^16 + 2550*cosh(x)^14 + 9100*cosh(x)^12 + 20020*cosh(x)^10 + 34650*cosh(x)^8 + 35280*x*cosh(x)^6 - 4900*cosh(x)^4 - 300*cosh(x)^2 - 5)*e^(4*x) + 2*(323*cosh(x)^16 + 2550*cosh(x)^14 + 9100*cosh(x)^12 + 20020*cosh(x)^10 + 34650*cosh(x)^8 + 35280*x*cosh(x)^6 - 4900*cosh(x)^4 - 300*cosh(x)^2 - 5)*e^(2*x) - 5)*sinh(x)^4 - 150*cosh(x)^4 + 120*(19*cosh(x)^17 + 170*cosh(x)^15 + 700*cosh(x)^13 + 1820*cosh(x)^11 + 3850*cosh(x)^9 + 5040*x*cosh(x)^7 - 980*cosh(x)^5 - 100*cosh(x)^3 + (19*cosh(x)^17 + 170*cosh(x)^15 + 700*cosh(x)^13 + 1820*cosh(x)^11 + 3850*cosh(x)^9 + 5040*x*cosh(x)^7 - 980*cosh(x)^5 - 100*cosh(x)^3 - 5*cosh(x))*e^(4*x) + 2*(19*cosh(x)^17 + 170*cosh(x)^15 + 700*cosh(x)^13 + 1820*cosh(x)^11 + 3850*cosh(x)^9 + 5040*x*cosh(x)^7 - 980*cosh(x)^5 - 100*cosh(x)^3 - 5*cosh(x))*e^(2*x) - 5*cosh(x))*sinh(x)^3 + 5*(76*cosh(x)^18 + 765*cosh(x)^16 + 3600*cosh(x)^14 + 10920*cosh(x)^12 + 27720*cosh(x)^10 + 45360*x*cosh(x)^8 - 11760*cosh(x)^6 - 1800*cosh(x)^4 - 180*cosh(x)^2 + (76*cosh(x)^18 + 765*cosh(x)^16 + 3600*cosh(x)^14 + 10920*cosh(x)^12 + 27720*cosh(x)^10 + 45360*x*cosh(x)^8 - 11760*cosh(x)^6 - 1800*cosh(x)^4 - 180*cosh(x)^2 - 5)*e^(4*x) + 2*(76*cosh(x)^18 + 765*cosh(x)^16 + 3600*cosh(x)^14 + 10920*cosh(x)^12 + 27720*cosh(x)^10 + 45360*x*cosh(x)^8 - 11760*cosh(x)^6 - 1800*cosh(x)^4 - 180*cosh(x)^2 - 5)*e^(2*x) - 5)*sinh(x)^2 - 25*cosh(x)^2 + (2*cosh(x)^20 + 25*cosh(x)^18 + 150*cosh(x)^16 + 600*cosh(x)^14 + 2100*cosh(x)^12 + 5040*x*cosh(x)^10 - 2100*cosh(x)^8 - 600*cosh(x)^6 - 150*cosh(x)^4 - 25*cosh(x)^2 - 2)*e^(4*x) + 2*(2*cosh(x)^20 + 25*cosh(x)^18 + 150*cosh(x)^16 + 600*cosh(x)^14 + 2100*cosh(x)^12 + 5040*x*cosh(x)^10 - 2100*cosh(x)^8 - 600*cosh(x)^6 - 150*cosh(x)^4 - 25*cosh(x)^2 - 2)*e^(2*x) + 10*(4*cosh(x)^19 + 45*cosh(x)^17 + 240*cosh(x)^15 + 840*cosh(x)^13 + 2520*cosh(x)^11 + 5040*x*cosh(x)^9 - 1680*cosh(x)^7 - 360*cosh(x)^5 - 60*cosh(x)^3 + (4*cosh(x)^19 + 45*cosh(x)^17 + 240*cosh(x)^15 + 840*cosh(x)^13 + 2520*cosh(x)^11 + 5040*x*cosh(x)^9 - 1680*cosh(x)^7 - 360*cosh(x)^5 - 60*cosh(x)^3 - 5*cosh(x))*e^(4*x) + 2*(4*cosh(x)^19 + 45*cosh(x)^17 + 240*cosh(x)^15 + 840*cosh(x)^13 + 2520*cosh(x)^11 + 5040*x*cosh(x)^9 - 1680*cosh(x)^7 - 360*cosh(x)^5 - 60*cosh(x)^3 - 5*cosh(x))*e^(2*x) - 5*cosh(x))*sinh(x) - 2)*sqrt(a/(e^(8*x) + 4*e^(6*x) + 6*e^(4*x) + 4*e^(2*x) + 1))*e^(2*x)/(a^3*cosh(x)^10*e^(2*x) + 10*a^3*cosh(x)^9*e^(2*x)*sinh(x) + 45*a^3*cosh(x)^8*e^(2*x)*sinh(x)^2 + 120*a^3*cosh(x)^7*e^(2*x)*sinh(x)^3 + 210*a^3*cosh(x)^6*e^(2*x)*sinh(x)^4 + 252*a^3*cosh(x)^5*e^(2*x)*sinh(x)^5 + 210*a^3*cosh(x)^4*e^(2*x)*sinh(x)^6 + 120*a^3*cosh(x)^3*e^(2*x)*sinh(x)^7 + 45*a^3*cosh(x)^2*e^(2*x)*sinh(x)^8 + 10*a^3*cosh(x)*e^(2*x)*sinh(x)^9 + a^3*e^(2*x)*sinh(x)^10)","B",0
52,1,36,0,0.413102," ","integrate(sinh(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{{\left(3 \, \cosh\left(x\right) - 2\right)} \sinh\left(x\right)^{3} + 3 \, {\left(\cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right) - 3 \, x}{24 \, a}"," ",0,"1/24*((3*cosh(x) - 2)*sinh(x)^3 + 3*(cosh(x)^3 - 2*cosh(x)^2 + 2)*sinh(x) - 3*x)/a","A",0
53,1,30,0,0.381702," ","integrate(sinh(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{3} + 3 \, {\left(\cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} - 3 \, \cosh\left(x\right)^{2} + 3 \, \cosh\left(x\right)}{12 \, a}"," ",0,"1/12*(cosh(x)^3 + 3*(cosh(x) - 1)*sinh(x)^2 - 3*cosh(x)^2 + 3*cosh(x))/a","A",0
54,1,14,0,0.397559," ","integrate(sinh(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(x\right) - 2\right)} \sinh\left(x\right) + x}{2 \, a}"," ",0,"1/2*((cosh(x) - 2)*sinh(x) + x)/a","A",0
55,1,50,0,0.398561," ","integrate(sinh(x)/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{2 \, x \cosh\left(x\right) + \cosh\left(x\right)^{2} - 4 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + 2 \, {\left(x + \cosh\left(x\right)\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1}{2 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)}}"," ",0,"1/2*(2*x*cosh(x) + cosh(x)^2 - 4*(cosh(x) + sinh(x))*log(cosh(x) + sinh(x) + 1) + 2*(x + cosh(x))*sinh(x) + sinh(x)^2 + 1)/(a*cosh(x) + a*sinh(x))","B",0
56,1,103,0,0.391365," ","integrate(csch(x)/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{{\left(\cosh\left(x\right)^{2} + 2 \, {\left(\cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left(\cosh\left(x\right)^{2} + 2 \, {\left(\cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, \cosh\left(x\right) + 2 \, \sinh\left(x\right)}{2 \, {\left(a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a\right)}}"," ",0,"-1/2*((cosh(x)^2 + 2*(cosh(x) + 1)*sinh(x) + sinh(x)^2 + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) + 1) - (cosh(x)^2 + 2*(cosh(x) + 1)*sinh(x) + sinh(x)^2 + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) - 1) + 2*cosh(x) + 2*sinh(x))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*a*cosh(x) + 2*(a*cosh(x) + a)*sinh(x) + a)","B",0
57,1,71,0,0.377159," ","integrate(csch(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{4 \, {\left(2 \, \cosh\left(x\right) + \sinh\left(x\right) + 1\right)}}{3 \, {\left(a \cosh\left(x\right)^{3} + a \sinh\left(x\right)^{3} + 2 \, a \cosh\left(x\right)^{2} + {\left(3 \, a \cosh\left(x\right) + 2 \, a\right)} \sinh\left(x\right)^{2} - a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} + 4 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right) - 2 \, a\right)}}"," ",0,"-4/3*(2*cosh(x) + sinh(x) + 1)/(a*cosh(x)^3 + a*sinh(x)^3 + 2*a*cosh(x)^2 + (3*a*cosh(x) + 2*a)*sinh(x)^2 - a*cosh(x) + (3*a*cosh(x)^2 + 4*a*cosh(x) + a)*sinh(x) - 2*a)","B",0
58,1,630,0,0.397950," ","integrate(csch(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, \cosh\left(x\right)^{5} + 2 \, {\left(5 \, \cosh\left(x\right) + 2\right)} \sinh\left(x\right)^{4} + 2 \, \sinh\left(x\right)^{5} + 4 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) + 5\right)} \sinh\left(x\right)^{3} + 20 \, \cosh\left(x\right)^{3} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 6 \, \cosh\left(x\right)^{2} + 15 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} - {\left(\cosh\left(x\right)^{6} + 2 \, {\left(3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 2 \, \cosh\left(x\right)^{5} + {\left(15 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{4} - \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{3} - 4 \, \cosh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 20 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - 12 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + {\left(\cosh\left(x\right)^{6} + 2 \, {\left(3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 2 \, \cosh\left(x\right)^{5} + {\left(15 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{4} - \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{3} - 4 \, \cosh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 20 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - 12 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(5 \, \cosh\left(x\right)^{4} + 8 \, \cosh\left(x\right)^{3} + 30 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right)}{8 \, {\left(a \cosh\left(x\right)^{6} + a \sinh\left(x\right)^{6} + 2 \, a \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{5} - a \cosh\left(x\right)^{4} + {\left(15 \, a \cosh\left(x\right)^{2} + 10 \, a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{4} - 4 \, a \cosh\left(x\right)^{3} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} + 5 \, a \cosh\left(x\right)^{2} - a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{3} - a \cosh\left(x\right)^{2} + {\left(15 \, a \cosh\left(x\right)^{4} + 20 \, a \cosh\left(x\right)^{3} - 6 \, a \cosh\left(x\right)^{2} - 12 \, a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + 2 \, {\left(3 \, a \cosh\left(x\right)^{5} + 5 \, a \cosh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{3} - 6 \, a \cosh\left(x\right)^{2} - a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a\right)}}"," ",0,"-1/8*(2*cosh(x)^5 + 2*(5*cosh(x) + 2)*sinh(x)^4 + 2*sinh(x)^5 + 4*cosh(x)^4 + 4*(5*cosh(x)^2 + 4*cosh(x) + 5)*sinh(x)^3 + 20*cosh(x)^3 + 4*(5*cosh(x)^3 + 6*cosh(x)^2 + 15*cosh(x) + 1)*sinh(x)^2 + 4*cosh(x)^2 - (cosh(x)^6 + 2*(3*cosh(x) + 1)*sinh(x)^5 + sinh(x)^6 + 2*cosh(x)^5 + (15*cosh(x)^2 + 10*cosh(x) - 1)*sinh(x)^4 - cosh(x)^4 + 4*(5*cosh(x)^3 + 5*cosh(x)^2 - cosh(x) - 1)*sinh(x)^3 - 4*cosh(x)^3 + (15*cosh(x)^4 + 20*cosh(x)^3 - 6*cosh(x)^2 - 12*cosh(x) - 1)*sinh(x)^2 - cosh(x)^2 + 2*(3*cosh(x)^5 + 5*cosh(x)^4 - 2*cosh(x)^3 - 6*cosh(x)^2 - cosh(x) + 1)*sinh(x) + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) + 1) + (cosh(x)^6 + 2*(3*cosh(x) + 1)*sinh(x)^5 + sinh(x)^6 + 2*cosh(x)^5 + (15*cosh(x)^2 + 10*cosh(x) - 1)*sinh(x)^4 - cosh(x)^4 + 4*(5*cosh(x)^3 + 5*cosh(x)^2 - cosh(x) - 1)*sinh(x)^3 - 4*cosh(x)^3 + (15*cosh(x)^4 + 20*cosh(x)^3 - 6*cosh(x)^2 - 12*cosh(x) - 1)*sinh(x)^2 - cosh(x)^2 + 2*(3*cosh(x)^5 + 5*cosh(x)^4 - 2*cosh(x)^3 - 6*cosh(x)^2 - cosh(x) + 1)*sinh(x) + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) - 1) + 2*(5*cosh(x)^4 + 8*cosh(x)^3 + 30*cosh(x)^2 + 4*cosh(x) + 1)*sinh(x) + 2*cosh(x))/(a*cosh(x)^6 + a*sinh(x)^6 + 2*a*cosh(x)^5 + 2*(3*a*cosh(x) + a)*sinh(x)^5 - a*cosh(x)^4 + (15*a*cosh(x)^2 + 10*a*cosh(x) - a)*sinh(x)^4 - 4*a*cosh(x)^3 + 4*(5*a*cosh(x)^3 + 5*a*cosh(x)^2 - a*cosh(x) - a)*sinh(x)^3 - a*cosh(x)^2 + (15*a*cosh(x)^4 + 20*a*cosh(x)^3 - 6*a*cosh(x)^2 - 12*a*cosh(x) - a)*sinh(x)^2 + 2*a*cosh(x) + 2*(3*a*cosh(x)^5 + 5*a*cosh(x)^4 - 2*a*cosh(x)^3 - 6*a*cosh(x)^2 - a*cosh(x) + a)*sinh(x) + a)","B",0
59,1,219,0,0.386478," ","integrate(csch(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{8 \, {\left(7 \, \cosh\left(x\right)^{2} + 4 \, {\left(4 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 7 \, \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)}}{15 \, {\left(a \cosh\left(x\right)^{6} + a \sinh\left(x\right)^{6} + 2 \, a \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{4} + {\left(15 \, a \cosh\left(x\right)^{2} + 10 \, a \cosh\left(x\right) - 2 \, a\right)} \sinh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{3} + 2 \, {\left(10 \, a \cosh\left(x\right)^{3} + 10 \, a \cosh\left(x\right)^{2} - 4 \, a \cosh\left(x\right) - 3 \, a\right)} \sinh\left(x\right)^{3} - a \cosh\left(x\right)^{2} + {\left(15 \, a \cosh\left(x\right)^{4} + 20 \, a \cosh\left(x\right)^{3} - 12 \, a \cosh\left(x\right)^{2} - 18 \, a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{2} + 4 \, a \cosh\left(x\right) + 2 \, {\left(3 \, a \cosh\left(x\right)^{5} + 5 \, a \cosh\left(x\right)^{4} - 4 \, a \cosh\left(x\right)^{3} - 9 \, a \cosh\left(x\right)^{2} + a \cosh\left(x\right) + 4 \, a\right)} \sinh\left(x\right) + 2 \, a\right)}}"," ",0,"-8/15*(7*cosh(x)^2 + 4*(4*cosh(x) + 1)*sinh(x) + 7*sinh(x)^2 + 2*cosh(x) + 1)/(a*cosh(x)^6 + a*sinh(x)^6 + 2*a*cosh(x)^5 + 2*(3*a*cosh(x) + a)*sinh(x)^5 - 2*a*cosh(x)^4 + (15*a*cosh(x)^2 + 10*a*cosh(x) - 2*a)*sinh(x)^4 - 6*a*cosh(x)^3 + 2*(10*a*cosh(x)^3 + 10*a*cosh(x)^2 - 4*a*cosh(x) - 3*a)*sinh(x)^3 - a*cosh(x)^2 + (15*a*cosh(x)^4 + 20*a*cosh(x)^3 - 12*a*cosh(x)^2 - 18*a*cosh(x) - a)*sinh(x)^2 + 4*a*cosh(x) + 2*(3*a*cosh(x)^5 + 5*a*cosh(x)^4 - 4*a*cosh(x)^3 - 9*a*cosh(x)^2 + a*cosh(x) + 4*a)*sinh(x) + 2*a)","B",0
60,1,1812,0,0.445492," ","integrate(sinh(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{3 \, a^{4} \cosh\left(x\right)^{8} + 3 \, a^{4} \sinh\left(x\right)^{8} - 8 \, a^{3} b \cosh\left(x\right)^{7} + 8 \, {\left(3 \, a^{4} \cosh\left(x\right) - a^{3} b\right)} \sinh\left(x\right)^{7} - 24 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(21 \, a^{4} \cosh\left(x\right)^{2} - 14 \, a^{3} b \cosh\left(x\right) - 6 \, a^{4} + 6 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 24 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{4} + 24 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 24 \, {\left(7 \, a^{4} \cosh\left(x\right)^{3} - 7 \, a^{3} b \cosh\left(x\right)^{2} + 5 \, a^{3} b - 4 \, a b^{3} - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 8 \, a^{3} b \cosh\left(x\right) + 2 \, {\left(105 \, a^{4} \cosh\left(x\right)^{4} - 140 \, a^{3} b \cosh\left(x\right)^{3} - 180 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x + 60 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 3 \, a^{4} - 24 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 8 \, {\left(21 \, a^{4} \cosh\left(x\right)^{5} - 35 \, a^{3} b \cosh\left(x\right)^{4} - 15 \, a^{3} b + 12 \, a b^{3} - 60 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right) + 30 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{3} + 24 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(7 \, a^{4} \cosh\left(x\right)^{6} - 14 \, a^{3} b \cosh\left(x\right)^{5} - 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, a^{4} - 2 \, a^{2} b^{2} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{2} + 20 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{3} - 6 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 192 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 8 \, {\left(3 \, a^{4} \cosh\left(x\right)^{7} - 7 \, a^{3} b \cosh\left(x\right)^{6} - 18 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{3} + 15 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} b - 9 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{192 \, {\left(a^{5} \cosh\left(x\right)^{4} + 4 \, a^{5} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, a^{5} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{5} \sinh\left(x\right)^{4}\right)}}, \frac{3 \, a^{4} \cosh\left(x\right)^{8} + 3 \, a^{4} \sinh\left(x\right)^{8} - 8 \, a^{3} b \cosh\left(x\right)^{7} + 8 \, {\left(3 \, a^{4} \cosh\left(x\right) - a^{3} b\right)} \sinh\left(x\right)^{7} - 24 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(21 \, a^{4} \cosh\left(x\right)^{2} - 14 \, a^{3} b \cosh\left(x\right) - 6 \, a^{4} + 6 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 24 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{4} + 24 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 24 \, {\left(7 \, a^{4} \cosh\left(x\right)^{3} - 7 \, a^{3} b \cosh\left(x\right)^{2} + 5 \, a^{3} b - 4 \, a b^{3} - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 8 \, a^{3} b \cosh\left(x\right) + 2 \, {\left(105 \, a^{4} \cosh\left(x\right)^{4} - 140 \, a^{3} b \cosh\left(x\right)^{3} - 180 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x + 60 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 3 \, a^{4} - 24 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 8 \, {\left(21 \, a^{4} \cosh\left(x\right)^{5} - 35 \, a^{3} b \cosh\left(x\right)^{4} - 15 \, a^{3} b + 12 \, a b^{3} - 60 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right) + 30 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{3} + 24 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(7 \, a^{4} \cosh\left(x\right)^{6} - 14 \, a^{3} b \cosh\left(x\right)^{5} - 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, a^{4} - 2 \, a^{2} b^{2} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{2} + 20 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{3} - 6 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 384 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 8 \, {\left(3 \, a^{4} \cosh\left(x\right)^{7} - 7 \, a^{3} b \cosh\left(x\right)^{6} - 18 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} x \cosh\left(x\right)^{3} + 15 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} b - 9 \, {\left(5 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{192 \, {\left(a^{5} \cosh\left(x\right)^{4} + 4 \, a^{5} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, a^{5} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, a^{5} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{5} \sinh\left(x\right)^{4}\right)}}\right]"," ",0,"[1/192*(3*a^4*cosh(x)^8 + 3*a^4*sinh(x)^8 - 8*a^3*b*cosh(x)^7 + 8*(3*a^4*cosh(x) - a^3*b)*sinh(x)^7 - 24*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(21*a^4*cosh(x)^2 - 14*a^3*b*cosh(x) - 6*a^4 + 6*a^2*b^2)*sinh(x)^6 + 24*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^4 + 24*(5*a^3*b - 4*a*b^3)*cosh(x)^5 + 24*(7*a^4*cosh(x)^3 - 7*a^3*b*cosh(x)^2 + 5*a^3*b - 4*a*b^3 - 6*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 8*a^3*b*cosh(x) + 2*(105*a^4*cosh(x)^4 - 140*a^3*b*cosh(x)^3 - 180*(a^4 - a^2*b^2)*cosh(x)^2 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x + 60*(5*a^3*b - 4*a*b^3)*cosh(x))*sinh(x)^4 - 3*a^4 - 24*(5*a^3*b - 4*a*b^3)*cosh(x)^3 + 8*(21*a^4*cosh(x)^5 - 35*a^3*b*cosh(x)^4 - 15*a^3*b + 12*a*b^3 - 60*(a^4 - a^2*b^2)*cosh(x)^3 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x) + 30*(5*a^3*b - 4*a*b^3)*cosh(x)^2)*sinh(x)^3 + 24*(a^4 - a^2*b^2)*cosh(x)^2 + 12*(7*a^4*cosh(x)^6 - 14*a^3*b*cosh(x)^5 - 30*(a^4 - a^2*b^2)*cosh(x)^4 + 2*a^4 - 2*a^2*b^2 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^2 + 20*(5*a^3*b - 4*a*b^3)*cosh(x)^3 - 6*(5*a^3*b - 4*a*b^3)*cosh(x))*sinh(x)^2 - 192*((a^2*b - b^3)*cosh(x)^4 + 4*(a^2*b - b^3)*cosh(x)^3*sinh(x) + 6*(a^2*b - b^3)*cosh(x)^2*sinh(x)^2 + 4*(a^2*b - b^3)*cosh(x)*sinh(x)^3 + (a^2*b - b^3)*sinh(x)^4)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 8*(3*a^4*cosh(x)^7 - 7*a^3*b*cosh(x)^6 - 18*(a^4 - a^2*b^2)*cosh(x)^5 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^3 + 15*(5*a^3*b - 4*a*b^3)*cosh(x)^4 + a^3*b - 9*(5*a^3*b - 4*a*b^3)*cosh(x)^2 + 6*(a^4 - a^2*b^2)*cosh(x))*sinh(x))/(a^5*cosh(x)^4 + 4*a^5*cosh(x)^3*sinh(x) + 6*a^5*cosh(x)^2*sinh(x)^2 + 4*a^5*cosh(x)*sinh(x)^3 + a^5*sinh(x)^4), 1/192*(3*a^4*cosh(x)^8 + 3*a^4*sinh(x)^8 - 8*a^3*b*cosh(x)^7 + 8*(3*a^4*cosh(x) - a^3*b)*sinh(x)^7 - 24*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(21*a^4*cosh(x)^2 - 14*a^3*b*cosh(x) - 6*a^4 + 6*a^2*b^2)*sinh(x)^6 + 24*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^4 + 24*(5*a^3*b - 4*a*b^3)*cosh(x)^5 + 24*(7*a^4*cosh(x)^3 - 7*a^3*b*cosh(x)^2 + 5*a^3*b - 4*a*b^3 - 6*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 8*a^3*b*cosh(x) + 2*(105*a^4*cosh(x)^4 - 140*a^3*b*cosh(x)^3 - 180*(a^4 - a^2*b^2)*cosh(x)^2 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x + 60*(5*a^3*b - 4*a*b^3)*cosh(x))*sinh(x)^4 - 3*a^4 - 24*(5*a^3*b - 4*a*b^3)*cosh(x)^3 + 8*(21*a^4*cosh(x)^5 - 35*a^3*b*cosh(x)^4 - 15*a^3*b + 12*a*b^3 - 60*(a^4 - a^2*b^2)*cosh(x)^3 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x) + 30*(5*a^3*b - 4*a*b^3)*cosh(x)^2)*sinh(x)^3 + 24*(a^4 - a^2*b^2)*cosh(x)^2 + 12*(7*a^4*cosh(x)^6 - 14*a^3*b*cosh(x)^5 - 30*(a^4 - a^2*b^2)*cosh(x)^4 + 2*a^4 - 2*a^2*b^2 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^2 + 20*(5*a^3*b - 4*a*b^3)*cosh(x)^3 - 6*(5*a^3*b - 4*a*b^3)*cosh(x))*sinh(x)^2 + 384*((a^2*b - b^3)*cosh(x)^4 + 4*(a^2*b - b^3)*cosh(x)^3*sinh(x) + 6*(a^2*b - b^3)*cosh(x)^2*sinh(x)^2 + 4*(a^2*b - b^3)*cosh(x)*sinh(x)^3 + (a^2*b - b^3)*sinh(x)^4)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 8*(3*a^4*cosh(x)^7 - 7*a^3*b*cosh(x)^6 - 18*(a^4 - a^2*b^2)*cosh(x)^5 + 12*(3*a^4 - 12*a^2*b^2 + 8*b^4)*x*cosh(x)^3 + 15*(5*a^3*b - 4*a*b^3)*cosh(x)^4 + a^3*b - 9*(5*a^3*b - 4*a*b^3)*cosh(x)^2 + 6*(a^4 - a^2*b^2)*cosh(x))*sinh(x))/(a^5*cosh(x)^4 + 4*a^5*cosh(x)^3*sinh(x) + 6*a^5*cosh(x)^2*sinh(x)^2 + 4*a^5*cosh(x)*sinh(x)^3 + a^5*sinh(x)^4)]","B",0
61,1,490,0,0.405679," ","integrate(sinh(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","\frac{a^{3} \cosh\left(x\right)^{6} + a^{3} \sinh\left(x\right)^{6} - 3 \, a^{2} b \cosh\left(x\right)^{5} + 3 \, {\left(2 \, a^{3} \cosh\left(x\right) - a^{2} b\right)} \sinh\left(x\right)^{5} - 24 \, {\left(a^{2} b - b^{3}\right)} x \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{3} \cosh\left(x\right)^{2} - 5 \, a^{2} b \cosh\left(x\right) - 3 \, a^{3} + 4 \, a b^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a^{2} b \cosh\left(x\right) + 2 \, {\left(10 \, a^{3} \cosh\left(x\right)^{3} - 15 \, a^{2} b \cosh\left(x\right)^{2} - 12 \, {\left(a^{2} b - b^{3}\right)} x - 6 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} - 3 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a^{3} \cosh\left(x\right)^{4} - 10 \, a^{2} b \cosh\left(x\right)^{3} - 3 \, a^{3} + 4 \, a b^{2} - 24 \, {\left(a^{2} b - b^{3}\right)} x \cosh\left(x\right) - 6 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 24 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)^{3}\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 3 \, {\left(2 \, a^{3} \cosh\left(x\right)^{5} - 5 \, a^{2} b \cosh\left(x\right)^{4} - 24 \, {\left(a^{2} b - b^{3}\right)} x \cosh\left(x\right)^{2} - 4 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)^{3} - a^{2} b - 2 \, {\left(3 \, a^{3} - 4 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left(a^{4} \cosh\left(x\right)^{3} + 3 \, a^{4} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{4} \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{4} \sinh\left(x\right)^{3}\right)}}"," ",0,"1/24*(a^3*cosh(x)^6 + a^3*sinh(x)^6 - 3*a^2*b*cosh(x)^5 + 3*(2*a^3*cosh(x) - a^2*b)*sinh(x)^5 - 24*(a^2*b - b^3)*x*cosh(x)^3 - 3*(3*a^3 - 4*a*b^2)*cosh(x)^4 + 3*(5*a^3*cosh(x)^2 - 5*a^2*b*cosh(x) - 3*a^3 + 4*a*b^2)*sinh(x)^4 - 3*a^2*b*cosh(x) + 2*(10*a^3*cosh(x)^3 - 15*a^2*b*cosh(x)^2 - 12*(a^2*b - b^3)*x - 6*(3*a^3 - 4*a*b^2)*cosh(x))*sinh(x)^3 + a^3 - 3*(3*a^3 - 4*a*b^2)*cosh(x)^2 + 3*(5*a^3*cosh(x)^4 - 10*a^2*b*cosh(x)^3 - 3*a^3 + 4*a*b^2 - 24*(a^2*b - b^3)*x*cosh(x) - 6*(3*a^3 - 4*a*b^2)*cosh(x)^2)*sinh(x)^2 + 24*((a^2*b - b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x)^2*sinh(x) + 3*(a^2*b - b^3)*cosh(x)*sinh(x)^2 + (a^2*b - b^3)*sinh(x)^3)*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) + 3*(2*a^3*cosh(x)^5 - 5*a^2*b*cosh(x)^4 - 24*(a^2*b - b^3)*x*cosh(x)^2 - 4*(3*a^3 - 4*a*b^2)*cosh(x)^3 - a^2*b - 2*(3*a^3 - 4*a*b^2)*cosh(x))*sinh(x))/(a^4*cosh(x)^3 + 3*a^4*cosh(x)^2*sinh(x) + 3*a^4*cosh(x)*sinh(x)^2 + a^4*sinh(x)^3)","B",0
62,1,536,0,0.431870," ","integrate(sinh(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{a^{2} \cosh\left(x\right)^{4} + a^{2} \sinh\left(x\right)^{4} - 4 \, a b \cosh\left(x\right)^{3} - 4 \, {\left(a^{2} - 2 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 4 \, {\left(a^{2} \cosh\left(x\right) - a b\right)} \sinh\left(x\right)^{3} + 4 \, a b \cosh\left(x\right) + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - 6 \, a b \cosh\left(x\right) - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) - a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - 3 \, a b \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} x \cosh\left(x\right) + a b\right)} \sinh\left(x\right)}{8 \, {\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}\right)}}, \frac{a^{2} \cosh\left(x\right)^{4} + a^{2} \sinh\left(x\right)^{4} - 4 \, a b \cosh\left(x\right)^{3} - 4 \, {\left(a^{2} - 2 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 4 \, {\left(a^{2} \cosh\left(x\right) - a b\right)} \sinh\left(x\right)^{3} + 4 \, a b \cosh\left(x\right) + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - 6 \, a b \cosh\left(x\right) - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{2} - 16 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) - a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - 3 \, a b \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} x \cosh\left(x\right) + a b\right)} \sinh\left(x\right)}{8 \, {\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}\right)}}\right]"," ",0,"[1/8*(a^2*cosh(x)^4 + a^2*sinh(x)^4 - 4*a*b*cosh(x)^3 - 4*(a^2 - 2*b^2)*x*cosh(x)^2 + 4*(a^2*cosh(x) - a*b)*sinh(x)^3 + 4*a*b*cosh(x) + 2*(3*a^2*cosh(x)^2 - 6*a*b*cosh(x) - 2*(a^2 - 2*b^2)*x)*sinh(x)^2 + 8*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) - a^2 + 4*(a^2*cosh(x)^3 - 3*a*b*cosh(x)^2 - 2*(a^2 - 2*b^2)*x*cosh(x) + a*b)*sinh(x))/(a^3*cosh(x)^2 + 2*a^3*cosh(x)*sinh(x) + a^3*sinh(x)^2), 1/8*(a^2*cosh(x)^4 + a^2*sinh(x)^4 - 4*a*b*cosh(x)^3 - 4*(a^2 - 2*b^2)*x*cosh(x)^2 + 4*(a^2*cosh(x) - a*b)*sinh(x)^3 + 4*a*b*cosh(x) + 2*(3*a^2*cosh(x)^2 - 6*a*b*cosh(x) - 2*(a^2 - 2*b^2)*x)*sinh(x)^2 - 16*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) - a^2 + 4*(a^2*cosh(x)^3 - 3*a*b*cosh(x)^2 - 2*(a^2 - 2*b^2)*x*cosh(x) + a*b)*sinh(x))/(a^3*cosh(x)^2 + 2*a^3*cosh(x)*sinh(x) + a^3*sinh(x)^2)]","B",0
63,1,78,0,0.398568," ","integrate(sinh(x)/(a+b*sech(x)),x, algorithm=""fricas"")","\frac{2 \, b x \cosh\left(x\right) + a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} - 2 \, {\left(b \cosh\left(x\right) + b \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(b x + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a}{2 \, {\left(a^{2} \cosh\left(x\right) + a^{2} \sinh\left(x\right)\right)}}"," ",0,"1/2*(2*b*x*cosh(x) + a*cosh(x)^2 + a*sinh(x)^2 - 2*(b*cosh(x) + b*sinh(x))*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) + 2*(b*x + a*cosh(x))*sinh(x) + a)/(a^2*cosh(x) + a^2*sinh(x))","B",0
64,1,58,0,0.408038," ","integrate(csch(x)/(a+b*sech(x)),x, algorithm=""fricas"")","\frac{b \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(a + b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + {\left(a - b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)}{a^{2} - b^{2}}"," ",0,"(b*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - (a + b)*log(cosh(x) + sinh(x) + 1) + (a - b)*log(cosh(x) + sinh(x) - 1))/(a^2 - b^2)","A",0
65,1,452,0,0.419854," ","integrate(csch(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{3} - 2 \, a b^{2} - {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) - 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) - 2 \, {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\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}}, \frac{2 \, {\left(a^{3} - a b^{2} + {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} - a b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) - {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right) - {\left(a^{2} b - b^{3}\right)} \sinh\left(x\right)\right)}}{a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\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,"[(2*a^3 - 2*a*b^2 - (a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) - 2*(a^2*b - b^3)*cosh(x) - 2*(a^2*b - b^3)*sinh(x))/(a^4 - 2*a^2*b^2 + b^4 - (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), 2*(a^3 - a*b^2 + (a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - a*b)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) - (a^2*b - b^3)*cosh(x) - (a^2*b - b^3)*sinh(x))/(a^4 - 2*a^2*b^2 + b^4 - (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
66,1,828,0,0.448564," ","integrate(csch(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a^{2} b - 2 \, b^{3} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right) + 2 \, {\left(a^{2} b \cosh\left(x\right)^{4} + 4 \, a^{2} b \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} b \sinh\left(x\right)^{4} - 2 \, a^{2} b \cosh\left(x\right)^{2} + a^{2} b + 2 \, {\left(3 \, a^{2} b \cosh\left(x\right)^{2} - a^{2} b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a^{2} b \cosh\left(x\right)^{3} - a^{2} b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} + 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + {\left({\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + a^{3} - 2 \, a^{2} b + a b^{2} - 2 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2} - 3 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(a^{3} - a b^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\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} - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/2*(2*(a^3 - a*b^2)*cosh(x)^3 + 2*(a^3 - a*b^2)*sinh(x)^3 - 4*(a^2*b - b^3)*cosh(x)^2 - 2*(2*a^2*b - 2*b^3 - 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^2 + 2*(a^3 - a*b^2)*cosh(x) + 2*(a^2*b*cosh(x)^4 + 4*a^2*b*cosh(x)*sinh(x)^3 + a^2*b*sinh(x)^4 - 2*a^2*b*cosh(x)^2 + a^2*b + 2*(3*a^2*b*cosh(x)^2 - a^2*b)*sinh(x)^2 + 4*(a^2*b*cosh(x)^3 - a^2*b*cosh(x))*sinh(x))*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - ((a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 + 2*a^2*b + a*b^2 - 2*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 + 2*a^2*b + a*b^2 - 3*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 2*a^2*b + a*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) + 1) + ((a^3 - 2*a^2*b + a*b^2)*cosh(x)^4 + 4*(a^3 - 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + (a^3 - 2*a^2*b + a*b^2)*sinh(x)^4 + a^3 - 2*a^2*b + a*b^2 - 2*(a^3 - 2*a^2*b + a*b^2)*cosh(x)^2 - 2*(a^3 - 2*a^2*b + a*b^2 - 3*(a^3 - 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 - 2*a^2*b + a*b^2)*cosh(x)^3 - (a^3 - 2*a^2*b + a*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) - 1) + 2*(a^3 - a*b^2 + 3*(a^3 - a*b^2)*cosh(x)^2 - 4*(a^2*b - b^3)*cosh(x))*sinh(x))/((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 4*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x)^3 + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 - 2*(a^4 - 2*a^2*b^2 + b^4 - 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 - (a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x))","B",0
67,1,2340,0,0.452311," ","integrate(csch(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sinh\left(x\right)^{5} - 4 \, a^{5} + 2 \, a^{3} b^{2} + 2 \, a b^{4} - 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{3} b^{2} - a b^{4} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 4 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)^{3} - 4 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5} - 15 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 12 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(a^{5} - a^{3} b^{2} + 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} - {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 3 \, {\left(a^{3} b \cosh\left(x\right)^{6} + 6 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{3} b \sinh\left(x\right)^{6} - 3 \, a^{3} b \cosh\left(x\right)^{4} + 3 \, a^{3} b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{2} - a^{3} b\right)} \sinh\left(x\right)^{4} - a^{3} b + 4 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{3} - 3 \, a^{3} b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{4} - 6 \, a^{3} b \cosh\left(x\right)^{2} + a^{3} b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a^{3} b \cosh\left(x\right)^{5} - 2 \, a^{3} b \cosh\left(x\right)^{3} + a^{3} b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right) + 6 \, {\left(a^{4} b - a^{2} b^{3} + 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{6} - a^{6} + 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} - 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\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)\right)} \sinh\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} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sinh\left(x\right)^{5} - 2 \, a^{5} + a^{3} b^{2} + a b^{4} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{3} b^{2} - a b^{4} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 2 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5} - 15 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 6 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, {\left(a^{5} - a^{3} b^{2} + 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} - {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 3 \, {\left(a^{3} b \cosh\left(x\right)^{6} + 6 \, a^{3} b \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{3} b \sinh\left(x\right)^{6} - 3 \, a^{3} b \cosh\left(x\right)^{4} + 3 \, a^{3} b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{2} - a^{3} b\right)} \sinh\left(x\right)^{4} - a^{3} b + 4 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{3} - 3 \, a^{3} b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a^{3} b \cosh\left(x\right)^{4} - 6 \, a^{3} b \cosh\left(x\right)^{2} + a^{3} b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a^{3} b \cosh\left(x\right)^{5} - 2 \, a^{3} b \cosh\left(x\right)^{3} + a^{3} b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right) + 3 \, {\left(a^{4} b - a^{2} b^{3} + 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}{3 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{6} - a^{6} + 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} - 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\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)\right)} \sinh\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} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/3*(6*(a^4*b - a^2*b^3)*cosh(x)^5 + 6*(a^4*b - a^2*b^3)*sinh(x)^5 - 4*a^5 + 2*a^3*b^2 + 2*a*b^4 - 6*(a^3*b^2 - a*b^4)*cosh(x)^4 - 6*(a^3*b^2 - a*b^4 - 5*(a^4*b - a^2*b^3)*cosh(x))*sinh(x)^4 - 4*(5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x)^3 - 4*(5*a^4*b - 7*a^2*b^3 + 2*b^5 - 15*(a^4*b - a^2*b^3)*cosh(x)^2 + 6*(a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^3 + 12*(a^5 - a^3*b^2)*cosh(x)^2 + 12*(a^5 - a^3*b^2 + 5*(a^4*b - a^2*b^3)*cosh(x)^3 - 3*(a^3*b^2 - a*b^4)*cosh(x)^2 - (5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x))*sinh(x)^2 + 3*(a^3*b*cosh(x)^6 + 6*a^3*b*cosh(x)*sinh(x)^5 + a^3*b*sinh(x)^6 - 3*a^3*b*cosh(x)^4 + 3*a^3*b*cosh(x)^2 + 3*(5*a^3*b*cosh(x)^2 - a^3*b)*sinh(x)^4 - a^3*b + 4*(5*a^3*b*cosh(x)^3 - 3*a^3*b*cosh(x))*sinh(x)^3 + 3*(5*a^3*b*cosh(x)^4 - 6*a^3*b*cosh(x)^2 + a^3*b)*sinh(x)^2 + 6*(a^3*b*cosh(x)^5 - 2*a^3*b*cosh(x)^3 + a^3*b*cosh(x))*sinh(x))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 6*(a^4*b - a^2*b^3)*cosh(x) + 6*(a^4*b - a^2*b^3 + 5*(a^4*b - a^2*b^3)*cosh(x)^4 - 4*(a^3*b^2 - a*b^4)*cosh(x)^3 - 2*(5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x)^2 + 4*(a^5 - a^3*b^2)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^6 + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^5 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^6 - a^6 + 3*a^4*b^2 - 3*a^2*b^4 + b^6 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^4 + 4*(5*(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))*sinh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 - 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^2 + 6*((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^5 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x)), -2/3*(3*(a^4*b - a^2*b^3)*cosh(x)^5 + 3*(a^4*b - a^2*b^3)*sinh(x)^5 - 2*a^5 + a^3*b^2 + a*b^4 - 3*(a^3*b^2 - a*b^4)*cosh(x)^4 - 3*(a^3*b^2 - a*b^4 - 5*(a^4*b - a^2*b^3)*cosh(x))*sinh(x)^4 - 2*(5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x)^3 - 2*(5*a^4*b - 7*a^2*b^3 + 2*b^5 - 15*(a^4*b - a^2*b^3)*cosh(x)^2 + 6*(a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^3 + 6*(a^5 - a^3*b^2)*cosh(x)^2 + 6*(a^5 - a^3*b^2 + 5*(a^4*b - a^2*b^3)*cosh(x)^3 - 3*(a^3*b^2 - a*b^4)*cosh(x)^2 - (5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x))*sinh(x)^2 - 3*(a^3*b*cosh(x)^6 + 6*a^3*b*cosh(x)*sinh(x)^5 + a^3*b*sinh(x)^6 - 3*a^3*b*cosh(x)^4 + 3*a^3*b*cosh(x)^2 + 3*(5*a^3*b*cosh(x)^2 - a^3*b)*sinh(x)^4 - a^3*b + 4*(5*a^3*b*cosh(x)^3 - 3*a^3*b*cosh(x))*sinh(x)^3 + 3*(5*a^3*b*cosh(x)^4 - 6*a^3*b*cosh(x)^2 + a^3*b)*sinh(x)^2 + 6*(a^3*b*cosh(x)^5 - 2*a^3*b*cosh(x)^3 + a^3*b*cosh(x))*sinh(x))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 3*(a^4*b - a^2*b^3)*cosh(x) + 3*(a^4*b - a^2*b^3 + 5*(a^4*b - a^2*b^3)*cosh(x)^4 - 4*(a^3*b^2 - a*b^4)*cosh(x)^3 - 2*(5*a^4*b - 7*a^2*b^3 + 2*b^5)*cosh(x)^2 + 4*(a^5 - a^3*b^2)*cosh(x))*sinh(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^6 + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^5 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^6 - a^6 + 3*a^4*b^2 - 3*a^2*b^4 + b^6 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^4 + 4*(5*(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))*sinh(x)^3 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 - 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^2 + 6*((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^5 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x))]","B",0
68,1,139,0,0.393853," ","integrate(cosh(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(x\right)^{5} + {\left(15 \, \cosh\left(x\right) - 8\right)} \sinh\left(x\right)^{4} + 3 \, \sinh\left(x\right)^{5} - 8 \, \cosh\left(x\right)^{4} + {\left(30 \, \cosh\left(x\right)^{2} - 8 \, \cosh\left(x\right) + 35\right)} \sinh\left(x\right)^{3} + 45 \, \cosh\left(x\right)^{3} + {\left(30 \, \cosh\left(x\right)^{3} - 48 \, \cosh\left(x\right)^{2} + 135 \, \cosh\left(x\right) - 160\right)} \sinh\left(x\right)^{2} + 24 \, {\left(15 \, x - 2\right)} \cosh\left(x\right) - 160 \, \cosh\left(x\right)^{2} + {\left(15 \, \cosh\left(x\right)^{4} - 8 \, \cosh\left(x\right)^{3} + 105 \, \cosh\left(x\right)^{2} + 360 \, x - 160 \, \cosh\left(x\right) - 288\right)} \sinh\left(x\right) + 360 \, x + 552}{192 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + a\right)}}"," ",0,"1/192*(3*cosh(x)^5 + (15*cosh(x) - 8)*sinh(x)^4 + 3*sinh(x)^5 - 8*cosh(x)^4 + (30*cosh(x)^2 - 8*cosh(x) + 35)*sinh(x)^3 + 45*cosh(x)^3 + (30*cosh(x)^3 - 48*cosh(x)^2 + 135*cosh(x) - 160)*sinh(x)^2 + 24*(15*x - 2)*cosh(x) - 160*cosh(x)^2 + (15*cosh(x)^4 - 8*cosh(x)^3 + 105*cosh(x)^2 + 360*x - 160*cosh(x) - 288)*sinh(x) + 360*x + 552)/(a*cosh(x) + a*sinh(x) + a)","B",0
69,1,100,0,0.385227," ","integrate(cosh(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{4} + {\left(4 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} - 3 \, \cosh\left(x\right)^{3} + {\left(6 \, \cosh\left(x\right)^{2} - 9 \, \cosh\left(x\right) + 20\right)} \sinh\left(x\right)^{2} - 3 \, {\left(12 \, x - 1\right)} \cosh\left(x\right) + 20 \, \cosh\left(x\right)^{2} + {\left(4 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)^{2} - 36 \, x + 32 \, \cosh\left(x\right) + 39\right)} \sinh\left(x\right) - 36 \, x - 69}{24 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + a\right)}}"," ",0,"1/24*(cosh(x)^4 + (4*cosh(x) - 1)*sinh(x)^3 + sinh(x)^4 - 3*cosh(x)^3 + (6*cosh(x)^2 - 9*cosh(x) + 20)*sinh(x)^2 - 3*(12*x - 1)*cosh(x) + 20*cosh(x)^2 + (4*cosh(x)^3 - 3*cosh(x)^2 - 36*x + 32*cosh(x) + 39)*sinh(x) - 36*x - 69)/(a*cosh(x) + a*sinh(x) + a)","B",0
70,1,70,0,0.381669," ","integrate(cosh(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right) - 4\right)} \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(12 \, x - 1\right)} \cosh\left(x\right) - 4 \, \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{2} + 12 \, x - 4 \, \cosh\left(x\right) - 7\right)} \sinh\left(x\right) + 12 \, x + 20}{8 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + a\right)}}"," ",0,"1/8*(cosh(x)^3 + (3*cosh(x) - 4)*sinh(x)^2 + sinh(x)^3 + (12*x - 1)*cosh(x) - 4*cosh(x)^2 + (3*cosh(x)^2 + 12*x - 4*cosh(x) - 7)*sinh(x) + 12*x + 20)/(a*cosh(x) + a*sinh(x) + a)","A",0
71,1,47,0,0.384348," ","integrate(cosh(x)/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, x \cosh\left(x\right) - \cosh\left(x\right)^{2} + 2 \, {\left(x - \cosh\left(x\right) - 1\right)} \sinh\left(x\right) - \sinh\left(x\right)^{2} + 2 \, x + 5}{2 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + a\right)}}"," ",0,"-1/2*(2*x*cosh(x) - cosh(x)^2 + 2*(x - cosh(x) - 1)*sinh(x) - sinh(x)^2 + 2*x + 5)/(a*cosh(x) + a*sinh(x) + a)","A",0
72,1,14,0,0.368303," ","integrate(sech(x)/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2}{a \cosh\left(x\right) + a \sinh\left(x\right) + a}"," ",0,"-2/(a*cosh(x) + a*sinh(x) + a)","A",0
73,1,29,0,0.387291," ","integrate(sech(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 1\right)}}{a \cosh\left(x\right) + a \sinh\left(x\right) + a}"," ",0,"2*((cosh(x) + sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + 1)/(a*cosh(x) + a*sinh(x) + a)","A",0
74,1,127,0,0.375823," ","integrate(sech(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(\cosh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \cosh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + \cosh\left(x\right)^{2} + {\left(2 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + \cosh\left(x\right) + 2\right)}}{a \cosh\left(x\right)^{3} + a \sinh\left(x\right)^{3} + a \cosh\left(x\right)^{2} + {\left(3 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{2} + a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a}"," ",0,"-2*((cosh(x)^3 + (3*cosh(x) + 1)*sinh(x)^2 + sinh(x)^3 + cosh(x)^2 + (3*cosh(x)^2 + 2*cosh(x) + 1)*sinh(x) + cosh(x) + 1)*arctan(cosh(x) + sinh(x)) + cosh(x)^2 + (2*cosh(x) + 1)*sinh(x) + sinh(x)^2 + cosh(x) + 2)/(a*cosh(x)^3 + a*sinh(x)^3 + a*cosh(x)^2 + (3*a*cosh(x) + a)*sinh(x)^2 + a*cosh(x) + (3*a*cosh(x)^2 + 2*a*cosh(x) + a)*sinh(x) + a)","B",0
75,1,325,0,0.384292," ","integrate(sech(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(x\right)^{4} + 3 \, {\left(4 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{3} + 3 \, \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{3} + {\left(18 \, \cosh\left(x\right)^{2} + 9 \, \cosh\left(x\right) + 5\right)} \sinh\left(x\right)^{2} + 3 \, {\left(\cosh\left(x\right)^{5} + {\left(5 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + \cosh\left(x\right)^{4} + 2 \, {\left(5 \, \cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{3} + 2 \, \cosh\left(x\right)^{3} + 2 \, {\left(5 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} + 3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} + 6 \, \cosh\left(x\right)^{2} + 4 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \cosh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 5 \, \cosh\left(x\right)^{2} + {\left(12 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \cosh\left(x\right) + 4}{a \cosh\left(x\right)^{5} + a \sinh\left(x\right)^{5} + a \cosh\left(x\right)^{4} + {\left(5 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{3} + 2 \, {\left(5 \, a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{3} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(5 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{2} + a \cosh\left(x\right) + {\left(5 \, a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right)^{3} + 6 \, a \cosh\left(x\right)^{2} + 4 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a}"," ",0,"(3*cosh(x)^4 + 3*(4*cosh(x) + 1)*sinh(x)^3 + 3*sinh(x)^4 + 3*cosh(x)^3 + (18*cosh(x)^2 + 9*cosh(x) + 5)*sinh(x)^2 + 3*(cosh(x)^5 + (5*cosh(x) + 1)*sinh(x)^4 + sinh(x)^5 + cosh(x)^4 + 2*(5*cosh(x)^2 + 2*cosh(x) + 1)*sinh(x)^3 + 2*cosh(x)^3 + 2*(5*cosh(x)^3 + 3*cosh(x)^2 + 3*cosh(x) + 1)*sinh(x)^2 + 2*cosh(x)^2 + (5*cosh(x)^4 + 4*cosh(x)^3 + 6*cosh(x)^2 + 4*cosh(x) + 1)*sinh(x) + cosh(x) + 1)*arctan(cosh(x) + sinh(x)) + 5*cosh(x)^2 + (12*cosh(x)^3 + 9*cosh(x)^2 + 10*cosh(x) + 1)*sinh(x) + cosh(x) + 4)/(a*cosh(x)^5 + a*sinh(x)^5 + a*cosh(x)^4 + (5*a*cosh(x) + a)*sinh(x)^4 + 2*a*cosh(x)^3 + 2*(5*a*cosh(x)^2 + 2*a*cosh(x) + a)*sinh(x)^3 + 2*a*cosh(x)^2 + 2*(5*a*cosh(x)^3 + 3*a*cosh(x)^2 + 3*a*cosh(x) + a)*sinh(x)^2 + a*cosh(x) + (5*a*cosh(x)^4 + 4*a*cosh(x)^3 + 6*a*cosh(x)^2 + 4*a*cosh(x) + a)*sinh(x) + a)","B",0
76,1,48,0,0.381016," ","integrate(1/(a+a*sech(d*x+c)),x, algorithm=""fricas"")","\frac{d x \cosh\left(d x + c\right) + d x \sinh\left(d x + c\right) + d x + 2}{a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) + a d}"," ",0,"(d*x*cosh(d*x + c) + d*x*sinh(d*x + c) + d*x + 2)/(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) + a*d)","A",0
77,1,50,0,0.378526," ","integrate(1/(a-a*sech(d*x+c)),x, algorithm=""fricas"")","\frac{d x \cosh\left(d x + c\right) + d x \sinh\left(d x + c\right) - d x - 2}{a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) - a d}"," ",0,"(d*x*cosh(d*x + c) + d*x*sinh(d*x + c) - d*x - 2)/(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) - a*d)","A",0
78,1,924,0,0.440165," ","integrate((a+a*sech(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2}\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) - 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) - 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} - 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} - 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} - 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) - 7\right)} \sinh\left(d x + c\right)^{2} - 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} - 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} - 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) - 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} - 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) - 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2}\right)} \sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right) + 8 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 4 \, a^{2} \sinh\left(d x + c\right)^{3} - 3 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} \cosh\left(d x + c\right) + 3 \, {\left(4 \, a^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, a^{2} + 3 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{\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}}}{6 \, {\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,"1/6*(3*(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2)*sqrt(a)*log(-(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) - 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) - 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 - 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 - 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 - 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) - 7)*sinh(d*x + c)^2 - 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 - 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 - 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) - 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 - 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) - 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + 3*(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2)*sqrt(a)*log((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + a*cosh(d*x + c) + (2*a*cosh(d*x + c) + a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))) + 8*(4*a^2*cosh(d*x + c)^3 + 4*a^2*sinh(d*x + c)^3 - 3*a^2*cosh(d*x + c)^2 + 3*a^2*cosh(d*x + c) + 3*(4*a^2*cosh(d*x + c) - a^2)*sinh(d*x + c)^2 - 4*a^2 + 3*(4*a^2*cosh(d*x + c)^2 - 2*a^2*cosh(d*x + c) + a^2)*sinh(d*x + c))*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(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
79,1,697,0,0.412261," ","integrate((a+a*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{a^{\frac{3}{2}} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) - 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) - 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} - 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} - 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} - 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) - 7\right)} \sinh\left(d x + c\right)^{2} - 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} - 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} - 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) - 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} - 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) - 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + a^{\frac{3}{2}} \log\left(\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right) + 4 \, {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - a\right)} \sqrt{\frac{a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1}}}{2 \, d}"," ",0,"1/2*(a^(3/2)*log(-(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) - 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) - 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 - 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 - 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 - 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) - 7)*sinh(d*x + c)^2 - 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 - 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 - 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) - 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 - 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) - 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + a^(3/2)*log((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + a*cosh(d*x + c) + (2*a*cosh(d*x + c) + a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))) + 4*(a*cosh(d*x + c) + a*sinh(d*x + c) - a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/d","B",0
80,1,637,0,0.406909," ","integrate((a+a*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) - 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) - 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} - 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} - 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} - 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) - 7\right)} \sinh\left(d x + c\right)^{2} - 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} - 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} - 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) - 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} - 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) - 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + \sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right)}{2 \, d}"," ",0,"1/2*(sqrt(a)*log(-(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) - 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) - 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 - 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 - 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 - 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) - 7)*sinh(d*x + c)^2 - 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 - 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 - 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) - 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 - 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) - 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + sqrt(a)*log((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + a*cosh(d*x + c) + (2*a*cosh(d*x + c) + a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))))/d","B",0
81,1,868,0,0.443783," ","integrate(1/(a+a*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{3 \, \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) + 3 \, \sinh\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) - 1\right)} \sqrt{\frac{a}{\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}}}{\sqrt{a}} - 2 \, \cosh\left(d x + c\right) + 3}{\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) - 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) - 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} - 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} - 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} - 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) - 7\right)} \sinh\left(d x + c\right)^{2} - 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} - 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} - 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) - 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} - 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) - 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + \sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right)}{2 \, a d}"," ",0,"1/2*(sqrt(2)*sqrt(a)*log(-(3*cosh(d*x + c)^2 + 2*(3*cosh(d*x + c) - 1)*sinh(d*x + c) + 3*sinh(d*x + c)^2 - 2*sqrt(2)*(cosh(d*x + c)^3 + (3*cosh(d*x + c) - 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 - cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) - 1)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1))/sqrt(a) - 2*cosh(d*x + c) + 3)/(cosh(d*x + c)^2 + 2*(cosh(d*x + c) + 1)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*cosh(d*x + c) + 1)) + sqrt(a)*log(-(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) - 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) - 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 - 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 - 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 - 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) - 7)*sinh(d*x + c)^2 - 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 - 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 - 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) - 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 - 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) - 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + sqrt(a)*log((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + a*cosh(d*x + c) + (2*a*cosh(d*x + c) + a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))))/(a*d)","B",0
82,1,1190,0,0.443296," ","integrate(1/(a+a*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{3 \, a \cosh\left(d x + c\right)^{2} + 3 \, a \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) - 1\right)} \sqrt{a} \sqrt{\frac{a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1}} - 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(3 \, a \cosh\left(d x + c\right) - a\right)} \sinh\left(d x + c\right) + 3 \, a}{\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1}\right) + 4 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} - 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) - 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} - 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) - 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} - 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} - 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} - 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) - 7\right)} \sinh\left(d x + c\right)^{2} - 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} - 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} - 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) - 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} - 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) - 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + 4 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) - 1\right)} \sqrt{\frac{a}{\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}}}{8 \, {\left(a^{2} d \cosh\left(d x + c\right)^{2} + a^{2} d \sinh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) + a^{2} d + 2 \, {\left(a^{2} d \cosh\left(d x + c\right) + a^{2} d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/8*(5*sqrt(2)*(cosh(d*x + c)^2 + 2*(cosh(d*x + c) + 1)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sqrt(a)*log(-(3*a*cosh(d*x + c)^2 + 3*a*sinh(d*x + c)^2 - 2*sqrt(2)*(cosh(d*x + c)^3 + (3*cosh(d*x + c) - 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 - cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) - 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 2*a*cosh(d*x + c) + 2*(3*a*cosh(d*x + c) - a)*sinh(d*x + c) + 3*a)/(cosh(d*x + c)^2 + 2*(cosh(d*x + c) + 1)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*cosh(d*x + c) + 1)) + 4*(cosh(d*x + c)^2 + 2*(cosh(d*x + c) + 1)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sqrt(a)*log(-(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 - 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) - 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 - 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) - 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 - 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 - 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 - 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) - 7)*sinh(d*x + c)^2 - 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 - 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 - 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) - 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 - 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) - 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + 4*(cosh(d*x + c)^2 + 2*(cosh(d*x + c) + 1)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sqrt(a)*log((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + a*cosh(d*x + c) + (2*a*cosh(d*x + c) + a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))) - 4*(cosh(d*x + c)^3 + (3*cosh(d*x + c) - 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 - cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) - 1)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)))/(a^2*d*cosh(d*x + c)^2 + a^2*d*sinh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c) + a^2*d + 2*(a^2*d*cosh(d*x + c) + a^2*d)*sinh(d*x + c))","B",0
83,1,642,0,0.401930," ","integrate((a-a*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) + 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} + 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} + 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) + 7\right)} \sinh\left(d x + c\right)^{2} + 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} + 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} + 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) + 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) - 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) - a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right)}{2 \, d}"," ",0,"1/2*(sqrt(a)*log((a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) + 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 + 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 + 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 + 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) + 7)*sinh(d*x + c)^2 + 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 + 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 + 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) + 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) + 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + sqrt(a)*log(-(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) - 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 - cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) - 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - a*cosh(d*x + c) + (2*a*cosh(d*x + c) - a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))))/d","B",0
84,1,871,0,0.420815," ","integrate(1/(a-a*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{3 \, \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 3 \, \sinh\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) + 1\right)} \sqrt{\frac{a}{\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}}}{\sqrt{a}} + 2 \, \cosh\left(d x + c\right) + 3}{\cosh\left(d x + c\right)^{2} + 2 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1}\right) + \sqrt{a} \log\left(\frac{a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + 3 \, a \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + 3 \, a\right)} \sinh\left(d x + c\right)^{3} + 5 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 9 \, a \cosh\left(d x + c\right) + 5 \, a\right)} \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{5} + {\left(5 \, \cosh\left(d x + c\right) + 3\right)} \sinh\left(d x + c\right)^{4} + \sinh\left(d x + c\right)^{5} + 3 \, \cosh\left(d x + c\right)^{4} + {\left(10 \, \cosh\left(d x + c\right)^{2} + 12 \, \cosh\left(d x + c\right) + 5\right)} \sinh\left(d x + c\right)^{3} + 5 \, \cosh\left(d x + c\right)^{3} + {\left(10 \, \cosh\left(d x + c\right)^{3} + 18 \, \cosh\left(d x + c\right)^{2} + 15 \, \cosh\left(d x + c\right) + 7\right)} \sinh\left(d x + c\right)^{2} + 7 \, \cosh\left(d x + c\right)^{2} + {\left(5 \, \cosh\left(d x + c\right)^{4} + 12 \, \cosh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} + 14 \, \cosh\left(d x + c\right) + 4\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 4\right)} \sqrt{a} \sqrt{\frac{a}{\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}} + 4 \, a \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 9 \, a \cosh\left(d x + c\right)^{2} + 10 \, a \cosh\left(d x + c\right) + 4 \, a\right)} \sinh\left(d x + c\right) + 4 \, a}{\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3}}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + {\left(\cosh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)^{2} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right) - 1\right)} \sqrt{a} \sqrt{\frac{a}{\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}} - a \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) - a\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right) + \sinh\left(d x + c\right)}\right)}{2 \, a d}"," ",0,"1/2*(sqrt(2)*sqrt(a)*log(-(3*cosh(d*x + c)^2 + 2*(3*cosh(d*x + c) + 1)*sinh(d*x + c) + 3*sinh(d*x + c)^2 - 2*sqrt(2)*(cosh(d*x + c)^3 + (3*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) + 1)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1))/sqrt(a) + 2*cosh(d*x + c) + 3)/(cosh(d*x + c)^2 + 2*(cosh(d*x + c) - 1)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*cosh(d*x + c) + 1)) + sqrt(a)*log((a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + 3*a*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + 3*a)*sinh(d*x + c)^3 + 5*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 9*a*cosh(d*x + c) + 5*a)*sinh(d*x + c)^2 + (cosh(d*x + c)^5 + (5*cosh(d*x + c) + 3)*sinh(d*x + c)^4 + sinh(d*x + c)^5 + 3*cosh(d*x + c)^4 + (10*cosh(d*x + c)^2 + 12*cosh(d*x + c) + 5)*sinh(d*x + c)^3 + 5*cosh(d*x + c)^3 + (10*cosh(d*x + c)^3 + 18*cosh(d*x + c)^2 + 15*cosh(d*x + c) + 7)*sinh(d*x + c)^2 + 7*cosh(d*x + c)^2 + (5*cosh(d*x + c)^4 + 12*cosh(d*x + c)^3 + 15*cosh(d*x + c)^2 + 14*cosh(d*x + c) + 4)*sinh(d*x + c) + 4*cosh(d*x + c) + 4)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) + 4*a*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 9*a*cosh(d*x + c)^2 + 10*a*cosh(d*x + c) + 4*a)*sinh(d*x + c) + 4*a)/(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2*sinh(d*x + c) + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3)) + sqrt(a)*log(-(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + (cosh(d*x + c)^3 + (3*cosh(d*x + c) - 1)*sinh(d*x + c)^2 + sinh(d*x + c)^3 - cosh(d*x + c)^2 + (3*cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c) + cosh(d*x + c) - 1)*sqrt(a)*sqrt(a/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)) - a*cosh(d*x + c) + (2*a*cosh(d*x + c) - a)*sinh(d*x + c) + a)/(cosh(d*x + c) + sinh(d*x + c))))/(a*d)","B",0
85,1,233,0,0.382240," ","integrate((3+3*sech(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{3} \log\left(-\frac{\cosh\left(x\right)^{4} + {\left(4 \, \cosh\left(x\right) - 3\right)} \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} - 3 \, \cosh\left(x\right)^{3} + {\left(6 \, \cosh\left(x\right)^{2} - 9 \, \cosh\left(x\right) + 5\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{3} + 3 \, {\left(\cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} - 3 \, \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{2} - 6 \, \cosh\left(x\right) + 4\right)} \sinh\left(x\right) + 4 \, \cosh\left(x\right) - 4\right)} \sqrt{\frac{\cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} + 5 \, \cosh\left(x\right)^{2} + {\left(4 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) - 4\right)} \sinh\left(x\right) - 4 \, \cosh\left(x\right) + 4}{\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) + \frac{1}{2} \, \sqrt{3} \log\left(\frac{\sqrt{2} \sqrt{\frac{\cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right)} + \cosh\left(x\right)^{2} + {\left(2 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + \cosh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right)}\right)"," ",0,"1/2*sqrt(3)*log(-(cosh(x)^4 + (4*cosh(x) - 3)*sinh(x)^3 + sinh(x)^4 - 3*cosh(x)^3 + (6*cosh(x)^2 - 9*cosh(x) + 5)*sinh(x)^2 + sqrt(2)*(cosh(x)^3 + 3*(cosh(x) - 1)*sinh(x)^2 + sinh(x)^3 - 3*cosh(x)^2 + (3*cosh(x)^2 - 6*cosh(x) + 4)*sinh(x) + 4*cosh(x) - 4)*sqrt(cosh(x)/(cosh(x) - sinh(x))) + 5*cosh(x)^2 + (4*cosh(x)^3 - 9*cosh(x)^2 + 10*cosh(x) - 4)*sinh(x) - 4*cosh(x) + 4)/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)) + 1/2*sqrt(3)*log((sqrt(2)*sqrt(cosh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x) + 1) + cosh(x)^2 + (2*cosh(x) + 1)*sinh(x) + sinh(x)^2 + cosh(x) + 1)/(cosh(x) + sinh(x)))","B",0
86,1,235,0,0.388888," ","integrate((3-3*sech(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{3} \log\left(\frac{\cosh\left(x\right)^{4} + {\left(4 \, \cosh\left(x\right) + 3\right)} \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{3} + {\left(6 \, \cosh\left(x\right)^{2} + 9 \, \cosh\left(x\right) + 5\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{3} + 3 \, {\left(\cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{2} + {\left(3 \, \cosh\left(x\right)^{2} + 6 \, \cosh\left(x\right) + 4\right)} \sinh\left(x\right) + 4 \, \cosh\left(x\right) + 4\right)} \sqrt{\frac{\cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} + 5 \, \cosh\left(x\right)^{2} + {\left(4 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) + 4\right)} \sinh\left(x\right) + 4 \, \cosh\left(x\right) + 4}{\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) + \frac{1}{2} \, \sqrt{3} \log\left(-\frac{\sqrt{2} \sqrt{\frac{\cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}} {\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)} + \cosh\left(x\right)^{2} + {\left(2 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} - \cosh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right)}\right)"," ",0,"1/2*sqrt(3)*log((cosh(x)^4 + (4*cosh(x) + 3)*sinh(x)^3 + sinh(x)^4 + 3*cosh(x)^3 + (6*cosh(x)^2 + 9*cosh(x) + 5)*sinh(x)^2 + sqrt(2)*(cosh(x)^3 + 3*(cosh(x) + 1)*sinh(x)^2 + sinh(x)^3 + 3*cosh(x)^2 + (3*cosh(x)^2 + 6*cosh(x) + 4)*sinh(x) + 4*cosh(x) + 4)*sqrt(cosh(x)/(cosh(x) - sinh(x))) + 5*cosh(x)^2 + (4*cosh(x)^3 + 9*cosh(x)^2 + 10*cosh(x) + 4)*sinh(x) + 4*cosh(x) + 4)/(cosh(x)^3 + 3*cosh(x)^2*sinh(x) + 3*cosh(x)*sinh(x)^2 + sinh(x)^3)) + 1/2*sqrt(3)*log(-(sqrt(2)*sqrt(cosh(x)/(cosh(x) - sinh(x)))*(cosh(x) + sinh(x) - 1) + cosh(x)^2 + (2*cosh(x) - 1)*sinh(x) + sinh(x)^2 - cosh(x) + 1)/(cosh(x) + sinh(x)))","B",0
87,1,1028,0,0.413011," ","integrate((a+b*sech(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} d x \cosh\left(d x + c\right)^{6} + 3 \, a^{4} d x \sinh\left(d x + c\right)^{6} + 12 \, a b^{3} \cosh\left(d x + c\right)^{5} + 3 \, a^{4} d x + 6 \, {\left(3 \, a^{4} d x \cosh\left(d x + c\right) + 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{5} - 12 \, a b^{3} \cosh\left(d x + c\right) + 9 \, {\left(a^{4} d x - 4 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{4} d x \cosh\left(d x + c\right)^{2} + 3 \, a^{4} d x + 20 \, a b^{3} \cosh\left(d x + c\right) - 12 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{4} - 36 \, a^{2} b^{2} - 4 \, b^{4} + 12 \, {\left(5 \, a^{4} d x \cosh\left(d x + c\right)^{3} + 10 \, a b^{3} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{4} d x - 4 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} d x - 24 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, a^{4} d x \cosh\left(d x + c\right)^{4} + 40 \, a b^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{4} d x - 24 \, a^{2} b^{2} - 4 \, b^{4} + 18 \, {\left(a^{4} d x - 4 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(2 \, a^{3} b + a b^{3}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{3} b + a b^{3} + 5 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} b + a b^{3} + 4 \, {\left(5 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b + a b^{3} + 6 \, {\left(2 \, 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(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(3 \, a^{4} d x \cosh\left(d x + c\right)^{5} + 10 \, a b^{3} \cosh\left(d x + c\right)^{4} - 2 \, a b^{3} + 6 \, {\left(a^{4} d x - 4 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} d x - 24 \, a^{2} b^{2} - 4 \, b^{4}\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*d*x*cosh(d*x + c)^6 + 3*a^4*d*x*sinh(d*x + c)^6 + 12*a*b^3*cosh(d*x + c)^5 + 3*a^4*d*x + 6*(3*a^4*d*x*cosh(d*x + c) + 2*a*b^3)*sinh(d*x + c)^5 - 12*a*b^3*cosh(d*x + c) + 9*(a^4*d*x - 4*a^2*b^2)*cosh(d*x + c)^4 + 3*(15*a^4*d*x*cosh(d*x + c)^2 + 3*a^4*d*x + 20*a*b^3*cosh(d*x + c) - 12*a^2*b^2)*sinh(d*x + c)^4 - 36*a^2*b^2 - 4*b^4 + 12*(5*a^4*d*x*cosh(d*x + c)^3 + 10*a*b^3*cosh(d*x + c)^2 + 3*(a^4*d*x - 4*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(3*a^4*d*x - 24*a^2*b^2 - 4*b^4)*cosh(d*x + c)^2 + 3*(15*a^4*d*x*cosh(d*x + c)^4 + 40*a*b^3*cosh(d*x + c)^3 + 3*a^4*d*x - 24*a^2*b^2 - 4*b^4 + 18*(a^4*d*x - 4*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((2*a^3*b + a*b^3)*cosh(d*x + c)^6 + 6*(2*a^3*b + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (2*a^3*b + a*b^3)*sinh(d*x + c)^6 + 3*(2*a^3*b + a*b^3)*cosh(d*x + c)^4 + 3*(2*a^3*b + a*b^3 + 5*(2*a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 2*a^3*b + a*b^3 + 4*(5*(2*a^3*b + a*b^3)*cosh(d*x + c)^3 + 3*(2*a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(2*a^3*b + a*b^3)*cosh(d*x + c)^2 + 3*(5*(2*a^3*b + a*b^3)*cosh(d*x + c)^4 + 2*a^3*b + a*b^3 + 6*(2*a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 6*((2*a^3*b + a*b^3)*cosh(d*x + c)^5 + 2*(2*a^3*b + a*b^3)*cosh(d*x + c)^3 + (2*a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 6*(3*a^4*d*x*cosh(d*x + c)^5 + 10*a*b^3*cosh(d*x + c)^4 - 2*a*b^3 + 6*(a^4*d*x - 4*a^2*b^2)*cosh(d*x + c)^3 + (3*a^4*d*x - 24*a^2*b^2 - 4*b^4)*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
88,1,521,0,0.402928," ","integrate((a+b*sech(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} d x \cosh\left(d x + c\right)^{4} + a^{3} d x \sinh\left(d x + c\right)^{4} + b^{3} \cosh\left(d x + c\right)^{3} + a^{3} d x - b^{3} \cosh\left(d x + c\right) + {\left(4 \, a^{3} d x \cosh\left(d x + c\right) + b^{3}\right)} \sinh\left(d x + c\right)^{3} - 6 \, a b^{2} + 2 \, {\left(a^{3} d x - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{3} d x \cosh\left(d x + c\right)^{2} + 2 \, a^{3} d x + 3 \, b^{3} \cosh\left(d x + c\right) - 6 \, a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(6 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a^{2} b + b^{3} + 2 \, {\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(4 \, a^{3} d x \cosh\left(d x + c\right)^{3} + 3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3} + 4 \, {\left(a^{3} d x - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} + 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d}"," ",0,"(a^3*d*x*cosh(d*x + c)^4 + a^3*d*x*sinh(d*x + c)^4 + b^3*cosh(d*x + c)^3 + a^3*d*x - b^3*cosh(d*x + c) + (4*a^3*d*x*cosh(d*x + c) + b^3)*sinh(d*x + c)^3 - 6*a*b^2 + 2*(a^3*d*x - 3*a*b^2)*cosh(d*x + c)^2 + (6*a^3*d*x*cosh(d*x + c)^2 + 2*a^3*d*x + 3*b^3*cosh(d*x + c) - 6*a*b^2)*sinh(d*x + c)^2 + ((6*a^2*b + b^3)*cosh(d*x + c)^4 + 4*(6*a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (6*a^2*b + b^3)*sinh(d*x + c)^4 + 6*a^2*b + b^3 + 2*(6*a^2*b + b^3)*cosh(d*x + c)^2 + 2*(6*a^2*b + b^3 + 3*(6*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((6*a^2*b + b^3)*cosh(d*x + c)^3 + (6*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + (4*a^3*d*x*cosh(d*x + c)^3 + 3*b^3*cosh(d*x + c)^2 - b^3 + 4*(a^3*d*x - 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 + 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
89,1,157,0,0.416076," ","integrate((a+b*sech(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d x \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d x \sinh\left(d x + c\right)^{2} + a^{2} d x - 2 \, b^{2} + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b\right)} \arctan\left(\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*d*x*cosh(d*x + c)^2 + 2*a^2*d*x*cosh(d*x + c)*sinh(d*x + c) + a^2*d*x*sinh(d*x + c)^2 + a^2*d*x - 2*b^2 + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + a*b)*arctan(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
90,1,26,0,0.400076," ","integrate(a+b*sech(d*x+c),x, algorithm=""fricas"")","\frac{a d x + 2 \, b \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{d}"," ",0,"(a*d*x + 2*b*arctan(cosh(d*x + c) + sinh(d*x + c)))/d","A",0
91,1,270,0,0.412502," ","integrate(1/(a+b*sech(d*x+c)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} - b^{2}\right)} d x - \sqrt{-a^{2} + b^{2}} b \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b\right)}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right)}{{\left(a^{3} - a b^{2}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x + 2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{{\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[((a^2 - b^2)*d*x - sqrt(-a^2 + b^2)*b*log((a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) - a^2 + 2*b^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(-a^2 + b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c) + b))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(a*cosh(d*x + c) + b)*sinh(d*x + c) + a)))/((a^3 - a*b^2)*d), ((a^2 - b^2)*d*x + 2*sqrt(a^2 - b^2)*b*arctan(-(a*cosh(d*x + c) + a*sinh(d*x + c) + b)/sqrt(a^2 - b^2)))/((a^3 - a*b^2)*d)]","A",0
92,1,1207,0,0.424814," ","integrate(1/(a+b*sech(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \sinh\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x + {\left(2 \, a^{3} b - a b^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{3} b - a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b\right)}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + 2 \, {\left(a^{2} b^{3} - b^{5} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cosh\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x\right)} \sinh\left(d x + c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)}, -\frac{2 \, a^{3} b^{2} - 2 \, a b^{4} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \sinh\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x - 2 \, {\left(2 \, a^{3} b - a b^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{3} b - a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 2 \, {\left(a^{2} b^{3} - b^{5} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b^{3} - b^{5} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cosh\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x\right)} \sinh\left(d x + c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[-(2*a^3*b^2 - 2*a*b^4 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*cosh(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*sinh(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x + (2*a^3*b - a*b^3 + (2*a^3*b - a*b^3)*cosh(d*x + c)^2 + (2*a^3*b - a*b^3)*sinh(d*x + c)^2 + 2*(2*a^2*b^2 - b^4)*cosh(d*x + c) + 2*(2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + b^2)*log((a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) - a^2 + 2*b^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(-a^2 + b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c) + b))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + 2*(a^2*b^3 - b^5 - (a^4*b - 2*a^2*b^3 + b^5)*d*x)*cosh(d*x + c) + 2*(a^2*b^3 - b^5 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*cosh(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*x)*sinh(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 - 2*a^5*b^2 + a^3*b^4)*d*sinh(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d + 2*((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c)), -(2*a^3*b^2 - 2*a*b^4 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*cosh(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*sinh(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x - 2*(2*a^3*b - a*b^3 + (2*a^3*b - a*b^3)*cosh(d*x + c)^2 + (2*a^3*b - a*b^3)*sinh(d*x + c)^2 + 2*(2*a^2*b^2 - b^4)*cosh(d*x + c) + 2*(2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cosh(d*x + c) + a*sinh(d*x + c) + b)/sqrt(a^2 - b^2)) + 2*(a^2*b^3 - b^5 - (a^4*b - 2*a^2*b^3 + b^5)*d*x)*cosh(d*x + c) + 2*(a^2*b^3 - b^5 - (a^5 - 2*a^3*b^2 + a*b^4)*d*x*cosh(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*x)*sinh(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 - 2*a^5*b^2 + a^3*b^4)*d*sinh(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d + 2*((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c))]","B",0
93,1,4125,0,0.502185," ","integrate(1/(a+b*sech(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, a^{6} b^{2} - 18 \, a^{4} b^{4} + 6 \, a^{2} b^{6} - 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right) - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x + 2 \, {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 6 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x + 3 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{4} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7} + 3 \, {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right) + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b\right)}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + 2 \, {\left(17 \, a^{5} b^{3} - 25 \, a^{3} b^{5} + 8 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right) + 2 \, {\left(17 \, a^{5} b^{3} - 25 \, a^{3} b^{5} + 8 \, a b^{7} - 4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x + 3 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right) + {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right) + {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d + 4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d \cosh\left(d x + c\right) + {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d\right)} \sinh\left(d x + c\right)\right)}}, -\frac{6 \, a^{6} b^{2} - 9 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{4} - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \sinh\left(d x + c\right)^{4} + {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right) - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x + {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 6 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x + 3 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{4} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7} + 3 \, {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right) + 4 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{6} b + 7 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + {\left(17 \, a^{5} b^{3} - 25 \, a^{3} b^{5} + 8 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right) + {\left(17 \, a^{5} b^{3} - 25 \, a^{3} b^{5} + 8 \, a b^{7} - 4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x + 3 \, {\left(7 \, a^{5} b^{3} - 11 \, a^{3} b^{5} + 4 \, a b^{7} - 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - 15 \, a^{2} b^{6} + 6 \, b^{8} - 2 \, {\left(a^{8} - a^{6} b^{2} - 3 \, a^{4} b^{4} + 5 \, a^{2} b^{6} - 2 \, b^{8}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right) + {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right) + {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d + 4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{11} - a^{9} b^{2} - 3 \, a^{7} b^{4} + 5 \, a^{5} b^{6} - 2 \, a^{3} b^{8}\right)} d \cosh\left(d x + c\right) + {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[-1/2*(12*a^6*b^2 - 18*a^4*b^4 + 6*a^2*b^6 - 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^4 - 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*sinh(d*x + c)^4 + 2*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c)^3 + 2*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c) - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*sinh(d*x + c)^3 - 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x + 2*(6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x)*cosh(d*x + c)^2 + 2*(6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 6*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^2 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x + 3*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^4 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*sinh(d*x + c)^4 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c)^3 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7)*cosh(d*x + c)^2 + 2*(6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7 + 3*(6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^2 + 6*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c) + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^3 + 3*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c)^2 + (6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + b^2)*log((a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) - a^2 + 2*b^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(-a^2 + b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c) + b))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + 2*(17*a^5*b^3 - 25*a^3*b^5 + 8*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c) + 2*(17*a^5*b^3 - 25*a^3*b^5 + 8*a*b^7 - 4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^3 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x + 3*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c)^2 + 2*(6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^4 + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*sinh(d*x + c)^4 + 4*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c)^3 + 2*(a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d*cosh(d*x + c)^2 + 4*((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c) + (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d)*sinh(d*x + c)^3 + 4*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c) + 2*(3*(a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^2 + 6*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c) + (a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d)*sinh(d*x + c)^2 + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d + 4*((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^3 + 3*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c)^2 + (a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d*cosh(d*x + c) + (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d)*sinh(d*x + c)), -(6*a^6*b^2 - 9*a^4*b^4 + 3*a^2*b^6 - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^4 - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*sinh(d*x + c)^4 + (7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c)^3 + (7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c) - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*sinh(d*x + c)^3 - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x + (6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x)*cosh(d*x + c)^2 + (6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 6*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^2 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x + 3*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 - (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^4 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*sinh(d*x + c)^4 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c)^3 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7)*cosh(d*x + c)^2 + 2*(6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7 + 3*(6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^2 + 6*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c) + 4*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*cosh(d*x + c)^3 + 3*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cosh(d*x + c)^2 + (6*a^6*b + 7*a^4*b^3 - 8*a^2*b^5 + 4*b^7)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cosh(d*x + c) + a*sinh(d*x + c) + b)/sqrt(a^2 - b^2)) + (17*a^5*b^3 - 25*a^3*b^5 + 8*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c) + (17*a^5*b^3 - 25*a^3*b^5 + 8*a*b^7 - 4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x*cosh(d*x + c)^3 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x + 3*(7*a^5*b^3 - 11*a^3*b^5 + 4*a*b^7 - 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x)*cosh(d*x + c)^2 + 2*(6*a^6*b^2 + 3*a^4*b^4 - 15*a^2*b^6 + 6*b^8 - 2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^4 + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*sinh(d*x + c)^4 + 4*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c)^3 + 2*(a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d*cosh(d*x + c)^2 + 4*((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c) + (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d)*sinh(d*x + c)^3 + 4*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c) + 2*(3*(a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^2 + 6*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c) + (a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d)*sinh(d*x + c)^2 + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d + 4*((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cosh(d*x + c)^3 + 3*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cosh(d*x + c)^2 + (a^11 - a^9*b^2 - 3*a^7*b^4 + 5*a^5*b^6 - 2*a^3*b^8)*d*cosh(d*x + c) + (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d)*sinh(d*x + c))]","B",0
94,0,0,0,2.252176," ","integrate(1/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \operatorname{sech}\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*sech(d*x + c) + a), x)","F",0
95,1,2402,0,0.474710," ","integrate(cosh(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{8} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \sinh\left(x\right)^{8} - 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{7} - 8 \, {\left(a^{5} b - a^{3} b^{3} - 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 24 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(6 \, a^{6} - 6 \, a^{2} b^{4} + 21 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{2} - 14 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} - 3 \, a^{6} + 3 \, a^{4} b^{2} + 24 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{4} - 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{5} - 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5} - 7 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + 7 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{4} - 140 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + 180 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x - 60 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 8 \, {\left(9 \, a^{5} b + 3 \, a^{3} b^{3} - 12 \, a b^{5} + 21 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{5} - 35 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 60 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right) - 30 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{3} - 24 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(7 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{6} - 2 \, a^{6} + 2 \, a^{2} b^{4} - 14 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{5} + 30 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{2} - 20 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 6 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 192 \, {\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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right) + 8 \, {\left(3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{6} + a^{5} b - a^{3} b^{3} + 18 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{3} - 15 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{192 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{7} - a^{5} b^{2}\right)} \sinh\left(x\right)^{4}\right)}}, \frac{3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{8} + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \sinh\left(x\right)^{8} - 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{7} - 8 \, {\left(a^{5} b - a^{3} b^{3} - 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 24 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(6 \, a^{6} - 6 \, a^{2} b^{4} + 21 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{2} - 14 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} - 3 \, a^{6} + 3 \, a^{4} b^{2} + 24 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{4} - 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{5} - 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5} - 7 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{3} + 7 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{4} - 140 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{3} + 180 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x - 60 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 24 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 8 \, {\left(9 \, a^{5} b + 3 \, a^{3} b^{3} - 12 \, a b^{5} + 21 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{5} - 35 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{4} + 60 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right) - 30 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{3} - 24 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 12 \, {\left(7 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{6} - 2 \, a^{6} + 2 \, a^{2} b^{4} - 14 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{5} + 30 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{2} - 20 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 6 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 384 \, {\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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right) + 8 \, {\left(3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cosh\left(x\right)^{6} + a^{5} b - a^{3} b^{3} + 18 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} x \cosh\left(x\right)^{3} - 15 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} b + a^{3} b^{3} - 4 \, a b^{5}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{192 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{7} - a^{5} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{7} - a^{5} b^{2}\right)} \sinh\left(x\right)^{4}\right)}}\right]"," ",0,"[1/192*(3*(a^6 - a^4*b^2)*cosh(x)^8 + 3*(a^6 - a^4*b^2)*sinh(x)^8 - 8*(a^5*b - a^3*b^3)*cosh(x)^7 - 8*(a^5*b - a^3*b^3 - 3*(a^6 - a^4*b^2)*cosh(x))*sinh(x)^7 + 24*(a^6 - a^2*b^4)*cosh(x)^6 + 4*(6*a^6 - 6*a^2*b^4 + 21*(a^6 - a^4*b^2)*cosh(x)^2 - 14*(a^5*b - a^3*b^3)*cosh(x))*sinh(x)^6 - 3*a^6 + 3*a^4*b^2 + 24*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^4 - 24*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^5 - 24*(3*a^5*b + a^3*b^3 - 4*a*b^5 - 7*(a^6 - a^4*b^2)*cosh(x)^3 + 7*(a^5*b - a^3*b^3)*cosh(x)^2 - 6*(a^6 - a^2*b^4)*cosh(x))*sinh(x)^5 + 2*(105*(a^6 - a^4*b^2)*cosh(x)^4 - 140*(a^5*b - a^3*b^3)*cosh(x)^3 + 180*(a^6 - a^2*b^4)*cosh(x)^2 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x - 60*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x))*sinh(x)^4 + 24*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^3 + 8*(9*a^5*b + 3*a^3*b^3 - 12*a*b^5 + 21*(a^6 - a^4*b^2)*cosh(x)^5 - 35*(a^5*b - a^3*b^3)*cosh(x)^4 + 60*(a^6 - a^2*b^4)*cosh(x)^3 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x) - 30*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^2)*sinh(x)^3 - 24*(a^6 - a^2*b^4)*cosh(x)^2 + 12*(7*(a^6 - a^4*b^2)*cosh(x)^6 - 2*a^6 + 2*a^2*b^4 - 14*(a^5*b - a^3*b^3)*cosh(x)^5 + 30*(a^6 - a^2*b^4)*cosh(x)^4 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^2 - 20*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^3 + 6*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x))*sinh(x)^2 - 192*(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)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 8*(a^5*b - a^3*b^3)*cosh(x) + 8*(3*(a^6 - a^4*b^2)*cosh(x)^7 - 7*(a^5*b - a^3*b^3)*cosh(x)^6 + a^5*b - a^3*b^3 + 18*(a^6 - a^2*b^4)*cosh(x)^5 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^3 - 15*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^4 + 9*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^2 - 6*(a^6 - a^2*b^4)*cosh(x))*sinh(x))/((a^7 - a^5*b^2)*cosh(x)^4 + 4*(a^7 - a^5*b^2)*cosh(x)^3*sinh(x) + 6*(a^7 - a^5*b^2)*cosh(x)^2*sinh(x)^2 + 4*(a^7 - a^5*b^2)*cosh(x)*sinh(x)^3 + (a^7 - a^5*b^2)*sinh(x)^4), 1/192*(3*(a^6 - a^4*b^2)*cosh(x)^8 + 3*(a^6 - a^4*b^2)*sinh(x)^8 - 8*(a^5*b - a^3*b^3)*cosh(x)^7 - 8*(a^5*b - a^3*b^3 - 3*(a^6 - a^4*b^2)*cosh(x))*sinh(x)^7 + 24*(a^6 - a^2*b^4)*cosh(x)^6 + 4*(6*a^6 - 6*a^2*b^4 + 21*(a^6 - a^4*b^2)*cosh(x)^2 - 14*(a^5*b - a^3*b^3)*cosh(x))*sinh(x)^6 - 3*a^6 + 3*a^4*b^2 + 24*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^4 - 24*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^5 - 24*(3*a^5*b + a^3*b^3 - 4*a*b^5 - 7*(a^6 - a^4*b^2)*cosh(x)^3 + 7*(a^5*b - a^3*b^3)*cosh(x)^2 - 6*(a^6 - a^2*b^4)*cosh(x))*sinh(x)^5 + 2*(105*(a^6 - a^4*b^2)*cosh(x)^4 - 140*(a^5*b - a^3*b^3)*cosh(x)^3 + 180*(a^6 - a^2*b^4)*cosh(x)^2 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x - 60*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x))*sinh(x)^4 + 24*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^3 + 8*(9*a^5*b + 3*a^3*b^3 - 12*a*b^5 + 21*(a^6 - a^4*b^2)*cosh(x)^5 - 35*(a^5*b - a^3*b^3)*cosh(x)^4 + 60*(a^6 - a^2*b^4)*cosh(x)^3 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x) - 30*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^2)*sinh(x)^3 - 24*(a^6 - a^2*b^4)*cosh(x)^2 + 12*(7*(a^6 - a^4*b^2)*cosh(x)^6 - 2*a^6 + 2*a^2*b^4 - 14*(a^5*b - a^3*b^3)*cosh(x)^5 + 30*(a^6 - a^2*b^4)*cosh(x)^4 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^2 - 20*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^3 + 6*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x))*sinh(x)^2 + 384*(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)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 8*(a^5*b - a^3*b^3)*cosh(x) + 8*(3*(a^6 - a^4*b^2)*cosh(x)^7 - 7*(a^5*b - a^3*b^3)*cosh(x)^6 + a^5*b - a^3*b^3 + 18*(a^6 - a^2*b^4)*cosh(x)^5 + 12*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*x*cosh(x)^3 - 15*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^4 + 9*(3*a^5*b + a^3*b^3 - 4*a*b^5)*cosh(x)^2 - 6*(a^6 - a^2*b^4)*cosh(x))*sinh(x))/((a^7 - a^5*b^2)*cosh(x)^4 + 4*(a^7 - a^5*b^2)*cosh(x)^3*sinh(x) + 6*(a^7 - a^5*b^2)*cosh(x)^2*sinh(x)^2 + 4*(a^7 - a^5*b^2)*cosh(x)*sinh(x)^3 + (a^7 - a^5*b^2)*sinh(x)^4)]","B",0
96,1,1562,0,0.458223," ","integrate(cosh(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + {\left(a^{5} - a^{3} b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{5} - 3 \, {\left(a^{4} b - a^{2} b^{3} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} + a^{3} b^{2} - 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4} + 5 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 2 \, {\left(10 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - 15 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x + 6 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4} - 5 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right) - 6 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\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{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right) + 3 \, {\left(2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + a^{4} b - a^{2} b^{3} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right)^{2} + 4 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\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)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} \sinh\left(x\right)^{3}\right)}}, \frac{{\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + {\left(a^{5} - a^{3} b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{5} - 3 \, {\left(a^{4} b - a^{2} b^{3} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} + a^{3} b^{2} - 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4} + 5 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 2 \, {\left(10 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - 15 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 6 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x + 6 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4} - 5 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right) - 6 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\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{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right) + 3 \, {\left(2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + a^{4} b - a^{2} b^{3} - 5 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} x \cosh\left(x\right)^{2} + 4 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(3 \, a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\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)^{2} \sinh\left(x\right) + 3 \, {\left(a^{6} - a^{4} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} \sinh\left(x\right)^{3}\right)}}\right]"," ",0,"[1/24*((a^5 - a^3*b^2)*cosh(x)^6 + (a^5 - a^3*b^2)*sinh(x)^6 - 3*(a^4*b - a^2*b^3)*cosh(x)^5 - 3*(a^4*b - a^2*b^3 - 2*(a^5 - a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 + a^3*b^2 - 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x)^3 + 3*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^4 + 3*(3*a^5 + a^3*b^2 - 4*a*b^4 + 5*(a^5 - a^3*b^2)*cosh(x)^2 - 5*(a^4*b - a^2*b^3)*cosh(x))*sinh(x)^4 + 2*(10*(a^5 - a^3*b^2)*cosh(x)^3 - 15*(a^4*b - a^2*b^3)*cosh(x)^2 - 6*(a^4*b + a^2*b^3 - 2*b^5)*x + 6*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^2 - 3*(3*a^5 + a^3*b^2 - 4*a*b^4 - 5*(a^5 - a^3*b^2)*cosh(x)^4 + 10*(a^4*b - a^2*b^3)*cosh(x)^3 + 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x) - 6*(3*a^5 + a^3*b^2 - 4*a*b^4)*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^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) - 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 3*(a^4*b - a^2*b^3)*cosh(x) + 3*(2*(a^5 - a^3*b^2)*cosh(x)^5 + a^4*b - a^2*b^3 - 5*(a^4*b - a^2*b^3)*cosh(x)^4 - 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x)^2 + 4*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^3 - 2*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x))*sinh(x))/((a^6 - a^4*b^2)*cosh(x)^3 + 3*(a^6 - a^4*b^2)*cosh(x)^2*sinh(x) + 3*(a^6 - a^4*b^2)*cosh(x)*sinh(x)^2 + (a^6 - a^4*b^2)*sinh(x)^3), 1/24*((a^5 - a^3*b^2)*cosh(x)^6 + (a^5 - a^3*b^2)*sinh(x)^6 - 3*(a^4*b - a^2*b^3)*cosh(x)^5 - 3*(a^4*b - a^2*b^3 - 2*(a^5 - a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 + a^3*b^2 - 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x)^3 + 3*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^4 + 3*(3*a^5 + a^3*b^2 - 4*a*b^4 + 5*(a^5 - a^3*b^2)*cosh(x)^2 - 5*(a^4*b - a^2*b^3)*cosh(x))*sinh(x)^4 + 2*(10*(a^5 - a^3*b^2)*cosh(x)^3 - 15*(a^4*b - a^2*b^3)*cosh(x)^2 - 6*(a^4*b + a^2*b^3 - 2*b^5)*x + 6*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x))*sinh(x)^3 - 3*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^2 - 3*(3*a^5 + a^3*b^2 - 4*a*b^4 - 5*(a^5 - a^3*b^2)*cosh(x)^4 + 10*(a^4*b - a^2*b^3)*cosh(x)^3 + 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x) - 6*(3*a^5 + a^3*b^2 - 4*a*b^4)*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(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 3*(a^4*b - a^2*b^3)*cosh(x) + 3*(2*(a^5 - a^3*b^2)*cosh(x)^5 + a^4*b - a^2*b^3 - 5*(a^4*b - a^2*b^3)*cosh(x)^4 - 12*(a^4*b + a^2*b^3 - 2*b^5)*x*cosh(x)^2 + 4*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x)^3 - 2*(3*a^5 + a^3*b^2 - 4*a*b^4)*cosh(x))*sinh(x))/((a^6 - a^4*b^2)*cosh(x)^3 + 3*(a^6 - a^4*b^2)*cosh(x)^2*sinh(x) + 3*(a^6 - a^4*b^2)*cosh(x)*sinh(x)^2 + (a^6 - a^4*b^2)*sinh(x)^3)]","B",0
97,1,860,0,0.436713," ","integrate(cosh(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{{\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + {\left(a^{4} - a^{2} b^{2}\right)} \sinh\left(x\right)^{4} - a^{4} + a^{2} b^{2} + 4 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x \cosh\left(x\right)^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{3} - 4 \, {\left(a^{3} b - a b^{3} - {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x - 6 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)\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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 4 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right) + 4 \, {\left(a^{3} b - a b^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x \cosh\left(x\right) - 3 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{5} - a^{3} b^{2}\right)} \sinh\left(x\right)^{2}\right)}}, \frac{{\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + {\left(a^{4} - a^{2} b^{2}\right)} \sinh\left(x\right)^{4} - a^{4} + a^{2} b^{2} + 4 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x \cosh\left(x\right)^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{3} - 4 \, {\left(a^{3} b - a b^{3} - {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x - 6 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 16 \, {\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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 4 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right) + 4 \, {\left(a^{3} b - a b^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} x \cosh\left(x\right) - 3 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} - a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{5} - a^{3} b^{2}\right)} \sinh\left(x\right)^{2}\right)}}\right]"," ",0,"[1/8*((a^4 - a^2*b^2)*cosh(x)^4 + (a^4 - a^2*b^2)*sinh(x)^4 - a^4 + a^2*b^2 + 4*(a^4 + a^2*b^2 - 2*b^4)*x*cosh(x)^2 - 4*(a^3*b - a*b^3)*cosh(x)^3 - 4*(a^3*b - a*b^3 - (a^4 - a^2*b^2)*cosh(x))*sinh(x)^3 + 2*(3*(a^4 - a^2*b^2)*cosh(x)^2 + 2*(a^4 + a^2*b^2 - 2*b^4)*x - 6*(a^3*b - a*b^3)*cosh(x))*sinh(x)^2 - 8*(b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 4*(a^3*b - a*b^3)*cosh(x) + 4*(a^3*b - a*b^3 + (a^4 - a^2*b^2)*cosh(x)^3 + 2*(a^4 + a^2*b^2 - 2*b^4)*x*cosh(x) - 3*(a^3*b - a*b^3)*cosh(x)^2)*sinh(x))/((a^5 - a^3*b^2)*cosh(x)^2 + 2*(a^5 - a^3*b^2)*cosh(x)*sinh(x) + (a^5 - a^3*b^2)*sinh(x)^2), 1/8*((a^4 - a^2*b^2)*cosh(x)^4 + (a^4 - a^2*b^2)*sinh(x)^4 - a^4 + a^2*b^2 + 4*(a^4 + a^2*b^2 - 2*b^4)*x*cosh(x)^2 - 4*(a^3*b - a*b^3)*cosh(x)^3 - 4*(a^3*b - a*b^3 - (a^4 - a^2*b^2)*cosh(x))*sinh(x)^3 + 2*(3*(a^4 - a^2*b^2)*cosh(x)^2 + 2*(a^4 + a^2*b^2 - 2*b^4)*x - 6*(a^3*b - a*b^3)*cosh(x))*sinh(x)^2 + 16*(b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 4*(a^3*b - a*b^3)*cosh(x) + 4*(a^3*b - a*b^3 + (a^4 - a^2*b^2)*cosh(x)^3 + 2*(a^4 + a^2*b^2 - 2*b^4)*x*cosh(x) - 3*(a^3*b - a*b^3)*cosh(x)^2)*sinh(x))/((a^5 - a^3*b^2)*cosh(x)^2 + 2*(a^5 - a^3*b^2)*cosh(x)*sinh(x) + (a^5 - a^3*b^2)*sinh(x)^2)]","B",0
98,1,430,0,0.430491," ","integrate(cosh(x)/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{a^{3} - a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} x \cosh\left(x\right) - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - {\left(a^{3} - a b^{2}\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{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} x - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{2 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right) + {\left(a^{4} - a^{2} b^{2}\right)} \sinh\left(x\right)\right)}}, -\frac{a^{3} - a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} x \cosh\left(x\right) - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - {\left(a^{3} - a b^{2}\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{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} x - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{2 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right) + {\left(a^{4} - a^{2} b^{2}\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/2*(a^3 - a*b^2 + 2*(a^2*b - b^3)*x*cosh(x) - (a^3 - a*b^2)*cosh(x)^2 - (a^3 - a*b^2)*sinh(x)^2 + 2*(b^2*cosh(x) + b^2*sinh(x))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) - 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 2*((a^2*b - b^3)*x - (a^3 - a*b^2)*cosh(x))*sinh(x))/((a^4 - a^2*b^2)*cosh(x) + (a^4 - a^2*b^2)*sinh(x)), -1/2*(a^3 - a*b^2 + 2*(a^2*b - b^3)*x*cosh(x) - (a^3 - a*b^2)*cosh(x)^2 - (a^3 - a*b^2)*sinh(x)^2 + 4*(b^2*cosh(x) + b^2*sinh(x))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + 2*((a^2*b - b^3)*x - (a^3 - a*b^2)*cosh(x))*sinh(x))/((a^4 - a^2*b^2)*cosh(x) + (a^4 - a^2*b^2)*sinh(x))]","B",0
99,1,165,0,0.408446," ","integrate(sech(x)/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right)}{a^{2} - b^{2}}, -\frac{2 \, \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{\sqrt{a^{2} - b^{2}}}\right]"," ",0,"[-sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) - 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a))/(a^2 - b^2), -2*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2))/sqrt(a^2 - b^2)]","A",0
100,1,219,0,0.442174," ","integrate(sech(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} a \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) - 2 \, {\left(a^{2} - b^{2}\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{a^{2} b - b^{3}}, \frac{2 \, {\left(\sqrt{a^{2} - b^{2}} a \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + {\left(a^{2} - b^{2}\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)\right)}}{a^{2} b - b^{3}}\right]"," ",0,"[-(sqrt(-a^2 + b^2)*a*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) - 2*(a^2 - b^2)*arctan(cosh(x) + sinh(x)))/(a^2*b - b^3), 2*(sqrt(a^2 - b^2)*a*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + (a^2 - b^2)*arctan(cosh(x) + sinh(x)))/(a^2*b - b^3)]","A",0
101,1,504,0,0.449243," ","integrate(sech(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{2 \, a^{2} b - 2 \, b^{3} + {\left(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}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + 2 \, {\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)} \arctan\left(\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}}, -\frac{2 \, {\left(a^{2} b - b^{3} + {\left(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}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\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)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\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}}\right]"," ",0,"[-(2*a^2*b - 2*b^3 + (a^2*cosh(x)^2 + 2*a^2*cosh(x)*sinh(x) + a^2*sinh(x)^2 + a^2)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) - 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + 2*(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)*arctan(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), -2*(a^2*b - b^3 + (a^2*cosh(x)^2 + 2*a^2*cosh(x)*sinh(x) + a^2*sinh(x)^2 + a^2)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + (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)*arctan(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
102,1,1444,0,0.526825," ","integrate(sech(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{3} b - 2 \, a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \sinh\left(x\right)^{3} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{2} + {\left(2 \, a^{3} b - 2 \, a b^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + 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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \sinh\left(x\right)^{4} + 2 \, a^{4} - a^{2} b^{2} - b^{4} + 2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4} + 3 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\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} b^{2} - b^{4}\right)} \cosh\left(x\right) - {\left(a^{2} b^{2} - b^{4} - 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} - 4 \, {\left(a^{3} b - a b^{3}\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)}, \frac{2 \, a^{3} b - 2 \, a b^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \sinh\left(x\right)^{3} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{2} + {\left(2 \, a^{3} b - 2 \, a b^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 2 \, {\left(a^{3} \cosh\left(x\right)^{4} + 4 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{3} \sinh\left(x\right)^{4} + 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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \sinh\left(x\right)^{4} + 2 \, a^{4} - a^{2} b^{2} - b^{4} + 2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4} + 3 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\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} b^{2} - b^{4}\right)} \cosh\left(x\right) - {\left(a^{2} b^{2} - b^{4} - 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} - 4 \, {\left(a^{3} b - a b^{3}\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)}\right]"," ",0,"[(2*a^3*b - 2*a*b^3 + (a^2*b^2 - b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*sinh(x)^3 + 2*(a^3*b - a*b^3)*cosh(x)^2 + (2*a^3*b - 2*a*b^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^2 - (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))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + ((2*a^4 - a^2*b^2 - b^4)*cosh(x)^4 + 4*(2*a^4 - a^2*b^2 - b^4)*cosh(x)*sinh(x)^3 + (2*a^4 - a^2*b^2 - b^4)*sinh(x)^4 + 2*a^4 - a^2*b^2 - b^4 + 2*(2*a^4 - a^2*b^2 - b^4)*cosh(x)^2 + 2*(2*a^4 - a^2*b^2 - b^4 + 3*(2*a^4 - a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^4 - a^2*b^2 - b^4)*cosh(x)^3 + (2*a^4 - a^2*b^2 - b^4)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (a^2*b^2 - b^4)*cosh(x) - (a^2*b^2 - b^4 - 3*(a^2*b^2 - b^4)*cosh(x)^2 - 4*(a^3*b - a*b^3)*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)), (2*a^3*b - 2*a*b^3 + (a^2*b^2 - b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*sinh(x)^3 + 2*(a^3*b - a*b^3)*cosh(x)^2 + (2*a^3*b - 2*a*b^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^2 + 2*(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))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + ((2*a^4 - a^2*b^2 - b^4)*cosh(x)^4 + 4*(2*a^4 - a^2*b^2 - b^4)*cosh(x)*sinh(x)^3 + (2*a^4 - a^2*b^2 - b^4)*sinh(x)^4 + 2*a^4 - a^2*b^2 - b^4 + 2*(2*a^4 - a^2*b^2 - b^4)*cosh(x)^2 + 2*(2*a^4 - a^2*b^2 - b^4 + 3*(2*a^4 - a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^4 - a^2*b^2 - b^4)*cosh(x)^3 + (2*a^4 - a^2*b^2 - b^4)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (a^2*b^2 - b^4)*cosh(x) - (a^2*b^2 - b^4 - 3*(a^2*b^2 - b^4)*cosh(x)^2 - 4*(a^3*b - a*b^3)*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
103,1,686,0,0.427468," ","integrate(tanh(x)^6/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{12 \, x \cosh\left(x\right)^{8} + 12 \, x \sinh\left(x\right)^{8} + 3 \, {\left(32 \, x \cosh\left(x\right) + 5\right)} \sinh\left(x\right)^{7} + 48 \, {\left(x + 1\right)} \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{7} + 3 \, {\left(112 \, x \cosh\left(x\right)^{2} + 16 \, x + 35 \, \cosh\left(x\right) + 16\right)} \sinh\left(x\right)^{6} + 3 \, {\left(224 \, x \cosh\left(x\right)^{3} + 96 \, {\left(x + 1\right)} \cosh\left(x\right) + 105 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{5} + 24 \, {\left(3 \, x + 4\right)} \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{5} + 3 \, {\left(280 \, x \cosh\left(x\right)^{4} + 240 \, {\left(x + 1\right)} \cosh\left(x\right)^{2} + 175 \, \cosh\left(x\right)^{3} + 24 \, x - 15 \, \cosh\left(x\right) + 32\right)} \sinh\left(x\right)^{4} + 3 \, {\left(224 \, x \cosh\left(x\right)^{5} + 320 \, {\left(x + 1\right)} \cosh\left(x\right)^{3} + 175 \, \cosh\left(x\right)^{4} + 32 \, {\left(3 \, x + 4\right)} \cosh\left(x\right) - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{3} + 16 \, {\left(3 \, x + 5\right)} \cosh\left(x\right)^{2} + 9 \, \cosh\left(x\right)^{3} + {\left(336 \, x \cosh\left(x\right)^{6} + 720 \, {\left(x + 1\right)} \cosh\left(x\right)^{4} + 315 \, \cosh\left(x\right)^{5} + 144 \, {\left(3 \, x + 4\right)} \cosh\left(x\right)^{2} - 90 \, \cosh\left(x\right)^{3} + 48 \, x + 27 \, \cosh\left(x\right) + 80\right)} \sinh\left(x\right)^{2} - 9 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + {\left(96 \, x \cosh\left(x\right)^{7} + 288 \, {\left(x + 1\right)} \cosh\left(x\right)^{5} + 105 \, \cosh\left(x\right)^{6} + 96 \, {\left(3 \, x + 4\right)} \cosh\left(x\right)^{3} - 45 \, \cosh\left(x\right)^{4} + 32 \, {\left(3 \, x + 5\right)} \cosh\left(x\right) + 27 \, \cosh\left(x\right)^{2} - 15\right)} \sinh\left(x\right) + 12 \, x - 15 \, \cosh\left(x\right) + 32}{12 \, {\left(a \cosh\left(x\right)^{8} + 8 \, a \cosh\left(x\right) \sinh\left(x\right)^{7} + a \sinh\left(x\right)^{8} + 4 \, a \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, a \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a \cosh\left(x\right)^{4} + 30 \, a \cosh\left(x\right)^{2} + 3 \, a\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a \cosh\left(x\right)^{5} + 10 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, a \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a \cosh\left(x\right)^{6} + 15 \, a \cosh\left(x\right)^{4} + 9 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a \cosh\left(x\right)^{7} + 3 \, a \cosh\left(x\right)^{5} + 3 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)}}"," ",0,"1/12*(12*x*cosh(x)^8 + 12*x*sinh(x)^8 + 3*(32*x*cosh(x) + 5)*sinh(x)^7 + 48*(x + 1)*cosh(x)^6 + 15*cosh(x)^7 + 3*(112*x*cosh(x)^2 + 16*x + 35*cosh(x) + 16)*sinh(x)^6 + 3*(224*x*cosh(x)^3 + 96*(x + 1)*cosh(x) + 105*cosh(x)^2 - 3)*sinh(x)^5 + 24*(3*x + 4)*cosh(x)^4 - 9*cosh(x)^5 + 3*(280*x*cosh(x)^4 + 240*(x + 1)*cosh(x)^2 + 175*cosh(x)^3 + 24*x - 15*cosh(x) + 32)*sinh(x)^4 + 3*(224*x*cosh(x)^5 + 320*(x + 1)*cosh(x)^3 + 175*cosh(x)^4 + 32*(3*x + 4)*cosh(x) - 30*cosh(x)^2 + 3)*sinh(x)^3 + 16*(3*x + 5)*cosh(x)^2 + 9*cosh(x)^3 + (336*x*cosh(x)^6 + 720*(x + 1)*cosh(x)^4 + 315*cosh(x)^5 + 144*(3*x + 4)*cosh(x)^2 - 90*cosh(x)^3 + 48*x + 27*cosh(x) + 80)*sinh(x)^2 - 9*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + (96*x*cosh(x)^7 + 288*(x + 1)*cosh(x)^5 + 105*cosh(x)^6 + 96*(3*x + 4)*cosh(x)^3 - 45*cosh(x)^4 + 32*(3*x + 5)*cosh(x) + 27*cosh(x)^2 - 15)*sinh(x) + 12*x - 15*cosh(x) + 32)/(a*cosh(x)^8 + 8*a*cosh(x)*sinh(x)^7 + a*sinh(x)^8 + 4*a*cosh(x)^6 + 4*(7*a*cosh(x)^2 + a)*sinh(x)^6 + 8*(7*a*cosh(x)^3 + 3*a*cosh(x))*sinh(x)^5 + 6*a*cosh(x)^4 + 2*(35*a*cosh(x)^4 + 30*a*cosh(x)^2 + 3*a)*sinh(x)^4 + 8*(7*a*cosh(x)^5 + 10*a*cosh(x)^3 + 3*a*cosh(x))*sinh(x)^3 + 4*a*cosh(x)^2 + 4*(7*a*cosh(x)^6 + 15*a*cosh(x)^4 + 9*a*cosh(x)^2 + a)*sinh(x)^2 + 8*(a*cosh(x)^7 + 3*a*cosh(x)^5 + 3*a*cosh(x)^3 + a*cosh(x))*sinh(x) + a)","B",0
104,1,437,0,0.404054," ","integrate(tanh(x)^5/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{3 \, x \cosh\left(x\right)^{6} + 3 \, x \sinh\left(x\right)^{6} + 6 \, {\left(3 \, x \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{5} + 3 \, {\left(3 \, x - 2\right)} \cosh\left(x\right)^{4} - 6 \, \cosh\left(x\right)^{5} + 3 \, {\left(15 \, x \cosh\left(x\right)^{2} + 3 \, x - 10 \, \cosh\left(x\right) - 2\right)} \sinh\left(x\right)^{4} + 4 \, {\left(15 \, x \cosh\left(x\right)^{3} + 3 \, {\left(3 \, x - 2\right)} \cosh\left(x\right) - 15 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{3} + 3 \, {\left(3 \, x - 2\right)} \cosh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{3} + 3 \, {\left(15 \, x \cosh\left(x\right)^{4} + 6 \, {\left(3 \, x - 2\right)} \cosh\left(x\right)^{2} - 20 \, \cosh\left(x\right)^{3} + 3 \, x - 4 \, \cosh\left(x\right) - 2\right)} \sinh\left(x\right)^{2} - 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)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 6 \, {\left(3 \, x \cosh\left(x\right)^{5} + 2 \, {\left(3 \, x - 2\right)} \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)^{4} + {\left(3 \, x - 2\right)} \cosh\left(x\right) - 2 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) + 3 \, x - 6 \, \cosh\left(x\right)}{3 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} + 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} + 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} + 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)}}"," ",0,"-1/3*(3*x*cosh(x)^6 + 3*x*sinh(x)^6 + 6*(3*x*cosh(x) - 1)*sinh(x)^5 + 3*(3*x - 2)*cosh(x)^4 - 6*cosh(x)^5 + 3*(15*x*cosh(x)^2 + 3*x - 10*cosh(x) - 2)*sinh(x)^4 + 4*(15*x*cosh(x)^3 + 3*(3*x - 2)*cosh(x) - 15*cosh(x)^2 - 1)*sinh(x)^3 + 3*(3*x - 2)*cosh(x)^2 - 4*cosh(x)^3 + 3*(15*x*cosh(x)^4 + 6*(3*x - 2)*cosh(x)^2 - 20*cosh(x)^3 + 3*x - 4*cosh(x) - 2)*sinh(x)^2 - 3*(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*cosh(x)/(cosh(x) - sinh(x))) + 6*(3*x*cosh(x)^5 + 2*(3*x - 2)*cosh(x)^3 - 5*cosh(x)^4 + (3*x - 2)*cosh(x) - 2*cosh(x)^2 - 1)*sinh(x) + 3*x - 6*cosh(x))/(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 + 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 + a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 + 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 + 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 + 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) + a)","B",0
105,1,210,0,0.398389," ","integrate(tanh(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{x \cosh\left(x\right)^{4} + x \sinh\left(x\right)^{4} + {\left(4 \, x \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{3} + 2 \, {\left(x + 1\right)} \cosh\left(x\right)^{2} + \cosh\left(x\right)^{3} + {\left(6 \, x \cosh\left(x\right)^{2} + 2 \, x + 3 \, \cosh\left(x\right) + 2\right)} \sinh\left(x\right)^{2} - {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + {\left(4 \, x \cosh\left(x\right)^{3} + 4 \, {\left(x + 1\right)} \cosh\left(x\right) + 3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) + x - \cosh\left(x\right) + 2}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a}"," ",0,"(x*cosh(x)^4 + x*sinh(x)^4 + (4*x*cosh(x) + 1)*sinh(x)^3 + 2*(x + 1)*cosh(x)^2 + cosh(x)^3 + (6*x*cosh(x)^2 + 2*x + 3*cosh(x) + 2)*sinh(x)^2 - (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + (4*x*cosh(x)^3 + 4*(x + 1)*cosh(x) + 3*cosh(x)^2 - 1)*sinh(x) + x - cosh(x) + 2)/(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a)*sinh(x)^2 + 4*(a*cosh(x)^3 + a*cosh(x))*sinh(x) + a)","B",0
106,1,85,0,0.402214," ","integrate(tanh(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{x \cosh\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 \, {\left(x \cosh\left(x\right) - 1\right)} \sinh\left(x\right) + x - 2 \, \cosh\left(x\right)}{a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a}"," ",0,"-(x*cosh(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*cosh(x) - 1)*sinh(x) + x - 2*cosh(x))/(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)","B",0
107,1,14,0,0.386359," ","integrate(tanh(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","\frac{x - 2 \, \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{a}"," ",0,"(x - 2*arctan(cosh(x) + sinh(x)))/a","A",0
108,1,16,0,0.421190," ","integrate(tanh(x)/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{x - 2 \, \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right)}{a}"," ",0,"-(x - 2*log(cosh(x) + sinh(x) + 1))/a","A",0
109,1,136,0,0.393375," ","integrate(coth(x)/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, x \cosh\left(x\right)^{2} + 2 \, x \sinh\left(x\right)^{2} + 2 \, {\left(2 \, x - 1\right)} \cosh\left(x\right) - 3 \, {\left(\cosh\left(x\right)^{2} + 2 \, {\left(\cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left(\cosh\left(x\right)^{2} + 2 \, {\left(\cosh\left(x\right) + 1\right)} \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(2 \, x \cosh\left(x\right) + 2 \, x - 1\right)} \sinh\left(x\right) + 2 \, x}{2 \, {\left(a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a\right)}}"," ",0,"-1/2*(2*x*cosh(x)^2 + 2*x*sinh(x)^2 + 2*(2*x - 1)*cosh(x) - 3*(cosh(x)^2 + 2*(cosh(x) + 1)*sinh(x) + sinh(x)^2 + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) + 1) - (cosh(x)^2 + 2*(cosh(x) + 1)*sinh(x) + sinh(x)^2 + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) - 1) + 2*(2*x*cosh(x) + 2*x - 1)*sinh(x) + 2*x)/(a*cosh(x)^2 + a*sinh(x)^2 + 2*a*cosh(x) + 2*(a*cosh(x) + a)*sinh(x) + a)","B",0
110,1,46,0,0.396942," ","integrate(coth(x)^2/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, \cosh\left(x\right)^{2} - {\left({\left(3 \, x + 4\right)} \cosh\left(x\right) + 3 \, x + 4\right)} \sinh\left(x\right) + 2 \, \sinh\left(x\right)^{2} + \cosh\left(x\right)}{3 \, {\left(a \cosh\left(x\right) + a\right)} \sinh\left(x\right)}"," ",0,"-1/3*(2*cosh(x)^2 - ((3*x + 4)*cosh(x) + 3*x + 4)*sinh(x) + 2*sinh(x)^2 + cosh(x))/((a*cosh(x) + a)*sinh(x))","A",0
111,1,773,0,0.406810," ","integrate(coth(x)^3/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{8 \, x \cosh\left(x\right)^{6} + 8 \, x \sinh\left(x\right)^{6} + 2 \, {\left(8 \, x - 5\right)} \cosh\left(x\right)^{5} + 2 \, {\left(24 \, x \cosh\left(x\right) + 8 \, x - 5\right)} \sinh\left(x\right)^{5} - 4 \, {\left(2 \, x - 3\right)} \cosh\left(x\right)^{4} + 2 \, {\left(60 \, x \cosh\left(x\right)^{2} + 5 \, {\left(8 \, x - 5\right)} \cosh\left(x\right) - 4 \, x + 6\right)} \sinh\left(x\right)^{4} - 4 \, {\left(8 \, x - 7\right)} \cosh\left(x\right)^{3} + 4 \, {\left(40 \, x \cosh\left(x\right)^{3} + 5 \, {\left(8 \, x - 5\right)} \cosh\left(x\right)^{2} - 4 \, {\left(2 \, x - 3\right)} \cosh\left(x\right) - 8 \, x + 7\right)} \sinh\left(x\right)^{3} - 4 \, {\left(2 \, x - 3\right)} \cosh\left(x\right)^{2} + 4 \, {\left(30 \, x \cosh\left(x\right)^{4} + 5 \, {\left(8 \, x - 5\right)} \cosh\left(x\right)^{3} - 6 \, {\left(2 \, x - 3\right)} \cosh\left(x\right)^{2} - 3 \, {\left(8 \, x - 7\right)} \cosh\left(x\right) - 2 \, x + 3\right)} \sinh\left(x\right)^{2} + 2 \, {\left(8 \, x - 5\right)} \cosh\left(x\right) - 11 \, {\left(\cosh\left(x\right)^{6} + 2 \, {\left(3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 2 \, \cosh\left(x\right)^{5} + {\left(15 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{4} - \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{3} - 4 \, \cosh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 20 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - 12 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - 5 \, {\left(\cosh\left(x\right)^{6} + 2 \, {\left(3 \, \cosh\left(x\right) + 1\right)} \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 2 \, \cosh\left(x\right)^{5} + {\left(15 \, \cosh\left(x\right)^{2} + 10 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{4} - \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{3} - 4 \, \cosh\left(x\right)^{3} + {\left(15 \, \cosh\left(x\right)^{4} + 20 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - 12 \, \cosh\left(x\right) - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{4} - 2 \, \cosh\left(x\right)^{3} - 6 \, \cosh\left(x\right)^{2} - \cosh\left(x\right) + 1\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right) + 1\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(24 \, x \cosh\left(x\right)^{5} + 5 \, {\left(8 \, x - 5\right)} \cosh\left(x\right)^{4} - 8 \, {\left(2 \, x - 3\right)} \cosh\left(x\right)^{3} - 6 \, {\left(8 \, x - 7\right)} \cosh\left(x\right)^{2} - 4 \, {\left(2 \, x - 3\right)} \cosh\left(x\right) + 8 \, x - 5\right)} \sinh\left(x\right) + 8 \, x}{8 \, {\left(a \cosh\left(x\right)^{6} + a \sinh\left(x\right)^{6} + 2 \, a \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{5} - a \cosh\left(x\right)^{4} + {\left(15 \, a \cosh\left(x\right)^{2} + 10 \, a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{4} - 4 \, a \cosh\left(x\right)^{3} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} + 5 \, a \cosh\left(x\right)^{2} - a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{3} - a \cosh\left(x\right)^{2} + {\left(15 \, a \cosh\left(x\right)^{4} + 20 \, a \cosh\left(x\right)^{3} - 6 \, a \cosh\left(x\right)^{2} - 12 \, a \cosh\left(x\right) - a\right)} \sinh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + 2 \, {\left(3 \, a \cosh\left(x\right)^{5} + 5 \, a \cosh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{3} - 6 \, a \cosh\left(x\right)^{2} - a \cosh\left(x\right) + a\right)} \sinh\left(x\right) + a\right)}}"," ",0,"-1/8*(8*x*cosh(x)^6 + 8*x*sinh(x)^6 + 2*(8*x - 5)*cosh(x)^5 + 2*(24*x*cosh(x) + 8*x - 5)*sinh(x)^5 - 4*(2*x - 3)*cosh(x)^4 + 2*(60*x*cosh(x)^2 + 5*(8*x - 5)*cosh(x) - 4*x + 6)*sinh(x)^4 - 4*(8*x - 7)*cosh(x)^3 + 4*(40*x*cosh(x)^3 + 5*(8*x - 5)*cosh(x)^2 - 4*(2*x - 3)*cosh(x) - 8*x + 7)*sinh(x)^3 - 4*(2*x - 3)*cosh(x)^2 + 4*(30*x*cosh(x)^4 + 5*(8*x - 5)*cosh(x)^3 - 6*(2*x - 3)*cosh(x)^2 - 3*(8*x - 7)*cosh(x) - 2*x + 3)*sinh(x)^2 + 2*(8*x - 5)*cosh(x) - 11*(cosh(x)^6 + 2*(3*cosh(x) + 1)*sinh(x)^5 + sinh(x)^6 + 2*cosh(x)^5 + (15*cosh(x)^2 + 10*cosh(x) - 1)*sinh(x)^4 - cosh(x)^4 + 4*(5*cosh(x)^3 + 5*cosh(x)^2 - cosh(x) - 1)*sinh(x)^3 - 4*cosh(x)^3 + (15*cosh(x)^4 + 20*cosh(x)^3 - 6*cosh(x)^2 - 12*cosh(x) - 1)*sinh(x)^2 - cosh(x)^2 + 2*(3*cosh(x)^5 + 5*cosh(x)^4 - 2*cosh(x)^3 - 6*cosh(x)^2 - cosh(x) + 1)*sinh(x) + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) + 1) - 5*(cosh(x)^6 + 2*(3*cosh(x) + 1)*sinh(x)^5 + sinh(x)^6 + 2*cosh(x)^5 + (15*cosh(x)^2 + 10*cosh(x) - 1)*sinh(x)^4 - cosh(x)^4 + 4*(5*cosh(x)^3 + 5*cosh(x)^2 - cosh(x) - 1)*sinh(x)^3 - 4*cosh(x)^3 + (15*cosh(x)^4 + 20*cosh(x)^3 - 6*cosh(x)^2 - 12*cosh(x) - 1)*sinh(x)^2 - cosh(x)^2 + 2*(3*cosh(x)^5 + 5*cosh(x)^4 - 2*cosh(x)^3 - 6*cosh(x)^2 - cosh(x) + 1)*sinh(x) + 2*cosh(x) + 1)*log(cosh(x) + sinh(x) - 1) + 2*(24*x*cosh(x)^5 + 5*(8*x - 5)*cosh(x)^4 - 8*(2*x - 3)*cosh(x)^3 - 6*(8*x - 7)*cosh(x)^2 - 4*(2*x - 3)*cosh(x) + 8*x - 5)*sinh(x) + 8*x)/(a*cosh(x)^6 + a*sinh(x)^6 + 2*a*cosh(x)^5 + 2*(3*a*cosh(x) + a)*sinh(x)^5 - a*cosh(x)^4 + (15*a*cosh(x)^2 + 10*a*cosh(x) - a)*sinh(x)^4 - 4*a*cosh(x)^3 + 4*(5*a*cosh(x)^3 + 5*a*cosh(x)^2 - a*cosh(x) - a)*sinh(x)^3 - a*cosh(x)^2 + (15*a*cosh(x)^4 + 20*a*cosh(x)^3 - 6*a*cosh(x)^2 - 12*a*cosh(x) - a)*sinh(x)^2 + 2*a*cosh(x) + 2*(3*a*cosh(x)^5 + 5*a*cosh(x)^4 - 2*a*cosh(x)^3 - 6*a*cosh(x)^2 - a*cosh(x) + a)*sinh(x) + a)","B",0
112,1,151,0,0.384118," ","integrate(coth(x)^4/(a+a*sech(x)),x, algorithm=""fricas"")","-\frac{23 \, \cosh\left(x\right)^{4} - 2 \, {\left(2 \, {\left(15 \, x + 23\right)} \cosh\left(x\right) + 15 \, x + 23\right)} \sinh\left(x\right)^{3} + 23 \, \sinh\left(x\right)^{4} + 16 \, \cosh\left(x\right)^{3} + 2 \, {\left(69 \, \cosh\left(x\right)^{2} + 24 \, \cosh\left(x\right) - 8\right)} \sinh\left(x\right)^{2} - 16 \, \cosh\left(x\right)^{2} - 2 \, {\left(2 \, {\left(15 \, x + 23\right)} \cosh\left(x\right)^{3} + 3 \, {\left(15 \, x + 23\right)} \cosh\left(x\right)^{2} - 2 \, {\left(15 \, x + 23\right)} \cosh\left(x\right) - 45 \, x - 69\right)} \sinh\left(x\right) - 8 \, \cosh\left(x\right) + 25}{30 \, {\left({\left(2 \, a \cosh\left(x\right) + a\right)} \sinh\left(x\right)^{3} + {\left(2 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} - 2 \, a \cosh\left(x\right) - 3 \, a\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/30*(23*cosh(x)^4 - 2*(2*(15*x + 23)*cosh(x) + 15*x + 23)*sinh(x)^3 + 23*sinh(x)^4 + 16*cosh(x)^3 + 2*(69*cosh(x)^2 + 24*cosh(x) - 8)*sinh(x)^2 - 16*cosh(x)^2 - 2*(2*(15*x + 23)*cosh(x)^3 + 3*(15*x + 23)*cosh(x)^2 - 2*(15*x + 23)*cosh(x) - 45*x - 69)*sinh(x) - 8*cosh(x) + 25)/((2*a*cosh(x) + a)*sinh(x)^3 + (2*a*cosh(x)^3 + 3*a*cosh(x)^2 - 2*a*cosh(x) - 3*a)*sinh(x))","B",0
113,1,4077,0,0.511718," ","integrate(tanh(x)^7/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{15 \, b^{6} x \cosh\left(x\right)^{10} + 15 \, b^{6} x \sinh\left(x\right)^{10} - 30 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{9} + 30 \, {\left(5 \, b^{6} x \cosh\left(x\right) - a^{5} b + 3 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sinh\left(x\right)^{9} + 15 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{8} + 15 \, {\left(45 \, b^{6} x \cosh\left(x\right)^{2} + 5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4} - 18 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{8} - 40 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{7} + 40 \, {\left(45 \, b^{6} x \cosh\left(x\right)^{3} - 3 \, a^{5} b + 8 \, a^{3} b^{3} - 6 \, a b^{5} - 27 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 15 \, b^{6} x + 30 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(315 \, b^{6} x \cosh\left(x\right)^{4} + 15 \, b^{6} x + 9 \, a^{4} b^{2} - 21 \, a^{2} b^{4} - 252 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 42 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2} - 28 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} - 4 \, {\left(45 \, a^{5} b - 115 \, a^{3} b^{3} + 99 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(945 \, b^{6} x \cosh\left(x\right)^{5} - 45 \, a^{5} b + 115 \, a^{3} b^{3} - 99 \, a b^{5} - 945 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 210 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} - 210 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 45 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 30 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(315 \, b^{6} x \cosh\left(x\right)^{6} + 15 \, b^{6} x + 9 \, a^{4} b^{2} - 21 \, a^{2} b^{4} - 378 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 105 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} - 140 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 45 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(45 \, a^{5} b - 115 \, a^{3} b^{3} + 99 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 40 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 40 \, {\left(45 \, b^{6} x \cosh\left(x\right)^{7} - 63 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} b + 8 \, a^{3} b^{3} - 6 \, a b^{5} + 21 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{5} - 35 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} - {\left(45 \, a^{5} b - 115 \, a^{3} b^{3} + 99 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 15 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(135 \, b^{6} x \cosh\left(x\right)^{8} - 216 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{7} + 15 \, b^{6} x + 84 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + 6 \, a^{4} b^{2} - 18 \, a^{2} b^{4} - 168 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 90 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} - 8 \, {\left(45 \, a^{5} b - 115 \, a^{3} b^{3} + 99 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 36 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2} - 24 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 30 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right) + 15 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 9 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 21 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 4 \, {\left(63 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 35 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} + 30 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 10 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - 15 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 9 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 21 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 4 \, {\left(63 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 35 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{6} + a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 30 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 10 \, {\left({\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} 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) + 10 \, {\left(15 \, b^{6} x \cosh\left(x\right)^{9} - 27 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{8} + 12 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{7} - 28 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} b + 9 \, a^{3} b^{3} - 9 \, a b^{5} + 18 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(45 \, a^{5} b - 115 \, a^{3} b^{3} + 99 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(5 \, b^{6} x + 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cosh\left(x\right)^{3} - 12 \, {\left(3 \, a^{5} b - 8 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b^{6} x + 2 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{15 \, {\left(a b^{6} \cosh\left(x\right)^{10} + 10 \, a b^{6} \cosh\left(x\right) \sinh\left(x\right)^{9} + a b^{6} \sinh\left(x\right)^{10} + 5 \, a b^{6} \cosh\left(x\right)^{8} + 10 \, a b^{6} \cosh\left(x\right)^{6} + 10 \, a b^{6} \cosh\left(x\right)^{4} + 5 \, a b^{6} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, a b^{6} \cosh\left(x\right)^{2} + a b^{6}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, a b^{6} \cosh\left(x\right)^{3} + a b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + a b^{6} + 10 \, {\left(21 \, a b^{6} \cosh\left(x\right)^{4} + 14 \, a b^{6} \cosh\left(x\right)^{2} + a b^{6}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, a b^{6} \cosh\left(x\right)^{5} + 70 \, a b^{6} \cosh\left(x\right)^{3} + 15 \, a b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, a b^{6} \cosh\left(x\right)^{6} + 35 \, a b^{6} \cosh\left(x\right)^{4} + 15 \, a b^{6} \cosh\left(x\right)^{2} + a b^{6}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, a b^{6} \cosh\left(x\right)^{7} + 7 \, a b^{6} \cosh\left(x\right)^{5} + 5 \, a b^{6} \cosh\left(x\right)^{3} + a b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, a b^{6} \cosh\left(x\right)^{8} + 28 \, a b^{6} \cosh\left(x\right)^{6} + 30 \, a b^{6} \cosh\left(x\right)^{4} + 12 \, a b^{6} \cosh\left(x\right)^{2} + a b^{6}\right)} \sinh\left(x\right)^{2} + 10 \, {\left(a b^{6} \cosh\left(x\right)^{9} + 4 \, a b^{6} \cosh\left(x\right)^{7} + 6 \, a b^{6} \cosh\left(x\right)^{5} + 4 \, a b^{6} \cosh\left(x\right)^{3} + a b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/15*(15*b^6*x*cosh(x)^10 + 15*b^6*x*sinh(x)^10 - 30*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^9 + 30*(5*b^6*x*cosh(x) - a^5*b + 3*a^3*b^3 - 3*a*b^5)*sinh(x)^9 + 15*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^8 + 15*(45*b^6*x*cosh(x)^2 + 5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4 - 18*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x))*sinh(x)^8 - 40*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^7 + 40*(45*b^6*x*cosh(x)^3 - 3*a^5*b + 8*a^3*b^3 - 6*a*b^5 - 27*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^2 + 3*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x))*sinh(x)^7 + 15*b^6*x + 30*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^6 + 10*(315*b^6*x*cosh(x)^4 + 15*b^6*x + 9*a^4*b^2 - 21*a^2*b^4 - 252*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^3 + 42*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^2 - 28*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x))*sinh(x)^6 - 4*(45*a^5*b - 115*a^3*b^3 + 99*a*b^5)*cosh(x)^5 + 4*(945*b^6*x*cosh(x)^5 - 45*a^5*b + 115*a^3*b^3 - 99*a*b^5 - 945*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^4 + 210*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^3 - 210*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^2 + 45*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x))*sinh(x)^5 + 30*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^4 + 10*(315*b^6*x*cosh(x)^6 + 15*b^6*x + 9*a^4*b^2 - 21*a^2*b^4 - 378*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^5 + 105*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^4 - 140*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^3 + 45*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^2 - 2*(45*a^5*b - 115*a^3*b^3 + 99*a*b^5)*cosh(x))*sinh(x)^4 - 40*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^3 + 40*(45*b^6*x*cosh(x)^7 - 63*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^6 - 3*a^5*b + 8*a^3*b^3 - 6*a*b^5 + 21*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^5 - 35*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^4 + 15*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^3 - (45*a^5*b - 115*a^3*b^3 + 99*a*b^5)*cosh(x)^2 + 3*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x))*sinh(x)^3 + 15*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^2 + 5*(135*b^6*x*cosh(x)^8 - 216*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^7 + 15*b^6*x + 84*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^6 + 6*a^4*b^2 - 18*a^2*b^4 - 168*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^5 + 90*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^4 - 8*(45*a^5*b - 115*a^3*b^3 + 99*a*b^5)*cosh(x)^3 + 36*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^2 - 24*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x))*sinh(x)^2 - 30*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x) + 15*((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^10 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)*sinh(x)^9 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sinh(x)^10 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^8 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 9*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^8 + 40*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x)^7 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^6 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 21*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 14*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 4*(63*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^5 + 70*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x)^5 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 10*(21*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 35*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^4 + 40*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^7 + 7*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^5 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x)^3 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2 + 5*(9*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^8 + 28*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 + 30*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^4 + 12*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^2)*sinh(x)^2 + 10*((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^9 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^7 + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^5 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cosh(x))*sinh(x))*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - 15*((a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^10 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)*sinh(x)^9 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4)*sinh(x)^10 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^8 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 + 9*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^2)*sinh(x)^8 + 40*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x))*sinh(x)^7 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^6 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 + 21*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^4 + 14*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^2)*sinh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 + 4*(63*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^5 + 70*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^3 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x))*sinh(x)^5 + 10*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^4 + 10*(21*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 + 35*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^4 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^2)*sinh(x)^4 + 40*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^7 + 7*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^5 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x))*sinh(x)^3 + 5*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^2 + 5*(9*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^8 + 28*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^6 + a^6 - 3*a^4*b^2 + 3*a^2*b^4 + 30*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^4 + 12*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^2)*sinh(x)^2 + 10*((a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^9 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^7 + 6*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^5 + 4*(a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x)^3 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4)*cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 10*(15*b^6*x*cosh(x)^9 - 27*(a^5*b - 3*a^3*b^3 + 3*a*b^5)*cosh(x)^8 + 12*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x)^7 - 28*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^6 - 3*a^5*b + 9*a^3*b^3 - 9*a*b^5 + 18*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^5 - 2*(45*a^5*b - 115*a^3*b^3 + 99*a*b^5)*cosh(x)^4 + 12*(5*b^6*x + 3*a^4*b^2 - 7*a^2*b^4)*cosh(x)^3 - 12*(3*a^5*b - 8*a^3*b^3 + 6*a*b^5)*cosh(x)^2 + 3*(5*b^6*x + 2*a^4*b^2 - 6*a^2*b^4)*cosh(x))*sinh(x))/(a*b^6*cosh(x)^10 + 10*a*b^6*cosh(x)*sinh(x)^9 + a*b^6*sinh(x)^10 + 5*a*b^6*cosh(x)^8 + 10*a*b^6*cosh(x)^6 + 10*a*b^6*cosh(x)^4 + 5*a*b^6*cosh(x)^2 + 5*(9*a*b^6*cosh(x)^2 + a*b^6)*sinh(x)^8 + 40*(3*a*b^6*cosh(x)^3 + a*b^6*cosh(x))*sinh(x)^7 + a*b^6 + 10*(21*a*b^6*cosh(x)^4 + 14*a*b^6*cosh(x)^2 + a*b^6)*sinh(x)^6 + 4*(63*a*b^6*cosh(x)^5 + 70*a*b^6*cosh(x)^3 + 15*a*b^6*cosh(x))*sinh(x)^5 + 10*(21*a*b^6*cosh(x)^6 + 35*a*b^6*cosh(x)^4 + 15*a*b^6*cosh(x)^2 + a*b^6)*sinh(x)^4 + 40*(3*a*b^6*cosh(x)^7 + 7*a*b^6*cosh(x)^5 + 5*a*b^6*cosh(x)^3 + a*b^6*cosh(x))*sinh(x)^3 + 5*(9*a*b^6*cosh(x)^8 + 28*a*b^6*cosh(x)^6 + 30*a*b^6*cosh(x)^4 + 12*a*b^6*cosh(x)^2 + a*b^6)*sinh(x)^2 + 10*(a*b^6*cosh(x)^9 + 4*a*b^6*cosh(x)^7 + 6*a*b^6*cosh(x)^5 + 4*a*b^6*cosh(x)^3 + a*b^6*cosh(x))*sinh(x))","B",0
114,1,4914,0,0.745908," ","integrate(tanh(x)^6/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{12 \, b^{5} x \cosh\left(x\right)^{8} + 12 \, b^{5} x \sinh\left(x\right)^{8} - 3 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(32 \, b^{5} x \cosh\left(x\right) - 4 \, a^{3} b^{2} + 9 \, a b^{4}\right)} \sinh\left(x\right)^{7} + 24 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 3 \, {\left(112 \, b^{5} x \cosh\left(x\right)^{2} + 16 \, b^{5} x - 8 \, a^{4} b + 24 \, a^{2} b^{3} - 7 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} + 12 \, b^{5} x - 3 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(224 \, b^{5} x \cosh\left(x\right)^{3} - 4 \, a^{3} b^{2} + a b^{4} - 21 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 48 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 24 \, a^{4} b + 56 \, a^{2} b^{3} + 24 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(280 \, b^{5} x \cosh\left(x\right)^{4} + 24 \, b^{5} x - 24 \, a^{4} b + 56 \, a^{2} b^{3} - 35 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 120 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 5 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 3 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(224 \, b^{5} x \cosh\left(x\right)^{5} + 4 \, a^{3} b^{2} - a b^{4} - 35 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 160 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - 10 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} + 32 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(6 \, b^{5} x - 9 \, a^{4} b + 19 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + {\left(336 \, b^{5} x \cosh\left(x\right)^{6} + 48 \, b^{5} x - 63 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{5} - 72 \, a^{4} b + 152 \, a^{2} b^{3} + 360 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} + 144 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 9 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 12 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} + 7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 6 \, a^{2} b^{2} + 3 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 9 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) - 3 \, {\left({\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 6 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(24 \, a^{5} - 60 \, a^{3} b^{2} + 45 \, a b^{4} + 35 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 3 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right) + {\left(96 \, b^{5} x \cosh\left(x\right)^{7} - 21 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 144 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 12 \, a^{3} b^{2} - 27 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{4} + 96 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 9 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} + 16 \, {\left(6 \, b^{5} x - 9 \, a^{4} b + 19 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{12 \, {\left(a b^{5} \cosh\left(x\right)^{8} + 8 \, a b^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{5} \sinh\left(x\right)^{8} + 4 \, a b^{5} \cosh\left(x\right)^{6} + 6 \, a b^{5} \cosh\left(x\right)^{4} + 4 \, a b^{5} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{2} + a b^{5}\right)} \sinh\left(x\right)^{6} + a b^{5} + 8 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{3} + 3 \, a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b^{5} \cosh\left(x\right)^{4} + 30 \, a b^{5} \cosh\left(x\right)^{2} + 3 \, a b^{5}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{5} + 10 \, a b^{5} \cosh\left(x\right)^{3} + 3 \, a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{6} + 15 \, a b^{5} \cosh\left(x\right)^{4} + 9 \, a b^{5} \cosh\left(x\right)^{2} + a b^{5}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a b^{5} \cosh\left(x\right)^{7} + 3 \, a b^{5} \cosh\left(x\right)^{5} + 3 \, a b^{5} \cosh\left(x\right)^{3} + a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{12 \, b^{5} x \cosh\left(x\right)^{8} + 12 \, b^{5} x \sinh\left(x\right)^{8} - 3 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(32 \, b^{5} x \cosh\left(x\right) - 4 \, a^{3} b^{2} + 9 \, a b^{4}\right)} \sinh\left(x\right)^{7} + 24 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 3 \, {\left(112 \, b^{5} x \cosh\left(x\right)^{2} + 16 \, b^{5} x - 8 \, a^{4} b + 24 \, a^{2} b^{3} - 7 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} + 12 \, b^{5} x - 3 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(224 \, b^{5} x \cosh\left(x\right)^{3} - 4 \, a^{3} b^{2} + a b^{4} - 21 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 48 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 24 \, a^{4} b + 56 \, a^{2} b^{3} + 24 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(280 \, b^{5} x \cosh\left(x\right)^{4} + 24 \, b^{5} x - 24 \, a^{4} b + 56 \, a^{2} b^{3} - 35 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 120 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 5 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 3 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(224 \, b^{5} x \cosh\left(x\right)^{5} + 4 \, a^{3} b^{2} - a b^{4} - 35 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 160 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - 10 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} + 32 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(6 \, b^{5} x - 9 \, a^{4} b + 19 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + {\left(336 \, b^{5} x \cosh\left(x\right)^{6} + 48 \, b^{5} x - 63 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{5} - 72 \, a^{4} b + 152 \, a^{2} b^{3} + 360 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{3} + 144 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 9 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} + 7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 6 \, a^{2} b^{2} + 3 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 9 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) - 3 \, {\left({\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 6 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(24 \, a^{5} - 60 \, a^{3} b^{2} + 45 \, a b^{4} + 35 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + 3 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right) + {\left(96 \, b^{5} x \cosh\left(x\right)^{7} - 21 \, {\left(4 \, a^{3} b^{2} - 9 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 144 \, {\left(2 \, b^{5} x - a^{4} b + 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 12 \, a^{3} b^{2} - 27 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{4} + 96 \, {\left(3 \, b^{5} x - 3 \, a^{4} b + 7 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + 9 \, {\left(4 \, a^{3} b^{2} - a b^{4}\right)} \cosh\left(x\right)^{2} + 16 \, {\left(6 \, b^{5} x - 9 \, a^{4} b + 19 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{12 \, {\left(a b^{5} \cosh\left(x\right)^{8} + 8 \, a b^{5} \cosh\left(x\right) \sinh\left(x\right)^{7} + a b^{5} \sinh\left(x\right)^{8} + 4 \, a b^{5} \cosh\left(x\right)^{6} + 6 \, a b^{5} \cosh\left(x\right)^{4} + 4 \, a b^{5} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{2} + a b^{5}\right)} \sinh\left(x\right)^{6} + a b^{5} + 8 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{3} + 3 \, a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a b^{5} \cosh\left(x\right)^{4} + 30 \, a b^{5} \cosh\left(x\right)^{2} + 3 \, a b^{5}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{5} + 10 \, a b^{5} \cosh\left(x\right)^{3} + 3 \, a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a b^{5} \cosh\left(x\right)^{6} + 15 \, a b^{5} \cosh\left(x\right)^{4} + 9 \, a b^{5} \cosh\left(x\right)^{2} + a b^{5}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a b^{5} \cosh\left(x\right)^{7} + 3 \, a b^{5} \cosh\left(x\right)^{5} + 3 \, a b^{5} \cosh\left(x\right)^{3} + a b^{5} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(12*b^5*x*cosh(x)^8 + 12*b^5*x*sinh(x)^8 - 3*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^7 + 3*(32*b^5*x*cosh(x) - 4*a^3*b^2 + 9*a*b^4)*sinh(x)^7 + 24*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^6 + 3*(112*b^5*x*cosh(x)^2 + 16*b^5*x - 8*a^4*b + 24*a^2*b^3 - 7*(4*a^3*b^2 - 9*a*b^4)*cosh(x))*sinh(x)^6 + 12*b^5*x - 3*(4*a^3*b^2 - a*b^4)*cosh(x)^5 + 3*(224*b^5*x*cosh(x)^3 - 4*a^3*b^2 + a*b^4 - 21*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^2 + 48*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x))*sinh(x)^5 - 24*a^4*b + 56*a^2*b^3 + 24*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^4 + 3*(280*b^5*x*cosh(x)^4 + 24*b^5*x - 24*a^4*b + 56*a^2*b^3 - 35*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^3 + 120*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^2 - 5*(4*a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^4 + 3*(4*a^3*b^2 - a*b^4)*cosh(x)^3 + 3*(224*b^5*x*cosh(x)^5 + 4*a^3*b^2 - a*b^4 - 35*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^4 + 160*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^3 - 10*(4*a^3*b^2 - a*b^4)*cosh(x)^2 + 32*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x))*sinh(x)^3 + 8*(6*b^5*x - 9*a^4*b + 19*a^2*b^3)*cosh(x)^2 + (336*b^5*x*cosh(x)^6 + 48*b^5*x - 63*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^5 - 72*a^4*b + 152*a^2*b^3 + 360*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^4 - 30*(4*a^3*b^2 - a*b^4)*cosh(x)^3 + 144*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^2 + 9*(4*a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^2 + 12*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^8 + 8*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x)^7 + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^8 + 4*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^6 + 4*(a^4 - 2*a^2*b^2 + b^4 + 7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x)^5 + 6*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 2*(35*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 3*a^4 - 6*a^2*b^2 + 3*b^4 + 30*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 8*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^5 + 10*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 + 4*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^6 + 15*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 9*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^7 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^5 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + (a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) - 3*((8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^8 + 8*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)*sinh(x)^7 + (8*a^5 - 20*a^3*b^2 + 15*a*b^4)*sinh(x)^8 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^6 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x)^5 + 8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 6*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 2*(24*a^5 - 60*a^3*b^2 + 45*a*b^4 + 35*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 30*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^4 + 8*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^5 + 10*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x)^3 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2 + 4*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^6 + 8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 15*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 9*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^7 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^5 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + (8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) + 3*(4*a^3*b^2 - 9*a*b^4)*cosh(x) + (96*b^5*x*cosh(x)^7 - 21*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^6 + 144*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^5 + 12*a^3*b^2 - 27*a*b^4 - 15*(4*a^3*b^2 - a*b^4)*cosh(x)^4 + 96*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^3 + 9*(4*a^3*b^2 - a*b^4)*cosh(x)^2 + 16*(6*b^5*x - 9*a^4*b + 19*a^2*b^3)*cosh(x))*sinh(x))/(a*b^5*cosh(x)^8 + 8*a*b^5*cosh(x)*sinh(x)^7 + a*b^5*sinh(x)^8 + 4*a*b^5*cosh(x)^6 + 6*a*b^5*cosh(x)^4 + 4*a*b^5*cosh(x)^2 + 4*(7*a*b^5*cosh(x)^2 + a*b^5)*sinh(x)^6 + a*b^5 + 8*(7*a*b^5*cosh(x)^3 + 3*a*b^5*cosh(x))*sinh(x)^5 + 2*(35*a*b^5*cosh(x)^4 + 30*a*b^5*cosh(x)^2 + 3*a*b^5)*sinh(x)^4 + 8*(7*a*b^5*cosh(x)^5 + 10*a*b^5*cosh(x)^3 + 3*a*b^5*cosh(x))*sinh(x)^3 + 4*(7*a*b^5*cosh(x)^6 + 15*a*b^5*cosh(x)^4 + 9*a*b^5*cosh(x)^2 + a*b^5)*sinh(x)^2 + 8*(a*b^5*cosh(x)^7 + 3*a*b^5*cosh(x)^5 + 3*a*b^5*cosh(x)^3 + a*b^5*cosh(x))*sinh(x)), 1/12*(12*b^5*x*cosh(x)^8 + 12*b^5*x*sinh(x)^8 - 3*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^7 + 3*(32*b^5*x*cosh(x) - 4*a^3*b^2 + 9*a*b^4)*sinh(x)^7 + 24*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^6 + 3*(112*b^5*x*cosh(x)^2 + 16*b^5*x - 8*a^4*b + 24*a^2*b^3 - 7*(4*a^3*b^2 - 9*a*b^4)*cosh(x))*sinh(x)^6 + 12*b^5*x - 3*(4*a^3*b^2 - a*b^4)*cosh(x)^5 + 3*(224*b^5*x*cosh(x)^3 - 4*a^3*b^2 + a*b^4 - 21*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^2 + 48*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x))*sinh(x)^5 - 24*a^4*b + 56*a^2*b^3 + 24*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^4 + 3*(280*b^5*x*cosh(x)^4 + 24*b^5*x - 24*a^4*b + 56*a^2*b^3 - 35*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^3 + 120*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^2 - 5*(4*a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^4 + 3*(4*a^3*b^2 - a*b^4)*cosh(x)^3 + 3*(224*b^5*x*cosh(x)^5 + 4*a^3*b^2 - a*b^4 - 35*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^4 + 160*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^3 - 10*(4*a^3*b^2 - a*b^4)*cosh(x)^2 + 32*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x))*sinh(x)^3 + 8*(6*b^5*x - 9*a^4*b + 19*a^2*b^3)*cosh(x)^2 + (336*b^5*x*cosh(x)^6 + 48*b^5*x - 63*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^5 - 72*a^4*b + 152*a^2*b^3 + 360*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^4 - 30*(4*a^3*b^2 - a*b^4)*cosh(x)^3 + 144*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^2 + 9*(4*a^3*b^2 - a*b^4)*cosh(x))*sinh(x)^2 - 24*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^8 + 8*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x)^7 + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^8 + 4*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^6 + 4*(a^4 - 2*a^2*b^2 + b^4 + 7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x)^5 + 6*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 2*(35*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 3*a^4 - 6*a^2*b^2 + 3*b^4 + 30*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 8*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^5 + 10*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x)^3 + 4*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 + 4*(7*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^6 + 15*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 9*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^7 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^5 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + (a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) - 3*((8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^8 + 8*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)*sinh(x)^7 + (8*a^5 - 20*a^3*b^2 + 15*a*b^4)*sinh(x)^8 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^6 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x)^5 + 8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 6*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 2*(24*a^5 - 60*a^3*b^2 + 45*a*b^4 + 35*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 30*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^4 + 8*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^5 + 10*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x)^3 + 4*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2 + 4*(7*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^6 + 8*a^5 - 20*a^3*b^2 + 15*a*b^4 + 15*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^4 + 9*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^7 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^5 + 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x)^3 + (8*a^5 - 20*a^3*b^2 + 15*a*b^4)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) + 3*(4*a^3*b^2 - 9*a*b^4)*cosh(x) + (96*b^5*x*cosh(x)^7 - 21*(4*a^3*b^2 - 9*a*b^4)*cosh(x)^6 + 144*(2*b^5*x - a^4*b + 3*a^2*b^3)*cosh(x)^5 + 12*a^3*b^2 - 27*a*b^4 - 15*(4*a^3*b^2 - a*b^4)*cosh(x)^4 + 96*(3*b^5*x - 3*a^4*b + 7*a^2*b^3)*cosh(x)^3 + 9*(4*a^3*b^2 - a*b^4)*cosh(x)^2 + 16*(6*b^5*x - 9*a^4*b + 19*a^2*b^3)*cosh(x))*sinh(x))/(a*b^5*cosh(x)^8 + 8*a*b^5*cosh(x)*sinh(x)^7 + a*b^5*sinh(x)^8 + 4*a*b^5*cosh(x)^6 + 6*a*b^5*cosh(x)^4 + 4*a*b^5*cosh(x)^2 + 4*(7*a*b^5*cosh(x)^2 + a*b^5)*sinh(x)^6 + a*b^5 + 8*(7*a*b^5*cosh(x)^3 + 3*a*b^5*cosh(x))*sinh(x)^5 + 2*(35*a*b^5*cosh(x)^4 + 30*a*b^5*cosh(x)^2 + 3*a*b^5)*sinh(x)^4 + 8*(7*a*b^5*cosh(x)^5 + 10*a*b^5*cosh(x)^3 + 3*a*b^5*cosh(x))*sinh(x)^3 + 4*(7*a*b^5*cosh(x)^6 + 15*a*b^5*cosh(x)^4 + 9*a*b^5*cosh(x)^2 + a*b^5)*sinh(x)^2 + 8*(a*b^5*cosh(x)^7 + 3*a*b^5*cosh(x)^5 + 3*a*b^5*cosh(x)^3 + a*b^5*cosh(x))*sinh(x))]","B",0
115,1,1280,0,0.445471," ","integrate(tanh(x)^5/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{3 \, b^{4} x \cosh\left(x\right)^{6} + 3 \, b^{4} x \sinh\left(x\right)^{6} + 6 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(3 \, b^{4} x \cosh\left(x\right) + a^{3} b - 2 \, a b^{3}\right)} \sinh\left(x\right)^{5} + 3 \, b^{4} x + 3 \, {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(15 \, b^{4} x \cosh\left(x\right)^{2} + 3 \, b^{4} x - 2 \, a^{2} b^{2} + 10 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + 4 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(15 \, b^{4} x \cosh\left(x\right)^{3} + 3 \, a^{3} b - 4 \, a b^{3} + 15 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(15 \, b^{4} x \cosh\left(x\right)^{4} + 3 \, b^{4} x - 2 \, a^{2} b^{2} + 20 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 6 \, {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right) - 3 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} + 5 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(5 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + 5 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - 2 \, a^{2} b^{2}\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 \, b^{4} x \cosh\left(x\right)^{5} + 5 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} b - 2 \, a b^{3} + 2 \, {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cosh\left(x\right)^{2} + {\left(3 \, b^{4} x - 2 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left(a b^{4} \cosh\left(x\right)^{6} + 6 \, a b^{4} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{4} \sinh\left(x\right)^{6} + 3 \, a b^{4} \cosh\left(x\right)^{4} + 3 \, a b^{4} \cosh\left(x\right)^{2} + a b^{4} + 3 \, {\left(5 \, a b^{4} \cosh\left(x\right)^{2} + a b^{4}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{4} \cosh\left(x\right)^{3} + 3 \, a b^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, a b^{4} \cosh\left(x\right)^{4} + 6 \, a b^{4} \cosh\left(x\right)^{2} + a b^{4}\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a b^{4} \cosh\left(x\right)^{5} + 2 \, a b^{4} \cosh\left(x\right)^{3} + a b^{4} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/3*(3*b^4*x*cosh(x)^6 + 3*b^4*x*sinh(x)^6 + 6*(a^3*b - 2*a*b^3)*cosh(x)^5 + 6*(3*b^4*x*cosh(x) + a^3*b - 2*a*b^3)*sinh(x)^5 + 3*b^4*x + 3*(3*b^4*x - 2*a^2*b^2)*cosh(x)^4 + 3*(15*b^4*x*cosh(x)^2 + 3*b^4*x - 2*a^2*b^2 + 10*(a^3*b - 2*a*b^3)*cosh(x))*sinh(x)^4 + 4*(3*a^3*b - 4*a*b^3)*cosh(x)^3 + 4*(15*b^4*x*cosh(x)^3 + 3*a^3*b - 4*a*b^3 + 15*(a^3*b - 2*a*b^3)*cosh(x)^2 + 3*(3*b^4*x - 2*a^2*b^2)*cosh(x))*sinh(x)^3 + 3*(3*b^4*x - 2*a^2*b^2)*cosh(x)^2 + 3*(15*b^4*x*cosh(x)^4 + 3*b^4*x - 2*a^2*b^2 + 20*(a^3*b - 2*a*b^3)*cosh(x)^3 + 6*(3*b^4*x - 2*a^2*b^2)*cosh(x)^2 + 4*(3*a^3*b - 4*a*b^3)*cosh(x))*sinh(x)^2 + 6*(a^3*b - 2*a*b^3)*cosh(x) - 3*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^6 + 6*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)*sinh(x)^5 + (a^4 - 2*a^2*b^2 + b^4)*sinh(x)^6 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + 3*(a^4 - 2*a^2*b^2 + b^4 + 5*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 4*(5*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x)^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2 + 3*(5*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^4 + a^4 - 2*a^2*b^2 + b^4 + 6*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 - 2*a^2*b^2 + b^4)*cosh(x)^5 + 2*(a^4 - 2*a^2*b^2 + b^4)*cosh(x)^3 + (a^4 - 2*a^2*b^2 + b^4)*cosh(x))*sinh(x))*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) + 3*((a^4 - 2*a^2*b^2)*cosh(x)^6 + 6*(a^4 - 2*a^2*b^2)*cosh(x)*sinh(x)^5 + (a^4 - 2*a^2*b^2)*sinh(x)^6 + 3*(a^4 - 2*a^2*b^2)*cosh(x)^4 + 3*(a^4 - 2*a^2*b^2 + 5*(a^4 - 2*a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 - 2*a^2*b^2 + 4*(5*(a^4 - 2*a^2*b^2)*cosh(x)^3 + 3*(a^4 - 2*a^2*b^2)*cosh(x))*sinh(x)^3 + 3*(a^4 - 2*a^2*b^2)*cosh(x)^2 + 3*(5*(a^4 - 2*a^2*b^2)*cosh(x)^4 + a^4 - 2*a^2*b^2 + 6*(a^4 - 2*a^2*b^2)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 - 2*a^2*b^2)*cosh(x)^5 + 2*(a^4 - 2*a^2*b^2)*cosh(x)^3 + (a^4 - 2*a^2*b^2)*cosh(x))*sinh(x))*log(2*cosh(x)/(cosh(x) - sinh(x))) + 6*(3*b^4*x*cosh(x)^5 + 5*(a^3*b - 2*a*b^3)*cosh(x)^4 + a^3*b - 2*a*b^3 + 2*(3*b^4*x - 2*a^2*b^2)*cosh(x)^3 + 2*(3*a^3*b - 4*a*b^3)*cosh(x)^2 + (3*b^4*x - 2*a^2*b^2)*cosh(x))*sinh(x))/(a*b^4*cosh(x)^6 + 6*a*b^4*cosh(x)*sinh(x)^5 + a*b^4*sinh(x)^6 + 3*a*b^4*cosh(x)^4 + 3*a*b^4*cosh(x)^2 + a*b^4 + 3*(5*a*b^4*cosh(x)^2 + a*b^4)*sinh(x)^4 + 4*(5*a*b^4*cosh(x)^3 + 3*a*b^4*cosh(x))*sinh(x)^3 + 3*(5*a*b^4*cosh(x)^4 + 6*a*b^4*cosh(x)^2 + a*b^4)*sinh(x)^2 + 6*(a*b^4*cosh(x)^5 + 2*a*b^4*cosh(x)^3 + a*b^4*cosh(x))*sinh(x))","B",0
116,1,1254,0,0.512825," ","integrate(tanh(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{b^{3} x \cosh\left(x\right)^{4} + b^{3} x \sinh\left(x\right)^{4} + a b^{2} \cosh\left(x\right)^{3} + b^{3} x - a b^{2} \cosh\left(x\right) + {\left(4 \, b^{3} x \cosh\left(x\right) + a b^{2}\right)} \sinh\left(x\right)^{3} + 2 \, a^{2} b + 2 \, {\left(b^{3} x + a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(6 \, b^{3} x \cosh\left(x\right)^{2} + 2 \, b^{3} x + 3 \, a b^{2} \cosh\left(x\right) + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} - {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - 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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} - 3 \, a b^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2} + 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} - 3 \, a 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(4 \, b^{3} x \cosh\left(x\right)^{3} + 3 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + 4 \, {\left(b^{3} x + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{a b^{3} \cosh\left(x\right)^{4} + 4 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{3} \sinh\left(x\right)^{4} + 2 \, a b^{3} \cosh\left(x\right)^{2} + a b^{3} + 2 \, {\left(3 \, a b^{3} \cosh\left(x\right)^{2} + a b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{3} \cosh\left(x\right)^{3} + a b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)}, \frac{b^{3} x \cosh\left(x\right)^{4} + b^{3} x \sinh\left(x\right)^{4} + a b^{2} \cosh\left(x\right)^{3} + b^{3} x - a b^{2} \cosh\left(x\right) + {\left(4 \, b^{3} x \cosh\left(x\right) + a b^{2}\right)} \sinh\left(x\right)^{3} + 2 \, a^{2} b + 2 \, {\left(b^{3} x + a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(6 \, b^{3} x \cosh\left(x\right)^{2} + 2 \, b^{3} x + 3 \, a b^{2} \cosh\left(x\right) + 2 \, a^{2} b\right)} \sinh\left(x\right)^{2} + 2 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - 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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} - 3 \, a b^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2} + 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} - 3 \, a 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(4 \, b^{3} x \cosh\left(x\right)^{3} + 3 \, a b^{2} \cosh\left(x\right)^{2} - a b^{2} + 4 \, {\left(b^{3} x + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{a b^{3} \cosh\left(x\right)^{4} + 4 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + a b^{3} \sinh\left(x\right)^{4} + 2 \, a b^{3} \cosh\left(x\right)^{2} + a b^{3} + 2 \, {\left(3 \, a b^{3} \cosh\left(x\right)^{2} + a b^{3}\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a b^{3} \cosh\left(x\right)^{3} + a b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right]"," ",0,"[(b^3*x*cosh(x)^4 + b^3*x*sinh(x)^4 + a*b^2*cosh(x)^3 + b^3*x - a*b^2*cosh(x) + (4*b^3*x*cosh(x) + a*b^2)*sinh(x)^3 + 2*a^2*b + 2*(b^3*x + a^2*b)*cosh(x)^2 + (6*b^3*x*cosh(x)^2 + 2*b^3*x + 3*a*b^2*cosh(x) + 2*a^2*b)*sinh(x)^2 - ((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 + 2*(a^2 - 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))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + ((2*a^3 - 3*a*b^2)*cosh(x)^4 + 4*(2*a^3 - 3*a*b^2)*cosh(x)*sinh(x)^3 + (2*a^3 - 3*a*b^2)*sinh(x)^4 + 2*a^3 - 3*a*b^2 + 2*(2*a^3 - 3*a*b^2)*cosh(x)^2 + 2*(2*a^3 - 3*a*b^2 + 3*(2*a^3 - 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 - 3*a*b^2)*cosh(x)^3 + (2*a^3 - 3*a*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) + (4*b^3*x*cosh(x)^3 + 3*a*b^2*cosh(x)^2 - a*b^2 + 4*(b^3*x + a^2*b)*cosh(x))*sinh(x))/(a*b^3*cosh(x)^4 + 4*a*b^3*cosh(x)*sinh(x)^3 + a*b^3*sinh(x)^4 + 2*a*b^3*cosh(x)^2 + a*b^3 + 2*(3*a*b^3*cosh(x)^2 + a*b^3)*sinh(x)^2 + 4*(a*b^3*cosh(x)^3 + a*b^3*cosh(x))*sinh(x)), (b^3*x*cosh(x)^4 + b^3*x*sinh(x)^4 + a*b^2*cosh(x)^3 + b^3*x - a*b^2*cosh(x) + (4*b^3*x*cosh(x) + a*b^2)*sinh(x)^3 + 2*a^2*b + 2*(b^3*x + a^2*b)*cosh(x)^2 + (6*b^3*x*cosh(x)^2 + 2*b^3*x + 3*a*b^2*cosh(x) + 2*a^2*b)*sinh(x)^2 + 2*((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 + 2*(a^2 - 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))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + ((2*a^3 - 3*a*b^2)*cosh(x)^4 + 4*(2*a^3 - 3*a*b^2)*cosh(x)*sinh(x)^3 + (2*a^3 - 3*a*b^2)*sinh(x)^4 + 2*a^3 - 3*a*b^2 + 2*(2*a^3 - 3*a*b^2)*cosh(x)^2 + 2*(2*a^3 - 3*a*b^2 + 3*(2*a^3 - 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 - 3*a*b^2)*cosh(x)^3 + (2*a^3 - 3*a*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) + (4*b^3*x*cosh(x)^3 + 3*a*b^2*cosh(x)^2 - a*b^2 + 4*(b^3*x + a^2*b)*cosh(x))*sinh(x))/(a*b^3*cosh(x)^4 + 4*a*b^3*cosh(x)*sinh(x)^3 + a*b^3*sinh(x)^4 + 2*a*b^3*cosh(x)^2 + a*b^3 + 2*(3*a*b^3*cosh(x)^2 + a*b^3)*sinh(x)^2 + 4*(a*b^3*cosh(x)^3 + a*b^3*cosh(x))*sinh(x))]","B",0
117,1,200,0,0.406779," ","integrate(tanh(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{b^{2} x \cosh\left(x\right)^{2} + b^{2} x \sinh\left(x\right)^{2} + b^{2} x - 2 \, a b \cosh\left(x\right) + {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2}\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left(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}\right)} \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(b^{2} x \cosh\left(x\right) - a b\right)} \sinh\left(x\right)}{a b^{2} \cosh\left(x\right)^{2} + 2 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right) + a b^{2} \sinh\left(x\right)^{2} + a b^{2}}"," ",0,"-(b^2*x*cosh(x)^2 + b^2*x*sinh(x)^2 + b^2*x - 2*a*b*cosh(x) + ((a^2 - b^2)*cosh(x)^2 + 2*(a^2 - b^2)*cosh(x)*sinh(x) + (a^2 - b^2)*sinh(x)^2 + a^2 - b^2)*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - (a^2*cosh(x)^2 + 2*a^2*cosh(x)*sinh(x) + a^2*sinh(x)^2 + a^2)*log(2*cosh(x)/(cosh(x) - sinh(x))) + 2*(b^2*x*cosh(x) - a*b)*sinh(x))/(a*b^2*cosh(x)^2 + 2*a*b^2*cosh(x)*sinh(x) + a*b^2*sinh(x)^2 + a*b^2)","B",0
118,1,193,0,0.446134," ","integrate(tanh(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{b x - 2 \, a \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right)}{a b}, \frac{b x - 2 \, a \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - 2 \, \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{a b}\right]"," ",0,"[(b*x - 2*a*arctan(cosh(x) + sinh(x)) + sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)))/(a*b), (b*x - 2*a*arctan(cosh(x) + sinh(x)) - 2*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)))/(a*b)]","A",0
119,1,27,0,0.428995," ","integrate(tanh(x)/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{x - \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right)}{a}"," ",0,"-(x - log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))))/a","A",0
120,1,81,0,0.428339," ","integrate(coth(x)/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{b^{2} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + {\left(a^{2} - b^{2}\right)} x - {\left(a^{2} + a b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left(a^{2} - a b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)}{a^{3} - a b^{2}}"," ",0,"-(b^2*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) + (a^2 - b^2)*x - (a^2 + a*b)*log(cosh(x) + sinh(x) + 1) - (a^2 - a*b)*log(cosh(x) + sinh(x) - 1))/(a^3 - a*b^2)","A",0
121,1,646,0,0.420635," ","integrate(coth(x)^2/(a+b*sech(x)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{4} - 2 \, a^{2} b^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \sinh\left(x\right)^{2} - {\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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x - 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right) - 2 \, {\left(a^{3} b - a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sinh\left(x\right)^{2}}, \frac{2 \, a^{4} - 2 \, a^{2} b^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \sinh\left(x\right)^{2} + 2 \, {\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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x - 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right) - 2 \, {\left(a^{3} b - a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sinh\left(x\right)^{2}}\right]"," ",0,"[(2*a^4 - 2*a^2*b^2 - (a^4 - 2*a^2*b^2 + b^4)*x*cosh(x)^2 - (a^4 - 2*a^2*b^2 + b^4)*x*sinh(x)^2 - (b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2 - b^3)*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) + (a^4 - 2*a^2*b^2 + b^4)*x - 2*(a^3*b - a*b^3)*cosh(x) - 2*(a^3*b - a*b^3 + (a^4 - 2*a^2*b^2 + b^4)*x*cosh(x))*sinh(x))/(a^5 - 2*a^3*b^2 + a*b^4 - (a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)*sinh(x) - (a^5 - 2*a^3*b^2 + a*b^4)*sinh(x)^2), (2*a^4 - 2*a^2*b^2 - (a^4 - 2*a^2*b^2 + b^4)*x*cosh(x)^2 - (a^4 - 2*a^2*b^2 + b^4)*x*sinh(x)^2 + 2*(b^3*cosh(x)^2 + 2*b^3*cosh(x)*sinh(x) + b^3*sinh(x)^2 - b^3)*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) + (a^4 - 2*a^2*b^2 + b^4)*x - 2*(a^3*b - a*b^3)*cosh(x) - 2*(a^3*b - a*b^3 + (a^4 - 2*a^2*b^2 + b^4)*x*cosh(x))*sinh(x))/(a^5 - 2*a^3*b^2 + a*b^4 - (a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)*sinh(x) - (a^5 - 2*a^3*b^2 + a*b^4)*sinh(x)^2)]","B",0
122,1,1222,0,0.466339," ","integrate(coth(x)^3/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)^{4} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \sinh\left(x\right)^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{3} - 2 \, {\left(a^{3} b - a b^{3} - 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - a^{2} b^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{4} - 2 \, a^{2} b^{2} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)^{2} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x - 3 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x - 2 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right) - 2 \, {\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(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left({\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3} - 2 \, {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3} - 3 \, {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left({\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3} - 2 \, {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3} - 3 \, {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x \cosh\left(x\right)^{3} - a^{3} b + a b^{3} - 3 \, {\left(a^{3} b - a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{4} - a^{2} b^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} - 3 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/2*(2*(a^4 - 2*a^2*b^2 + b^4)*x*cosh(x)^4 + 2*(a^4 - 2*a^2*b^2 + b^4)*x*sinh(x)^4 - 2*(a^3*b - a*b^3)*cosh(x)^3 - 2*(a^3*b - a*b^3 - 4*(a^4 - 2*a^2*b^2 + b^4)*x*cosh(x))*sinh(x)^3 + 4*(a^4 - a^2*b^2 - (a^4 - 2*a^2*b^2 + b^4)*x)*cosh(x)^2 + 2*(2*a^4 - 2*a^2*b^2 + 6*(a^4 - 2*a^2*b^2 + b^4)*x*cosh(x)^2 - 2*(a^4 - 2*a^2*b^2 + b^4)*x - 3*(a^3*b - a*b^3)*cosh(x))*sinh(x)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*x - 2*(a^3*b - a*b^3)*cosh(x) - 2*(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*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - ((2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x)^4 + 4*(2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x)*sinh(x)^3 + (2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*sinh(x)^4 + 2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3 - 2*(2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x)^2 - 2*(2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3 - 3*(2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x)^3 - (2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) + 1) - ((2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x)^4 + 4*(2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x)*sinh(x)^3 + (2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*sinh(x)^4 + 2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3 - 2*(2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x)^2 - 2*(2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3 - 3*(2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x)^3 - (2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) - 1) + 2*(4*(a^4 - 2*a^2*b^2 + b^4)*x*cosh(x)^3 - a^3*b + a*b^3 - 3*(a^3*b - a*b^3)*cosh(x)^2 + 4*(a^4 - a^2*b^2 - (a^4 - 2*a^2*b^2 + b^4)*x)*cosh(x))*sinh(x))/(a^5 - 2*a^3*b^2 + a*b^4 + (a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^4 + 4*(a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)*sinh(x)^3 + (a^5 - 2*a^3*b^2 + a*b^4)*sinh(x)^4 - 2*(a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4 - 3*(a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 - 2*a^3*b^2 + a*b^4)*cosh(x)^3 - (a^5 - 2*a^3*b^2 + a*b^4)*cosh(x))*sinh(x))","B",0
123,1,3530,0,0.487226," ","integrate(coth(x)^4/(a+b*sech(x)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{6} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \sinh\left(x\right)^{6} - 8 \, a^{6} + 22 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{4} - 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} - 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{2} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 10 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{3} - 15 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{4} + 20 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 6 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 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)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) - a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(x\right) + a b\right)} \sinh\left(x\right) + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right) + b\right)}}{a \cosh\left(x\right)^{2} + a \sinh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) + 2 \, {\left(a \cosh\left(x\right) + b\right)} \sinh\left(x\right) + a}\right) - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right) + 6 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{5} + a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + 5 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{3} - 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)^{2} + {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{6} - 6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - 5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 4 \, {\left(5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + 5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 6 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{6} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \sinh\left(x\right)^{6} - 8 \, a^{6} + 22 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{4} - 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} - 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{2} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 10 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{3} - 15 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 15 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{4} + 20 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 6 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 4 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 6 \, {\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)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cosh\left(x\right) + a \sinh\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right) - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x + 6 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right) + 6 \, {\left(3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{5} + a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + 5 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(4 \, a^{6} - 10 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{3} - 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cosh\left(x\right)^{2} + {\left(4 \, a^{6} - 12 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{6} - 6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - 5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 4 \, {\left(5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + 5 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 6 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/3*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^6 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*sinh(x)^6 - 8*a^6 + 22*a^4*b^2 - 14*a^2*b^4 + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^5 + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x))*sinh(x)^5 - 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^4 - 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 - 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 10*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x))*sinh(x)^4 - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x)^3 - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^3 - 15*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^2 + 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x)^3 + 3*(4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 + 3*(4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^4 + 20*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^3 - 6*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x))*sinh(x)^2 - 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))*sqrt(-a^2 + b^2)*log((a^2*cosh(x)^2 + a^2*sinh(x)^2 + 2*a*b*cosh(x) - a^2 + 2*b^2 + 2*(a^2*cosh(x) + a*b)*sinh(x) + 2*sqrt(-a^2 + b^2)*(a*cosh(x) + a*sinh(x) + b))/(a*cosh(x)^2 + a*sinh(x)^2 + 2*b*cosh(x) + 2*(a*cosh(x) + b)*sinh(x) + a)) - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x) + 6*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^5 + a^5*b - 3*a^3*b^3 + 2*a*b^5 + 5*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^4 - 2*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^3 - 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x)^2 + (4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x))/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^6 - 6*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)*sinh(x)^5 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sinh(x)^6 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - 5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^4 - 4*(5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x)^3 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + 5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 - 6*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^2 - 6*((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^5 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x)), -1/3*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^6 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*sinh(x)^6 - 8*a^6 + 22*a^4*b^2 - 14*a^2*b^4 + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^5 + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x))*sinh(x)^5 - 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^4 - 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 - 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 10*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x))*sinh(x)^4 - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x)^3 - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^3 - 15*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^2 + 3*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x)^3 + 3*(4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 + 3*(4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 15*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^4 + 20*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^3 - 6*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 4*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x))*sinh(x)^2 + 6*(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))*sqrt(a^2 - b^2)*arctan(-(a*cosh(x) + a*sinh(x) + b)/sqrt(a^2 - b^2)) - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x + 6*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x) + 6*(3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^5 + a^5*b - 3*a^3*b^3 + 2*a*b^5 + 5*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cosh(x)^4 - 2*(4*a^6 - 10*a^4*b^2 + 6*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^3 - 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cosh(x)^2 + (4*a^6 - 12*a^4*b^2 + 8*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x))/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^6 - 6*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)*sinh(x)^5 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sinh(x)^6 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - 5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^4 - 4*(5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x)^3 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + 5*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 - 6*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^2 - 6*((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^5 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x))]","B",0
124,1,5181,0,0.609064," ","integrate(coth(x)^5/(a+b*sech(x)),x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \sinh\left(x\right)^{8} - 2 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{7} - 2 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5} - 32 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 16 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{6} + 2 \, {\left(16 \, a^{6} - 40 \, a^{4} b^{2} + 24 \, a^{2} b^{4} + 112 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{2} - 16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 7 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{6} - 2 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5} - 224 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{3} + 21 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{2} - 48 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 16 \, {\left(2 \, a^{6} - 6 \, a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{4} - 2 \, {\left(16 \, a^{6} - 48 \, a^{4} b^{2} + 32 \, a^{2} b^{4} - 280 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{4} + 35 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 120 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} - 24 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x + 5 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 2 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(224 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{5} - 3 \, a^{5} b + 2 \, a^{3} b^{3} + a b^{5} - 35 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 160 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{3} - 10 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{2} - 32 \, {\left(2 \, a^{6} - 6 \, a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 16 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} + 2 \, {\left(112 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{6} + 16 \, a^{6} - 40 \, a^{4} b^{2} + 24 \, a^{2} b^{4} - 21 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 120 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{4} - 10 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{3} - 48 \, {\left(2 \, a^{6} - 6 \, a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{2} - 16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 3 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x - 2 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right) + 8 \, {\left(b^{6} \cosh\left(x\right)^{8} + 8 \, b^{6} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{6} \sinh\left(x\right)^{8} - 4 \, b^{6} \cosh\left(x\right)^{6} + 6 \, b^{6} \cosh\left(x\right)^{4} - 4 \, b^{6} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b^{6} \cosh\left(x\right)^{2} - b^{6}\right)} \sinh\left(x\right)^{6} + b^{6} + 8 \, {\left(7 \, b^{6} \cosh\left(x\right)^{3} - 3 \, b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{6} \cosh\left(x\right)^{4} - 30 \, b^{6} \cosh\left(x\right)^{2} + 3 \, b^{6}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b^{6} \cosh\left(x\right)^{5} - 10 \, b^{6} \cosh\left(x\right)^{3} + 3 \, b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{6} \cosh\left(x\right)^{6} - 15 \, b^{6} \cosh\left(x\right)^{4} + 9 \, b^{6} \cosh\left(x\right)^{2} - b^{6}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(b^{6} \cosh\left(x\right)^{7} - 3 \, b^{6} \cosh\left(x\right)^{5} + 3 \, b^{6} \cosh\left(x\right)^{3} - b^{6} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(a \cosh\left(x\right) + b\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) - {\left({\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5} - 7 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5} + 8 \, {\left(7 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(24 \, a^{6} + 9 \, a^{5} b - 72 \, a^{4} b^{2} - 30 \, a^{3} b^{3} + 72 \, a^{2} b^{4} + 45 \, a b^{5} + 35 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 8 \, a^{6} - 3 \, a^{5} b + 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 24 \, a^{2} b^{4} - 15 \, a b^{5} - 15 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - {\left({\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5} - 7 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5} + 8 \, {\left(7 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(24 \, a^{6} - 9 \, a^{5} b - 72 \, a^{4} b^{2} + 30 \, a^{3} b^{3} + 72 \, a^{2} b^{4} - 45 \, a b^{5} + 35 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 8 \, a^{6} + 3 \, a^{5} b + 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} - 24 \, a^{2} b^{4} + 15 \, a b^{5} - 15 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(32 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x \cosh\left(x\right)^{7} - 7 \, {\left(5 \, a^{5} b - 14 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \cosh\left(x\right)^{6} - 5 \, a^{5} b + 14 \, a^{3} b^{3} - 9 \, a b^{5} + 48 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{5} - 5 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{4} - 32 \, {\left(2 \, a^{6} - 6 \, a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cosh\left(x\right)^{2} + 16 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} x\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sinh\left(x\right)^{8} + a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - 4 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - 7 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{7} - 9 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 3 \, a b^{6} + 35 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2} - 4 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - 7 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{4} - 9 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)^{3} - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}"," ",0,"-1/8*(8*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^8 + 8*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*sinh(x)^8 - 2*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^7 - 2*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5 - 32*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x))*sinh(x)^7 + 16*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^6 + 2*(16*a^6 - 40*a^4*b^2 + 24*a^2*b^4 + 112*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^2 - 16*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 7*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x))*sinh(x)^6 - 2*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^5 - 2*(3*a^5*b - 2*a^3*b^3 - a*b^5 - 224*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^3 + 21*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^2 - 48*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x)^5 - 16*(2*a^6 - 6*a^4*b^2 + 4*a^2*b^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^4 - 2*(16*a^6 - 48*a^4*b^2 + 32*a^2*b^4 - 280*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^4 + 35*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^3 - 120*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 - 24*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x + 5*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x))*sinh(x)^4 - 2*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^3 + 2*(224*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^5 - 3*a^5*b + 2*a^3*b^3 + a*b^5 - 35*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^4 + 160*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^3 - 10*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^2 - 32*(2*a^6 - 6*a^4*b^2 + 4*a^2*b^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x)^3 + 16*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 + 2*(112*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^6 + 16*a^6 - 40*a^4*b^2 + 24*a^2*b^4 - 21*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^5 + 120*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^4 - 10*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^3 - 48*(2*a^6 - 6*a^4*b^2 + 4*a^2*b^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^2 - 16*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 3*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x))*sinh(x)^2 + 8*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x - 2*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x) + 8*(b^6*cosh(x)^8 + 8*b^6*cosh(x)*sinh(x)^7 + b^6*sinh(x)^8 - 4*b^6*cosh(x)^6 + 6*b^6*cosh(x)^4 - 4*b^6*cosh(x)^2 + 4*(7*b^6*cosh(x)^2 - b^6)*sinh(x)^6 + b^6 + 8*(7*b^6*cosh(x)^3 - 3*b^6*cosh(x))*sinh(x)^5 + 2*(35*b^6*cosh(x)^4 - 30*b^6*cosh(x)^2 + 3*b^6)*sinh(x)^4 + 8*(7*b^6*cosh(x)^5 - 10*b^6*cosh(x)^3 + 3*b^6*cosh(x))*sinh(x)^3 + 4*(7*b^6*cosh(x)^6 - 15*b^6*cosh(x)^4 + 9*b^6*cosh(x)^2 - b^6)*sinh(x)^2 + 8*(b^6*cosh(x)^7 - 3*b^6*cosh(x)^5 + 3*b^6*cosh(x)^3 - b^6*cosh(x))*sinh(x))*log(2*(a*cosh(x) + b)/(cosh(x) - sinh(x))) - ((8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^8 + 8*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)*sinh(x)^7 + (8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*sinh(x)^8 - 4*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^6 - 4*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5 - 7*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^2)*sinh(x)^6 + 8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5 + 8*(7*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^3 - 3*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x))*sinh(x)^5 + 6*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^4 + 2*(24*a^6 + 9*a^5*b - 72*a^4*b^2 - 30*a^3*b^3 + 72*a^2*b^4 + 45*a*b^5 + 35*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^4 - 30*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^5 - 10*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^3 + 3*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x))*sinh(x)^3 - 4*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^2 + 4*(7*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^6 - 8*a^6 - 3*a^5*b + 24*a^4*b^2 + 10*a^3*b^3 - 24*a^2*b^4 - 15*a*b^5 - 15*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^4 + 9*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^7 - 3*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^5 + 3*(8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x)^3 - (8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) + 1) - ((8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^8 + 8*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)*sinh(x)^7 + (8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*sinh(x)^8 - 4*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^6 - 4*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5 - 7*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^2)*sinh(x)^6 + 8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5 + 8*(7*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^3 - 3*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x))*sinh(x)^5 + 6*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^4 + 2*(24*a^6 - 9*a^5*b - 72*a^4*b^2 + 30*a^3*b^3 + 72*a^2*b^4 - 45*a*b^5 + 35*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^4 - 30*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^5 - 10*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^3 + 3*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x))*sinh(x)^3 - 4*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^2 + 4*(7*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^6 - 8*a^6 + 3*a^5*b + 24*a^4*b^2 - 10*a^3*b^3 - 24*a^2*b^4 + 15*a*b^5 - 15*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^4 + 9*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^7 - 3*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^5 + 3*(8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x)^3 - (8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) - 1) + 2*(32*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x*cosh(x)^7 - 7*(5*a^5*b - 14*a^3*b^3 + 9*a*b^5)*cosh(x)^6 - 5*a^5*b + 14*a^3*b^3 - 9*a*b^5 + 48*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^5 - 5*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^4 - 32*(2*a^6 - 6*a^4*b^2 + 4*a^2*b^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x)^3 - 3*(3*a^5*b - 2*a^3*b^3 - a*b^5)*cosh(x)^2 + 16*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*x)*cosh(x))*sinh(x))/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^8 + 8*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)*sinh(x)^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sinh(x)^8 + a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - 4*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^6 - 4*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - 7*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x)^5 + 6*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 + 2*(3*a^7 - 9*a^5*b^2 + 9*a^3*b^4 - 3*a*b^6 + 35*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 - 30*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^5 - 10*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x)^3 - 4*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2 - 4*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - 7*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^6 + 15*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^4 - 9*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^2)*sinh(x)^2 + 8*((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^7 - 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^5 + 3*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x)^3 - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cosh(x))*sinh(x))","B",0
125,1,4363,0,1.103956," ","integrate((a+b*sech(d*x+c))^(1/2)*tanh(d*x+c)^5,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, b^{4} \cosh\left(d x + c\right)^{6} + 6 \, b^{4} \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, b^{4} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 30 \, b^{4} \cosh\left(d x + c\right)^{2} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, b^{4} \cosh\left(d x + c\right)^{4} + 9 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, b^{4} \cosh\left(d x + c\right)^{5} + 3 \, b^{4} \cosh\left(d x + c\right)^{3} + b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 4 \, {\left({\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3} - 2 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4} + 7 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3} - 14 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4} - 70 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(14 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} b + 53 \, a b^{3} + 20 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 21 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(2 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b + 21 \, a b^{3} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{630 \, {\left(b^{4} d \cosh\left(d x + c\right)^{8} + 8 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} d \sinh\left(d x + c\right)^{8} + 4 \, b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, b^{4} d \cosh\left(d x + c\right)^{4} + 4 \, b^{4} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, 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)^{5} + b^{4} d + 2 \, {\left(35 \, b^{4} d \cosh\left(d x + c\right)^{4} + 30 \, b^{4} d \cosh\left(d x + c\right)^{2} + 3 \, b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{5} + 10 \, 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} + 4 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{6} + 15 \, b^{4} d \cosh\left(d x + c\right)^{4} + 9 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} d \cosh\left(d x + c\right)^{7} + 3 \, b^{4} d \cosh\left(d x + c\right)^{5} + 3 \, 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{315 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, b^{4} \cosh\left(d x + c\right)^{6} + 6 \, b^{4} \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, b^{4} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 30 \, b^{4} \cosh\left(d x + c\right)^{2} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, b^{4} \cosh\left(d x + c\right)^{4} + 9 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, b^{4} \cosh\left(d x + c\right)^{5} + 3 \, b^{4} \cosh\left(d x + c\right)^{3} + b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) - 2 \, {\left({\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3} - 2 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4} + 7 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3} - 14 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4} - 70 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4} - 4 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(14 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} b + 53 \, a b^{3} + 20 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 21 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4} - 10 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(2 \, {\left(16 \, a^{4} - 84 \, a^{2} b^{2} - 315 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{3} b - 21 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b + 21 \, a b^{3} + 2 \, {\left(48 \, a^{4} - 228 \, a^{2} b^{2} - 721 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(12 \, a^{3} b - 53 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(16 \, a^{4} - 78 \, a^{2} b^{2} - 189 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{315 \, {\left(b^{4} d \cosh\left(d x + c\right)^{8} + 8 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} d \sinh\left(d x + c\right)^{8} + 4 \, b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, b^{4} d \cosh\left(d x + c\right)^{4} + 4 \, b^{4} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, 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)^{5} + b^{4} d + 2 \, {\left(35 \, b^{4} d \cosh\left(d x + c\right)^{4} + 30 \, b^{4} d \cosh\left(d x + c\right)^{2} + 3 \, b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{5} + 10 \, 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} + 4 \, {\left(7 \, b^{4} d \cosh\left(d x + c\right)^{6} + 15 \, b^{4} d \cosh\left(d x + c\right)^{4} + 9 \, b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} d \cosh\left(d x + c\right)^{7} + 3 \, b^{4} d \cosh\left(d x + c\right)^{5} + 3 \, 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,"[1/630*(315*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*b^4*cosh(d*x + c)^6 + 6*b^4*cosh(d*x + c)^4 + 4*(7*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^6 + 4*b^4*cosh(d*x + c)^2 + 8*(7*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^4*cosh(d*x + c)^4 + 30*b^4*cosh(d*x + c)^2 + 3*b^4)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^4*cosh(d*x + c)^6 + 15*b^4*cosh(d*x + c)^4 + 9*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*b^4*cosh(d*x + c)^5 + 3*b^4*cosh(d*x + c)^3 + b^4*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*((16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^8 + (16*a^4 - 84*a^2*b^2 - 315*b^4)*sinh(d*x + c)^8 - 4*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^7 - 4*(4*a^3*b - 21*a*b^3 - 2*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^6 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4 + 7*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^2 - 7*(4*a^3*b - 21*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 4*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^5 - 4*(12*a^3*b - 53*a*b^3 - 14*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^3 + 21*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^2 - 6*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^4 + 2*(35*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^4 + 48*a^4 - 228*a^2*b^2 - 721*b^4 - 70*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^3 + 30*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^2 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 16*a^4 - 84*a^2*b^2 - 315*b^4 - 4*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^3 + 4*(14*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^5 - 35*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^4 - 12*a^3*b + 53*a*b^3 + 20*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^3 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^2 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^2 + 4*(7*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^6 - 21*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^5 + 15*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^4 + 16*a^4 - 78*a^2*b^2 - 189*b^4 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^3 + 3*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^2 - 3*(12*a^3*b - 53*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(4*a^3*b - 21*a*b^3)*cosh(d*x + c) + 4*(2*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^7 - 7*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^6 + 6*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^5 - 5*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^4 - 4*a^3*b + 21*a*b^3 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^3 - 3*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^2 + 2*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(b^4*d*cosh(d*x + c)^8 + 8*b^4*d*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*d*sinh(d*x + c)^8 + 4*b^4*d*cosh(d*x + c)^6 + 6*b^4*d*cosh(d*x + c)^4 + 4*b^4*d*cosh(d*x + c)^2 + 4*(7*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^6 + 8*(7*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^5 + b^4*d + 2*(35*b^4*d*cosh(d*x + c)^4 + 30*b^4*d*cosh(d*x + c)^2 + 3*b^4*d)*sinh(d*x + c)^4 + 8*(7*b^4*d*cosh(d*x + c)^5 + 10*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^4*d*cosh(d*x + c)^6 + 15*b^4*d*cosh(d*x + c)^4 + 9*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^2 + 8*(b^4*d*cosh(d*x + c)^7 + 3*b^4*d*cosh(d*x + c)^5 + 3*b^4*d*cosh(d*x + c)^3 + b^4*d*cosh(d*x + c))*sinh(d*x + c)), -1/315*(315*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*b^4*cosh(d*x + c)^6 + 6*b^4*cosh(d*x + c)^4 + 4*(7*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^6 + 4*b^4*cosh(d*x + c)^2 + 8*(7*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^4*cosh(d*x + c)^4 + 30*b^4*cosh(d*x + c)^2 + 3*b^4)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^4*cosh(d*x + c)^6 + 15*b^4*cosh(d*x + c)^4 + 9*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*b^4*cosh(d*x + c)^5 + 3*b^4*cosh(d*x + c)^3 + b^4*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) - 2*((16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^8 + (16*a^4 - 84*a^2*b^2 - 315*b^4)*sinh(d*x + c)^8 - 4*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^7 - 4*(4*a^3*b - 21*a*b^3 - 2*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^6 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4 + 7*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^2 - 7*(4*a^3*b - 21*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 4*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^5 - 4*(12*a^3*b - 53*a*b^3 - 14*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^3 + 21*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^2 - 6*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^4 + 2*(35*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^4 + 48*a^4 - 228*a^2*b^2 - 721*b^4 - 70*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^3 + 30*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^2 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 16*a^4 - 84*a^2*b^2 - 315*b^4 - 4*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^3 + 4*(14*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^5 - 35*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^4 - 12*a^3*b + 53*a*b^3 + 20*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^3 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^2 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^2 + 4*(7*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^6 - 21*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^5 + 15*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^4 + 16*a^4 - 78*a^2*b^2 - 189*b^4 - 10*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^3 + 3*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^2 - 3*(12*a^3*b - 53*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(4*a^3*b - 21*a*b^3)*cosh(d*x + c) + 4*(2*(16*a^4 - 84*a^2*b^2 - 315*b^4)*cosh(d*x + c)^7 - 7*(4*a^3*b - 21*a*b^3)*cosh(d*x + c)^6 + 6*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c)^5 - 5*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^4 - 4*a^3*b + 21*a*b^3 + 2*(48*a^4 - 228*a^2*b^2 - 721*b^4)*cosh(d*x + c)^3 - 3*(12*a^3*b - 53*a*b^3)*cosh(d*x + c)^2 + 2*(16*a^4 - 78*a^2*b^2 - 189*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(b^4*d*cosh(d*x + c)^8 + 8*b^4*d*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*d*sinh(d*x + c)^8 + 4*b^4*d*cosh(d*x + c)^6 + 6*b^4*d*cosh(d*x + c)^4 + 4*b^4*d*cosh(d*x + c)^2 + 4*(7*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^6 + 8*(7*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^5 + b^4*d + 2*(35*b^4*d*cosh(d*x + c)^4 + 30*b^4*d*cosh(d*x + c)^2 + 3*b^4*d)*sinh(d*x + c)^4 + 8*(7*b^4*d*cosh(d*x + c)^5 + 10*b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^4*d*cosh(d*x + c)^6 + 15*b^4*d*cosh(d*x + c)^4 + 9*b^4*d*cosh(d*x + c)^2 + b^4*d)*sinh(d*x + c)^2 + 8*(b^4*d*cosh(d*x + c)^7 + 3*b^4*d*cosh(d*x + c)^5 + 3*b^4*d*cosh(d*x + c)^3 + b^4*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
126,1,1589,0,1.070284," ","integrate((a+b*sech(d*x+c))^(1/2)*tanh(d*x+c)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 4 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(2 \, a^{2} + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b - 2 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, a b \cosh\left(d x + c\right) - 2 \, {\left(2 \, a^{2} + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right) - 3 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} - 15 \, b^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + a b - 2 \, {\left(2 \, a^{2} + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{30 \, {\left(b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} d \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{15 \, {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) - 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(2 \, a^{2} + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b - 2 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, a b \cosh\left(d x + c\right) - 2 \, {\left(2 \, a^{2} + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right) - 3 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} - 15 \, b^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{2} + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + a b - 2 \, {\left(2 \, a^{2} + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{15 \, {\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)}}\right]"," ",0,"[1/30*(15*(b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b*cosh(d*x + c)^3 - (2*a^2 + 15*b^2)*cosh(d*x + c)^4 - (2*a^2 + 15*b^2)*sinh(d*x + c)^4 + 2*(a*b - 2*(2*a^2 + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*a*b*cosh(d*x + c) - 2*(2*a^2 + 9*b^2)*cosh(d*x + c)^2 + 2*(3*a*b*cosh(d*x + c) - 3*(2*a^2 + 15*b^2)*cosh(d*x + c)^2 - 2*a^2 - 9*b^2)*sinh(d*x + c)^2 - 2*a^2 - 15*b^2 + 2*(3*a*b*cosh(d*x + c)^2 - 2*(2*a^2 + 15*b^2)*cosh(d*x + c)^3 + a*b - 2*(2*a^2 + 9*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(b^2*d*cosh(d*x + c)^4 + 4*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*d*sinh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + b^2*d + 2*(3*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 4*(b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c)), -1/15*(15*(b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) - 2*(2*a*b*cosh(d*x + c)^3 - (2*a^2 + 15*b^2)*cosh(d*x + c)^4 - (2*a^2 + 15*b^2)*sinh(d*x + c)^4 + 2*(a*b - 2*(2*a^2 + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*a*b*cosh(d*x + c) - 2*(2*a^2 + 9*b^2)*cosh(d*x + c)^2 + 2*(3*a*b*cosh(d*x + c) - 3*(2*a^2 + 15*b^2)*cosh(d*x + c)^2 - 2*a^2 - 9*b^2)*sinh(d*x + c)^2 - 2*a^2 - 15*b^2 + 2*(3*a*b*cosh(d*x + c)^2 - 2*(2*a^2 + 15*b^2)*cosh(d*x + c)^3 + a*b - 2*(2*a^2 + 9*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(b^2*d*cosh(d*x + c)^4 + 4*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*d*sinh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + b^2*d + 2*(3*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 4*(b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
127,1,605,0,1.035596," ","integrate((a+b*sech(d*x+c))^(1/2)*tanh(d*x+c),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{2 \, d}, -\frac{\sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{d}\right]"," ",0,"[1/2*(sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 4*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/d, -(sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) + 2*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/d]","B",0
128,1,8620,0,0.974357," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) + \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right) + 2 \, \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, d}, -\frac{4 \, \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) - \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) - \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, d}, -\frac{2 \, \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right) - 2 \, \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, d}, -\frac{4 \, \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + 2 \, \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, d}, \frac{2 \, \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) + \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) + 2 \, \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, d}, -\frac{4 \, \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) - 2 \, \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) - \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, d}, -\frac{\sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) - \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{2 \, d}, -\frac{2 \, \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right)}{2 \, d}\right]"," ",0,"[1/4*(sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) + sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)) + 2*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, -1/4*(4*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) - sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) - sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)))/d, -1/4*(2*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)) - 2*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, -1/4*(4*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + 2*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)))/d, 1/4*(2*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) + sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) + 2*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, -1/4*(4*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) - 2*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) - sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)))/d, -1/2*(sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) - sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, -1/2*(2*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)))/d]","B",0
129,-1,0,0,0.000000," ","integrate(coth(d*x+c)^3*(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.630596," ","integrate((a+b*sech(d*x+c))^(1/2)*tanh(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right) + a} \tanh\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c) + a)*tanh(d*x + c)^2, x)","F",0
131,0,0,0,2.245154," ","integrate((a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c) + a), x)","F",0
132,0,0,0,1.269352," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \operatorname{sech}\left(d x + c\right) + a} \coth\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c) + a)*coth(d*x + c)^2, x)","F",0
133,1,2813,0,1.085300," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} \cosh\left(d x + c\right)^{6} + 6 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{4} \sinh\left(d x + c\right)^{6} + 3 \, b^{4} \cosh\left(d x + c\right)^{4} + 3 \, b^{4} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 4 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{4} + 6 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b^{4} \cosh\left(d x + c\right)^{5} + 2 \, b^{4} \cosh\left(d x + c\right)^{3} + b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 16 \, {\left({\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} - {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(12 \, a^{3} b - 35 \, a b^{3} - 6 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(36 \, a^{4} - 87 \, a^{2} b^{2} + 15 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 12 \, a^{4} - 35 \, a^{2} b^{2} - 8 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(12 \, a^{3} b - 20 \, a b^{3} - 10 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{4} - 87 \, a^{2} b^{2} - 10 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right) + {\left(6 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} b + 35 \, a b^{3} + 12 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 24 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{210 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{4} d \sinh\left(d x + c\right)^{6} + 3 \, a b^{4} d \cosh\left(d x + c\right)^{4} + 3 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d + 3 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{4} + 6 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{5} + 2 \, a b^{4} d \cosh\left(d x + c\right)^{3} + a b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{105 \, {\left(b^{4} \cosh\left(d x + c\right)^{6} + 6 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{4} \sinh\left(d x + c\right)^{6} + 3 \, b^{4} \cosh\left(d x + c\right)^{4} + 3 \, b^{4} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 4 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{4} \cosh\left(d x + c\right)^{4} + 6 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b^{4} \cosh\left(d x + c\right)^{5} + 2 \, b^{4} \cosh\left(d x + c\right)^{3} + b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) - 8 \, {\left({\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} - {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(12 \, a^{3} b - 35 \, a b^{3} - 6 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(36 \, a^{4} - 87 \, a^{2} b^{2} + 15 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 12 \, a^{4} - 35 \, a^{2} b^{2} - 8 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(12 \, a^{3} b - 20 \, a b^{3} - 10 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{4} - 87 \, a^{2} b^{2} - 10 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right) + {\left(6 \, {\left(12 \, a^{4} - 35 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b - 35 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} b + 35 \, a b^{3} + 12 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 24 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(12 \, a^{4} - 29 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{105 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{4} d \sinh\left(d x + c\right)^{6} + 3 \, a b^{4} d \cosh\left(d x + c\right)^{4} + 3 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d + 3 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{4} + 6 \, a b^{4} d \cosh\left(d x + c\right)^{2} + a b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{5} + 2 \, a b^{4} d \cosh\left(d x + c\right)^{3} + a b^{4} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/210*(105*(b^4*cosh(d*x + c)^6 + 6*b^4*cosh(d*x + c)*sinh(d*x + c)^5 + b^4*sinh(d*x + c)^6 + 3*b^4*cosh(d*x + c)^4 + 3*b^4*cosh(d*x + c)^2 + 3*(5*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^4 + b^4 + 4*(5*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^4*cosh(d*x + c)^4 + 6*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^2 + 6*(b^4*cosh(d*x + c)^5 + 2*b^4*cosh(d*x + c)^3 + b^4*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 16*((12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^6 + (12*a^4 - 35*a^2*b^2)*sinh(d*x + c)^6 - (12*a^3*b - 35*a*b^3)*cosh(d*x + c)^5 - (12*a^3*b - 35*a*b^3 - 6*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^4 + (36*a^4 - 87*a^2*b^2 + 15*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^2 - 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 12*a^4 - 35*a^2*b^2 - 8*(3*a^3*b - 5*a*b^3)*cosh(d*x + c)^3 - 2*(12*a^3*b - 20*a*b^3 - 10*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^3 + 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^2 - 6*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^2 + (15*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^4 + 36*a^4 - 87*a^2*b^2 - 10*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^3 + 18*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^2 - 24*(3*a^3*b - 5*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - (12*a^3*b - 35*a*b^3)*cosh(d*x + c) + (6*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^5 - 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^4 - 12*a^3*b + 35*a*b^3 + 12*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^3 - 24*(3*a^3*b - 5*a*b^3)*cosh(d*x + c)^2 + 6*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a*b^4*d*cosh(d*x + c)^6 + 6*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^4*d*sinh(d*x + c)^6 + 3*a*b^4*d*cosh(d*x + c)^4 + 3*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d + 3*(5*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d)*sinh(d*x + c)^4 + 4*(5*a*b^4*d*cosh(d*x + c)^3 + 3*a*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*b^4*d*cosh(d*x + c)^4 + 6*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d)*sinh(d*x + c)^2 + 6*(a*b^4*d*cosh(d*x + c)^5 + 2*a*b^4*d*cosh(d*x + c)^3 + a*b^4*d*cosh(d*x + c))*sinh(d*x + c)), -1/105*(105*(b^4*cosh(d*x + c)^6 + 6*b^4*cosh(d*x + c)*sinh(d*x + c)^5 + b^4*sinh(d*x + c)^6 + 3*b^4*cosh(d*x + c)^4 + 3*b^4*cosh(d*x + c)^2 + 3*(5*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^4 + b^4 + 4*(5*b^4*cosh(d*x + c)^3 + 3*b^4*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^4*cosh(d*x + c)^4 + 6*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^2 + 6*(b^4*cosh(d*x + c)^5 + 2*b^4*cosh(d*x + c)^3 + b^4*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) - 8*((12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^6 + (12*a^4 - 35*a^2*b^2)*sinh(d*x + c)^6 - (12*a^3*b - 35*a*b^3)*cosh(d*x + c)^5 - (12*a^3*b - 35*a*b^3 - 6*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^4 + (36*a^4 - 87*a^2*b^2 + 15*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^2 - 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 12*a^4 - 35*a^2*b^2 - 8*(3*a^3*b - 5*a*b^3)*cosh(d*x + c)^3 - 2*(12*a^3*b - 20*a*b^3 - 10*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^3 + 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^2 - 6*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^2 + (15*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^4 + 36*a^4 - 87*a^2*b^2 - 10*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^3 + 18*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^2 - 24*(3*a^3*b - 5*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - (12*a^3*b - 35*a*b^3)*cosh(d*x + c) + (6*(12*a^4 - 35*a^2*b^2)*cosh(d*x + c)^5 - 5*(12*a^3*b - 35*a*b^3)*cosh(d*x + c)^4 - 12*a^3*b + 35*a*b^3 + 12*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c)^3 - 24*(3*a^3*b - 5*a*b^3)*cosh(d*x + c)^2 + 6*(12*a^4 - 29*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a*b^4*d*cosh(d*x + c)^6 + 6*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^4*d*sinh(d*x + c)^6 + 3*a*b^4*d*cosh(d*x + c)^4 + 3*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d + 3*(5*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d)*sinh(d*x + c)^4 + 4*(5*a*b^4*d*cosh(d*x + c)^3 + 3*a*b^4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*b^4*d*cosh(d*x + c)^4 + 6*a*b^4*d*cosh(d*x + c)^2 + a*b^4*d)*sinh(d*x + c)^2 + 6*(a*b^4*d*cosh(d*x + c)^5 + 2*a*b^4*d*cosh(d*x + c)^3 + a*b^4*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
134,1,925,0,1.040871," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{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{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} - a b \cosh\left(d x + c\right) + a^{2} + {\left(2 \, a^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{6 \, {\left(a b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)^{2} + a b^{2} d\right)}}, -\frac{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{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} - a b \cosh\left(d x + c\right) + a^{2} + {\left(2 \, a^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{3 \, {\left(a b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)^{2} + a b^{2} d\right)}}\right]"," ",0,"[1/6*(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(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 8*(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 - a*b*cosh(d*x + c) + a^2 + (2*a^2*cosh(d*x + c) - a*b)*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a*b^2*d*cosh(d*x + c)^2 + 2*a*b^2*d*cosh(d*x + c)*sinh(d*x + c) + a*b^2*d*sinh(d*x + c)^2 + a*b^2*d), -1/3*(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(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) + 4*(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 - a*b*cosh(d*x + c) + a^2 + (2*a^2*cosh(d*x + c) - a*b)*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a*b^2*d*cosh(d*x + c)^2 + 2*a*b^2*d*cosh(d*x + c)*sinh(d*x + c) + a*b^2*d*sinh(d*x + c)^2 + a*b^2*d)]","B",0
135,1,558,0,1.023405," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{2 \, \sqrt{a} d}, -\frac{\sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right)}{a d}\right]"," ",0,"[1/2*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(sqrt(a)*d), -sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)))/(a*d)]","B",0
136,1,8908,0,1.305265," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + a b\right)} \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) + {\left(a^{2} - a b\right)} \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right) + 2 \, {\left(a^{2} - b^{2}\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{2 \, {\left(a^{2} - a b\right)} \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) + {\left(a^{2} + a b\right)} \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) + 2 \, {\left(a^{2} - b^{2}\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{2 \, {\left(a^{2} + a b\right)} \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - {\left(a^{2} - a b\right)} \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right) - 2 \, {\left(a^{2} - b^{2}\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{{\left(a^{2} + a b\right)} \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - {\left(a^{2} - a b\right)} \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) - {\left(a^{2} - b^{2}\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{4 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) - {\left(a^{2} + a b\right)} \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right) - {\left(a^{2} - a b\right)} \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{4 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) - 2 \, {\left(a^{2} - a b\right)} \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right) - {\left(a^{2} + a b\right)} \sqrt{a - b} \log\left(-\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b\right)} \sqrt{a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} - 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 3 \, b^{2} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{4 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + 2 \, {\left(a^{2} + a b\right)} \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - {\left(a^{2} - a b\right)} \sqrt{a + b} \log\left(-\frac{{\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + 3 \, b^{2} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} - 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b\right)} \sqrt{a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 4 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(8 \, a^{2} + 8 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{4} + 4 \, {\left(\cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right)^{3} + 6 \, {\left(\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) + 1\right)} \sinh\left(d x + c\right)^{2} + 6 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)^{2} + 3 \, \cosh\left(d x + c\right) - 1\right)} \sinh\left(d x + c\right) - 4 \, \cosh\left(d x + c\right) + 1}\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{2 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a} \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} + 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a}\right) + {\left(a^{2} + a b\right)} \sqrt{-a + b} \arctan\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{-a + b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a - b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a - b}\right) - {\left(a^{2} - a b\right)} \sqrt{-a - b} \arctan\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{-a - b} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{{\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + 2 \, a + b}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[1/4*((a^2 + a*b)*sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) + (a^2 - a*b)*sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)) + 2*(a^2 - b^2)*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^3 - a*b^2)*d), 1/4*(2*(a^2 - a*b)*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) + (a^2 + a*b)*sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) + 2*(a^2 - b^2)*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^3 - a*b^2)*d), -1/4*(2*(a^2 + a*b)*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - (a^2 - a*b)*sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)) - 2*(a^2 - b^2)*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^3 - a*b^2)*d), -1/2*((a^2 + a*b)*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - (a^2 - a*b)*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) - (a^2 - b^2)*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^3 - a*b^2)*d), -1/4*(4*(a^2 - b^2)*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) - (a^2 + a*b)*sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)) - (a^2 - a*b)*sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)))/((a^3 - a*b^2)*d), -1/4*(4*(a^2 - b^2)*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) - 2*(a^2 - a*b)*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)) - (a^2 + a*b)*sqrt(a - b)*log(-((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 - 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b - 3*b^2 + (8*a^2 - 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2 + 6*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 - 4*((2*a - b)*cosh(d*x + c)^4 + (2*a - b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*(2*a - b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a - b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)*sqrt(a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b - 3*b^2)*cosh(d*x + c) + 4*((8*a^2 - 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a*b - 3*b^2 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) + 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 + 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) + 1)*sinh(d*x + c) + 4*cosh(d*x + c) + 1)))/((a^3 - a*b^2)*d), -1/4*(4*(a^2 - b^2)*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + 2*(a^2 + a*b)*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - (a^2 - a*b)*sqrt(a + b)*log(-((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^4 + (8*a^2 + 8*a*b + b^2)*sinh(d*x + c)^4 + 4*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 4*(4*a*b + 3*b^2 + (8*a^2 + 8*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 6*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + b^2 - 4*((2*a + b)*cosh(d*x + c)^4 + (2*a + b)*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^3 + 2*(2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(2*(2*a + b)*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 2*(2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)*sqrt(a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 4*(4*a*b + 3*b^2)*cosh(d*x + c) + 4*((8*a^2 + 8*a*b + b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^4 + 4*(cosh(d*x + c) - 1)*sinh(d*x + c)^3 + sinh(d*x + c)^4 - 4*cosh(d*x + c)^3 + 6*(cosh(d*x + c)^2 - 2*cosh(d*x + c) + 1)*sinh(d*x + c)^2 + 6*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - 3*cosh(d*x + c)^2 + 3*cosh(d*x + c) - 1)*sinh(d*x + c) - 4*cosh(d*x + c) + 1)))/((a^3 - a*b^2)*d), -1/2*(2*(a^2 - b^2)*sqrt(-a)*arctan((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)) + (a^2 + a*b)*sqrt(-a + b)*arctan(-2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a + b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a - b)*cosh(d*x + c)^2 + (2*a - b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a - b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a - b)) - (a^2 - a*b)*sqrt(-a - b)*arctan(2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-a - b)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/((2*a + b)*cosh(d*x + c)^2 + (2*a + b)*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*((2*a + b)*cosh(d*x + c) + b)*sinh(d*x + c) + 2*a + b)))/((a^3 - a*b^2)*d)]","B",0
137,-1,0,0,0.000000," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,0,0,0,0.667498," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(d x + c\right)^{4}}{\sqrt{b \operatorname{sech}\left(d x + c\right) + a}}, x\right)"," ",0,"integral(tanh(d*x + c)^4/sqrt(b*sech(d*x + c) + a), x)","F",0
139,-1,0,0,0.000000," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,0,0,0,3.432683," ","integrate(1/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \operatorname{sech}\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*sech(d*x + c) + a), x)","F",0
141,-1,0,0,0.000000," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,1,3745,0,2.682308," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a b^{4} \cosh\left(d x + c\right)^{6} + a b^{4} \sinh\left(d x + c\right)^{6} + 2 \, b^{5} \cosh\left(d x + c\right)^{5} + 3 \, a b^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} \cosh\left(d x + c\right)^{3} + 3 \, a b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{5} \cosh\left(d x + c\right) + 2 \, {\left(3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)^{5} + a b^{4} + {\left(15 \, a b^{4} \cosh\left(d x + c\right)^{2} + 10 \, b^{5} \cosh\left(d x + c\right) + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} \cosh\left(d x + c\right)^{3} + 5 \, b^{5} \cosh\left(d x + c\right)^{2} + 3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a b^{4} \cosh\left(d x + c\right)^{4} + 20 \, b^{5} \cosh\left(d x + c\right)^{3} + 18 \, a b^{4} \cosh\left(d x + c\right)^{2} + 12 \, b^{5} \cosh\left(d x + c\right) + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} \cosh\left(d x + c\right)^{5} + 5 \, b^{5} \cosh\left(d x + c\right)^{4} + 6 \, a b^{4} \cosh\left(d x + c\right)^{3} + 6 \, b^{5} \cosh\left(d x + c\right)^{2} + 3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 4 \, {\left({\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + 5 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 96 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, a^{4} b - 10 \, a^{2} b^{3} + 10 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 48 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{10 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{6} + a^{3} b^{4} d \sinh\left(d x + c\right)^{6} + 2 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{5} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b^{5} d \cosh\left(d x + c\right) + a^{3} b^{4} d + 2 \, {\left(3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 10 \, a^{2} b^{5} d \cosh\left(d x + c\right) + 3 \, a^{3} b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 5 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 18 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 12 \, a^{2} b^{5} d \cosh\left(d x + c\right) + 3 \, a^{3} b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{4} + 6 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 6 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)\right)}}, -\frac{5 \, {\left(a b^{4} \cosh\left(d x + c\right)^{6} + a b^{4} \sinh\left(d x + c\right)^{6} + 2 \, b^{5} \cosh\left(d x + c\right)^{5} + 3 \, a b^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} \cosh\left(d x + c\right)^{3} + 3 \, a b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{5} \cosh\left(d x + c\right) + 2 \, {\left(3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)^{5} + a b^{4} + {\left(15 \, a b^{4} \cosh\left(d x + c\right)^{2} + 10 \, b^{5} \cosh\left(d x + c\right) + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} \cosh\left(d x + c\right)^{3} + 5 \, b^{5} \cosh\left(d x + c\right)^{2} + 3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a b^{4} \cosh\left(d x + c\right)^{4} + 20 \, b^{5} \cosh\left(d x + c\right)^{3} + 18 \, a b^{4} \cosh\left(d x + c\right)^{2} + 12 \, b^{5} \cosh\left(d x + c\right) + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} \cosh\left(d x + c\right)^{5} + 5 \, b^{5} \cosh\left(d x + c\right)^{4} + 6 \, a b^{4} \cosh\left(d x + c\right)^{3} + 6 \, b^{5} \cosh\left(d x + c\right)^{2} + 3 \, a b^{4} \cosh\left(d x + c\right) + b^{5}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) + 2 \, {\left({\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} b - 8 \, a^{2} b^{3} + 5 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4} + 15 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 96 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(16 \, a^{5} - 20 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, a^{4} b - 10 \, a^{2} b^{3} + 10 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 48 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 \, a^{5} - 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{5 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{6} + a^{3} b^{4} d \sinh\left(d x + c\right)^{6} + 2 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{5} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b^{5} d \cosh\left(d x + c\right) + a^{3} b^{4} d + 2 \, {\left(3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 10 \, a^{2} b^{5} d \cosh\left(d x + c\right) + 3 \, a^{3} b^{4} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 5 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 18 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + 12 \, a^{2} b^{5} d \cosh\left(d x + c\right) + 3 \, a^{3} b^{4} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{4} + 6 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 6 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} b^{4} d \cosh\left(d x + c\right) + a^{2} b^{5} d\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/10*(5*(a*b^4*cosh(d*x + c)^6 + a*b^4*sinh(d*x + c)^6 + 2*b^5*cosh(d*x + c)^5 + 3*a*b^4*cosh(d*x + c)^4 + 4*b^5*cosh(d*x + c)^3 + 3*a*b^4*cosh(d*x + c)^2 + 2*b^5*cosh(d*x + c) + 2*(3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c)^5 + a*b^4 + (15*a*b^4*cosh(d*x + c)^2 + 10*b^5*cosh(d*x + c) + 3*a*b^4)*sinh(d*x + c)^4 + 4*(5*a*b^4*cosh(d*x + c)^3 + 5*b^5*cosh(d*x + c)^2 + 3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c)^3 + (15*a*b^4*cosh(d*x + c)^4 + 20*b^5*cosh(d*x + c)^3 + 18*a*b^4*cosh(d*x + c)^2 + 12*b^5*cosh(d*x + c) + 3*a*b^4)*sinh(d*x + c)^2 + 2*(3*a*b^4*cosh(d*x + c)^5 + 5*b^5*cosh(d*x + c)^4 + 6*a*b^4*cosh(d*x + c)^3 + 6*b^5*cosh(d*x + c)^2 + 3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c))*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 4*((16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^6 + (16*a^5 - 20*a^3*b^2 + 5*a*b^4)*sinh(d*x + c)^6 + 4*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^5 + 2*(8*a^4*b - 10*a^2*b^3 + 3*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 16*a^5 - 20*a^3*b^2 + 5*a*b^4 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^4 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4 + 15*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^2 + 20*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 32*(a^4*b - a^2*b^3)*cosh(d*x + c)^3 + 4*(8*a^4*b - 8*a^2*b^3 + 5*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^3 + 10*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4 + 15*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^4 + 40*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^3 + 6*(48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^2 + 96*(a^4*b - a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c) + 2*(3*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^5 + 8*a^4*b - 10*a^2*b^3 + 10*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^4 + 2*(48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^3 + 48*(a^4*b - a^2*b^3)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*b^4*d*cosh(d*x + c)^6 + a^3*b^4*d*sinh(d*x + c)^6 + 2*a^2*b^5*d*cosh(d*x + c)^5 + 3*a^3*b^4*d*cosh(d*x + c)^4 + 4*a^2*b^5*d*cosh(d*x + c)^3 + 3*a^3*b^4*d*cosh(d*x + c)^2 + 2*a^2*b^5*d*cosh(d*x + c) + a^3*b^4*d + 2*(3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c)^5 + (15*a^3*b^4*d*cosh(d*x + c)^2 + 10*a^2*b^5*d*cosh(d*x + c) + 3*a^3*b^4*d)*sinh(d*x + c)^4 + 4*(5*a^3*b^4*d*cosh(d*x + c)^3 + 5*a^2*b^5*d*cosh(d*x + c)^2 + 3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c)^3 + (15*a^3*b^4*d*cosh(d*x + c)^4 + 20*a^2*b^5*d*cosh(d*x + c)^3 + 18*a^3*b^4*d*cosh(d*x + c)^2 + 12*a^2*b^5*d*cosh(d*x + c) + 3*a^3*b^4*d)*sinh(d*x + c)^2 + 2*(3*a^3*b^4*d*cosh(d*x + c)^5 + 5*a^2*b^5*d*cosh(d*x + c)^4 + 6*a^3*b^4*d*cosh(d*x + c)^3 + 6*a^2*b^5*d*cosh(d*x + c)^2 + 3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c)), -1/5*(5*(a*b^4*cosh(d*x + c)^6 + a*b^4*sinh(d*x + c)^6 + 2*b^5*cosh(d*x + c)^5 + 3*a*b^4*cosh(d*x + c)^4 + 4*b^5*cosh(d*x + c)^3 + 3*a*b^4*cosh(d*x + c)^2 + 2*b^5*cosh(d*x + c) + 2*(3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c)^5 + a*b^4 + (15*a*b^4*cosh(d*x + c)^2 + 10*b^5*cosh(d*x + c) + 3*a*b^4)*sinh(d*x + c)^4 + 4*(5*a*b^4*cosh(d*x + c)^3 + 5*b^5*cosh(d*x + c)^2 + 3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c)^3 + (15*a*b^4*cosh(d*x + c)^4 + 20*b^5*cosh(d*x + c)^3 + 18*a*b^4*cosh(d*x + c)^2 + 12*b^5*cosh(d*x + c) + 3*a*b^4)*sinh(d*x + c)^2 + 2*(3*a*b^4*cosh(d*x + c)^5 + 5*b^5*cosh(d*x + c)^4 + 6*a*b^4*cosh(d*x + c)^3 + 6*b^5*cosh(d*x + c)^2 + 3*a*b^4*cosh(d*x + c) + b^5)*sinh(d*x + c))*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) + 2*((16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^6 + (16*a^5 - 20*a^3*b^2 + 5*a*b^4)*sinh(d*x + c)^6 + 4*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^5 + 2*(8*a^4*b - 10*a^2*b^3 + 3*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 16*a^5 - 20*a^3*b^2 + 5*a*b^4 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^4 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4 + 15*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^2 + 20*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 32*(a^4*b - a^2*b^3)*cosh(d*x + c)^3 + 4*(8*a^4*b - 8*a^2*b^3 + 5*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^3 + 10*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4 + 15*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^4 + 40*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^3 + 6*(48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^2 + 96*(a^4*b - a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c) + 2*(3*(16*a^5 - 20*a^3*b^2 + 5*a*b^4)*cosh(d*x + c)^5 + 8*a^4*b - 10*a^2*b^3 + 10*(4*a^4*b - 5*a^2*b^3)*cosh(d*x + c)^4 + 2*(48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c)^3 + 48*(a^4*b - a^2*b^3)*cosh(d*x + c)^2 + (48*a^5 - 68*a^3*b^2 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*b^4*d*cosh(d*x + c)^6 + a^3*b^4*d*sinh(d*x + c)^6 + 2*a^2*b^5*d*cosh(d*x + c)^5 + 3*a^3*b^4*d*cosh(d*x + c)^4 + 4*a^2*b^5*d*cosh(d*x + c)^3 + 3*a^3*b^4*d*cosh(d*x + c)^2 + 2*a^2*b^5*d*cosh(d*x + c) + a^3*b^4*d + 2*(3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c)^5 + (15*a^3*b^4*d*cosh(d*x + c)^2 + 10*a^2*b^5*d*cosh(d*x + c) + 3*a^3*b^4*d)*sinh(d*x + c)^4 + 4*(5*a^3*b^4*d*cosh(d*x + c)^3 + 5*a^2*b^5*d*cosh(d*x + c)^2 + 3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c)^3 + (15*a^3*b^4*d*cosh(d*x + c)^4 + 20*a^2*b^5*d*cosh(d*x + c)^3 + 18*a^3*b^4*d*cosh(d*x + c)^2 + 12*a^2*b^5*d*cosh(d*x + c) + 3*a^3*b^4*d)*sinh(d*x + c)^2 + 2*(3*a^3*b^4*d*cosh(d*x + c)^5 + 5*a^2*b^5*d*cosh(d*x + c)^4 + 6*a^3*b^4*d*cosh(d*x + c)^3 + 6*a^2*b^5*d*cosh(d*x + c)^2 + 3*a^3*b^4*d*cosh(d*x + c) + a^2*b^5*d)*sinh(d*x + c))]","B",0
143,1,1107,0,1.239455," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} \sinh\left(d x + c\right)^{2} + 2 \, b^{3} \cosh\left(d x + c\right) + a b^{2} + 2 \, {\left(a b^{2} \cosh\left(d x + c\right) + b^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 4 \, {\left(2 \, a^{2} b \cosh\left(d x + c\right) + 2 \, a^{3} - a b^{2} + {\left(2 \, a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} - a b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + {\left(2 \, a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{2 \, {\left(a^{3} b^{2} d \cosh\left(d x + c\right)^{2} + a^{3} b^{2} d \sinh\left(d x + c\right)^{2} + 2 \, a^{2} b^{3} d \cosh\left(d x + c\right) + a^{3} b^{2} d + 2 \, {\left(a^{3} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{3} d\right)} \sinh\left(d x + c\right)\right)}}, -\frac{{\left(a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} \sinh\left(d x + c\right)^{2} + 2 \, b^{3} \cosh\left(d x + c\right) + a b^{2} + 2 \, {\left(a b^{2} \cosh\left(d x + c\right) + b^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) - 2 \, {\left(2 \, a^{2} b \cosh\left(d x + c\right) + 2 \, a^{3} - a b^{2} + {\left(2 \, a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} - a b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + {\left(2 \, a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{3} b^{2} d \cosh\left(d x + c\right)^{2} + a^{3} b^{2} d \sinh\left(d x + c\right)^{2} + 2 \, a^{2} b^{3} d \cosh\left(d x + c\right) + a^{3} b^{2} d + 2 \, {\left(a^{3} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{3} d\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[1/2*((a*b^2*cosh(d*x + c)^2 + a*b^2*sinh(d*x + c)^2 + 2*b^3*cosh(d*x + c) + a*b^2 + 2*(a*b^2*cosh(d*x + c) + b^3)*sinh(d*x + c))*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a^2*b*cosh(d*x + c) + 2*a^3 - a*b^2 + (2*a^3 - a*b^2)*cosh(d*x + c)^2 + (2*a^3 - a*b^2)*sinh(d*x + c)^2 + 2*(a^2*b + (2*a^3 - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*b^2*d*cosh(d*x + c)^2 + a^3*b^2*d*sinh(d*x + c)^2 + 2*a^2*b^3*d*cosh(d*x + c) + a^3*b^2*d + 2*(a^3*b^2*d*cosh(d*x + c) + a^2*b^3*d)*sinh(d*x + c)), -((a*b^2*cosh(d*x + c)^2 + a*b^2*sinh(d*x + c)^2 + 2*b^3*cosh(d*x + c) + a*b^2 + 2*(a*b^2*cosh(d*x + c) + b^3)*sinh(d*x + c))*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) - 2*(2*a^2*b*cosh(d*x + c) + 2*a^3 - a*b^2 + (2*a^3 - a*b^2)*cosh(d*x + c)^2 + (2*a^3 - a*b^2)*sinh(d*x + c)^2 + 2*(a^2*b + (2*a^3 - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*b^2*d*cosh(d*x + c)^2 + a^3*b^2*d*sinh(d*x + c)^2 + 2*a^2*b^3*d*cosh(d*x + c) + a^3*b^2*d + 2*(a^3*b^2*d*cosh(d*x + c) + a^2*b^3*d)*sinh(d*x + c))]","B",0
144,1,917,0,1.056750," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \log\left(-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, a^{2} \cosh\left(d x + c\right)^{2} + 12 \, a b \cosh\left(d x + c\right) + 4 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right)^{2} + {\left(6 \, a \cosh\left(d x + c\right)^{2} + 3 \, b \cosh\left(d x + c\right) + 2 \, a\right)} \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(4 \, a \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}} + 2 \, {\left(4 \, a^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b + {\left(4 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{2 \, {\left(a^{3} d \cosh\left(d x + c\right)^{2} + a^{3} d \sinh\left(d x + c\right)^{2} + 2 \, a^{2} b d \cosh\left(d x + c\right) + a^{3} d + 2 \, {\left(a^{3} d \cosh\left(d x + c\right) + a^{2} b d\right)} \sinh\left(d x + c\right)\right)}}, -\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} + b \cosh\left(d x + c\right) + {\left(2 \, a \cosh\left(d x + c\right) + b\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{2} \cosh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}\right) + 2 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{\frac{a \cosh\left(d x + c\right) + b}{\cosh\left(d x + c\right)}}}{a^{3} d \cosh\left(d x + c\right)^{2} + a^{3} d \sinh\left(d x + c\right)^{2} + 2 \, a^{2} b d \cosh\left(d x + c\right) + a^{3} d + 2 \, {\left(a^{3} d \cosh\left(d x + c\right) + a^{2} b d\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[1/2*((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*log(-(2*a^2*cosh(d*x + c)^4 + 2*a^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 + 4*(2*a^2*cosh(d*x + c) + a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + (4*a^2 + b^2)*cosh(d*x + c)^2 + (12*a^2*cosh(d*x + c)^2 + 12*a*b*cosh(d*x + c) + 4*a^2 + b^2)*sinh(d*x + c)^2 + 2*a^2 + 2*(a*cosh(d*x + c)^4 + a*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (4*a*cosh(d*x + c) + b)*sinh(d*x + c)^3 + 2*a*cosh(d*x + c)^2 + (6*a*cosh(d*x + c)^2 + 3*b*cosh(d*x + c) + 2*a)*sinh(d*x + c)^2 + b*cosh(d*x + c) + (4*a*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 4*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)) + 2*(4*a^2*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)^2 + 2*a*b + (4*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*d*cosh(d*x + c)^2 + a^3*d*sinh(d*x + c)^2 + 2*a^2*b*d*cosh(d*x + c) + a^3*d + 2*(a^3*d*cosh(d*x + c) + a^2*b*d)*sinh(d*x + c)), -((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + 2*b*cosh(d*x + c) + 2*(a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*arctan((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 + b*cosh(d*x + c) + (2*a*cosh(d*x + c) + b)*sinh(d*x + c) + a)*sqrt(-a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c))/(a^2*cosh(d*x + c)^2 + a^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + a^2 + 2*(a^2*cosh(d*x + c) + a*b)*sinh(d*x + c))) + 2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*sqrt((a*cosh(d*x + c) + b)/cosh(d*x + c)))/(a^3*d*cosh(d*x + c)^2 + a^3*d*sinh(d*x + c)^2 + 2*a^2*b*d*cosh(d*x + c) + a^3*d + 2*(a^3*d*cosh(d*x + c) + a^2*b*d)*sinh(d*x + c))]","B",0
145,-1,0,0,0.000000," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,7.754411," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right) + a} \tanh\left(d x + c\right)^{4}}{b^{2} \operatorname{sech}\left(d x + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c) + a)*tanh(d*x + c)^4/(b^2*sech(d*x + c)^2 + 2*a*b*sech(d*x + c) + a^2), x)","F",0
148,0,0,0,9.076293," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \operatorname{sech}\left(d x + c\right) + a} \tanh\left(d x + c\right)^{2}}{b^{2} \operatorname{sech}\left(d x + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sech(d*x + c) + a)*tanh(d*x + c)^2/(b^2*sech(d*x + c)^2 + 2*a*b*sech(d*x + c) + a^2), x)","F",0
149,-1,0,0,0.000000," ","integrate(1/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,1,589,0,0.773745," ","integrate(exp(c*(b*x+a))*(sech(b*c*x+a*c)^2)^(7/2),x, algorithm=""fricas"")","-\frac{16 \, {\left(21 \, \cosh\left(b c x + a c\right)^{3} + 63 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{2} + 19 \, \sinh\left(b c x + a c\right)^{3} + 3 \, {\left(19 \, \cosh\left(b c x + a c\right)^{2} + 3\right)} \sinh\left(b c x + a c\right) + 21 \, \cosh\left(b c x + a c\right)\right)}}{15 \, {\left(b c \cosh\left(b c x + a c\right)^{9} + 9 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{8} + b c \sinh\left(b c x + a c\right)^{9} + 6 \, b c \cosh\left(b c x + a c\right)^{7} + 6 \, {\left(6 \, b c \cosh\left(b c x + a c\right)^{2} + b c\right)} \sinh\left(b c x + a c\right)^{7} + 15 \, b c \cosh\left(b c x + a c\right)^{5} + 42 \, {\left(2 \, 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)^{6} + 3 \, {\left(42 \, b c \cosh\left(b c x + a c\right)^{4} + 42 \, b c \cosh\left(b c x + a c\right)^{2} + 5 \, b c\right)} \sinh\left(b c x + a c\right)^{5} + 21 \, b c \cosh\left(b c x + a c\right)^{3} + 3 \, {\left(42 \, b c \cosh\left(b c x + a c\right)^{5} + 70 \, b c \cosh\left(b c x + a c\right)^{3} + 25 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{4} + {\left(84 \, b c \cosh\left(b c x + a c\right)^{6} + 210 \, b c \cosh\left(b c x + a c\right)^{4} + 150 \, b c \cosh\left(b c x + a c\right)^{2} + 19 \, b c\right)} \sinh\left(b c x + a c\right)^{3} + 21 \, b c \cosh\left(b c x + a c\right) + 3 \, {\left(12 \, b c \cosh\left(b c x + a c\right)^{7} + 42 \, b c \cosh\left(b c x + a c\right)^{5} + 50 \, b c \cosh\left(b c x + a c\right)^{3} + 21 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} + 3 \, {\left(3 \, b c \cosh\left(b c x + a c\right)^{8} + 14 \, b c \cosh\left(b c x + a c\right)^{6} + 25 \, b c \cosh\left(b c x + a c\right)^{4} + 19 \, b c \cosh\left(b c x + a c\right)^{2} + 3 \, b c\right)} \sinh\left(b c x + a c\right)\right)}}"," ",0,"-16/15*(21*cosh(b*c*x + a*c)^3 + 63*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^2 + 19*sinh(b*c*x + a*c)^3 + 3*(19*cosh(b*c*x + a*c)^2 + 3)*sinh(b*c*x + a*c) + 21*cosh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^9 + 9*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^8 + b*c*sinh(b*c*x + a*c)^9 + 6*b*c*cosh(b*c*x + a*c)^7 + 6*(6*b*c*cosh(b*c*x + a*c)^2 + b*c)*sinh(b*c*x + a*c)^7 + 15*b*c*cosh(b*c*x + a*c)^5 + 42*(2*b*c*cosh(b*c*x + a*c)^3 + b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^6 + 3*(42*b*c*cosh(b*c*x + a*c)^4 + 42*b*c*cosh(b*c*x + a*c)^2 + 5*b*c)*sinh(b*c*x + a*c)^5 + 21*b*c*cosh(b*c*x + a*c)^3 + 3*(42*b*c*cosh(b*c*x + a*c)^5 + 70*b*c*cosh(b*c*x + a*c)^3 + 25*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^4 + (84*b*c*cosh(b*c*x + a*c)^6 + 210*b*c*cosh(b*c*x + a*c)^4 + 150*b*c*cosh(b*c*x + a*c)^2 + 19*b*c)*sinh(b*c*x + a*c)^3 + 21*b*c*cosh(b*c*x + a*c) + 3*(12*b*c*cosh(b*c*x + a*c)^7 + 42*b*c*cosh(b*c*x + a*c)^5 + 50*b*c*cosh(b*c*x + a*c)^3 + 21*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 + 3*(3*b*c*cosh(b*c*x + a*c)^8 + 14*b*c*cosh(b*c*x + a*c)^6 + 25*b*c*cosh(b*c*x + a*c)^4 + 19*b*c*cosh(b*c*x + a*c)^2 + 3*b*c)*sinh(b*c*x + a*c))","B",0
152,1,315,0,0.504159," ","integrate(exp(c*(b*x+a))*(sech(b*c*x+a*c)^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(7 \, \cosh\left(b c x + a c\right)^{2} + 10 \, \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)^{2} + 4\right)}}{3 \, {\left(b c \cosh\left(b c x + a c\right)^{6} + 6 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{5} + b c \sinh\left(b c x + a c\right)^{6} + 4 \, b c \cosh\left(b c x + a c\right)^{4} + {\left(15 \, b c \cosh\left(b c x + a c\right)^{2} + 4 \, b c\right)} \sinh\left(b c x + a c\right)^{4} + 7 \, b c \cosh\left(b c x + a c\right)^{2} + 4 \, {\left(5 \, b c \cosh\left(b c x + a c\right)^{3} + 4 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{3} + {\left(15 \, b c \cosh\left(b c x + a c\right)^{4} + 24 \, b c \cosh\left(b c x + a c\right)^{2} + 7 \, b c\right)} \sinh\left(b c x + a c\right)^{2} + 4 \, b c + 2 \, {\left(3 \, b c \cosh\left(b c x + a c\right)^{5} + 8 \, b c \cosh\left(b c x + a c\right)^{3} + 5 \, b c \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)\right)}}"," ",0,"-4/3*(7*cosh(b*c*x + a*c)^2 + 10*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + 7*sinh(b*c*x + a*c)^2 + 4)/(b*c*cosh(b*c*x + a*c)^6 + 6*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^5 + b*c*sinh(b*c*x + a*c)^6 + 4*b*c*cosh(b*c*x + a*c)^4 + (15*b*c*cosh(b*c*x + a*c)^2 + 4*b*c)*sinh(b*c*x + a*c)^4 + 7*b*c*cosh(b*c*x + a*c)^2 + 4*(5*b*c*cosh(b*c*x + a*c)^3 + 4*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^3 + (15*b*c*cosh(b*c*x + a*c)^4 + 24*b*c*cosh(b*c*x + a*c)^2 + 7*b*c)*sinh(b*c*x + a*c)^2 + 4*b*c + 2*(3*b*c*cosh(b*c*x + a*c)^5 + 8*b*c*cosh(b*c*x + a*c)^3 + 5*b*c*cosh(b*c*x + a*c))*sinh(b*c*x + a*c))","B",0
153,1,120,0,0.609218," ","integrate(exp(c*(b*x+a))*(sech(b*c*x+a*c)^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)}}{b c \cosh\left(b c x + a c\right)^{3} + 3 \, b c \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{2} + b c \sinh\left(b c x + a c\right)^{3} + 3 \, b c \cosh\left(b c x + a c\right) + {\left(3 \, b c \cosh\left(b c x + a c\right)^{2} + b c\right)} \sinh\left(b c x + a c\right)}"," ",0,"-2*(3*cosh(b*c*x + a*c) + sinh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c)^3 + 3*b*c*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^2 + b*c*sinh(b*c*x + a*c)^3 + 3*b*c*cosh(b*c*x + a*c) + (3*b*c*cosh(b*c*x + a*c)^2 + b*c)*sinh(b*c*x + a*c))","B",0
154,1,42,0,0.420469," ","integrate(exp(c*(b*x+a))*(sech(b*c*x+a*c)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(\frac{2 \, \cosh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{b c}"," ",0,"log(2*cosh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c)))/(b*c)","A",0
155,1,66,0,0.401943," ","integrate(exp(c*(b*x+a))/(sech(b*c*x+a*c)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b c x + 1\right)} \cosh\left(b c x + a c\right) - {\left(2 \, b c x - 1\right)} \sinh\left(b c x + a c\right)}{4 \, {\left(b c \cosh\left(b c x + a c\right) - b c \sinh\left(b c x + a c\right)\right)}}"," ",0,"1/4*((2*b*c*x + 1)*cosh(b*c*x + a*c) - (2*b*c*x - 1)*sinh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c) - b*c*sinh(b*c*x + a*c))","A",0
156,1,126,0,0.411194," ","integrate(exp(c*(b*x+a))/(sech(b*c*x+a*c)^2)^(3/2),x, algorithm=""fricas"")","-\frac{\cosh\left(b c x + a c\right)^{3} + 3 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right)^{2} - 3 \, \sinh\left(b c x + a c\right)^{3} - 6 \, {\left(2 \, b c x + 1\right)} \cosh\left(b c x + a c\right) + 3 \, {\left(4 \, b c x - 3 \, \cosh\left(b c x + a c\right)^{2} - 2\right)} \sinh\left(b c x + a c\right)}{32 \, {\left(b c \cosh\left(b c x + a c\right) - b c \sinh\left(b c x + a c\right)\right)}}"," ",0,"-1/32*(cosh(b*c*x + a*c)^3 + 3*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^2 - 3*sinh(b*c*x + a*c)^3 - 6*(2*b*c*x + 1)*cosh(b*c*x + a*c) + 3*(4*b*c*x - 3*cosh(b*c*x + a*c)^2 - 2)*sinh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c) - b*c*sinh(b*c*x + a*c))","A",0
157,1,218,0,0.434124," ","integrate(exp(c*(b*x+a))/(sech(b*c*x+a*c)^2)^(5/2),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} - 5 \, \sinh\left(b c x + a c\right)^{5} - 5 \, {\left(10 \, \cosh\left(b c x + a c\right)^{2} + 9\right)} \sinh\left(b c x + a c\right)^{3} + 15 \, \cosh\left(b c x + a c\right)^{3} + 5 \, {\left(2 \, \cosh\left(b c x + a c\right)^{3} + 9 \, \cosh\left(b c x + a c\right)\right)} \sinh\left(b c x + a c\right)^{2} - 60 \, {\left(2 \, b c x + 1\right)} \cosh\left(b c x + a c\right) - 5 \, {\left(5 \, \cosh\left(b c x + a c\right)^{4} - 24 \, b c x + 27 \, \cosh\left(b c x + a c\right)^{2} + 12\right)} \sinh\left(b c x + a c\right)}{384 \, {\left(b c \cosh\left(b c x + a c\right) - b c \sinh\left(b c x + a c\right)\right)}}"," ",0,"-1/384*(cosh(b*c*x + a*c)^5 + 5*cosh(b*c*x + a*c)*sinh(b*c*x + a*c)^4 - 5*sinh(b*c*x + a*c)^5 - 5*(10*cosh(b*c*x + a*c)^2 + 9)*sinh(b*c*x + a*c)^3 + 15*cosh(b*c*x + a*c)^3 + 5*(2*cosh(b*c*x + a*c)^3 + 9*cosh(b*c*x + a*c))*sinh(b*c*x + a*c)^2 - 60*(2*b*c*x + 1)*cosh(b*c*x + a*c) - 5*(5*cosh(b*c*x + a*c)^4 - 24*b*c*x + 27*cosh(b*c*x + a*c)^2 + 12)*sinh(b*c*x + a*c))/(b*c*cosh(b*c*x + a*c) - b*c*sinh(b*c*x + a*c))","A",0
158,0,0,0,0.415177," ","integrate(x^5/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}, x\right)"," ",0,"integral(x^5/sqrt(sech(2*log(c*x))), x)","F",0
159,1,48,0,0.410437," ","integrate(x^4/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(c^{8} x^{8} + 2 \, c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{12 \, c^{6} x}"," ",0,"1/12*sqrt(2)*(c^8*x^8 + 2*c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1))/(c^6*x)","A",0
160,0,0,0,0.427102," ","integrate(x^3/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}, x\right)"," ",0,"integral(x^3/sqrt(sech(2*log(c*x))), x)","F",0
161,1,90,0,0.405173," ","integrate(x^2/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(c^{5} x^{5} + c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} + \sqrt{2} \log\left(-2 \, c^{4} x^{4} - 2 \, {\left(c^{5} x^{5} + c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} - 1\right)}{16 \, c^{3}}"," ",0,"1/16*(2*sqrt(2)*(c^5*x^5 + c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) + sqrt(2)*log(-2*c^4*x^4 - 2*(c^5*x^5 + c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) - 1))/c^3","A",0
162,0,0,0,0.406030," ","integrate(x/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}, x\right)"," ",0,"integral(x/sqrt(sech(2*log(c*x))), x)","F",0
163,1,100,0,0.405205," ","integrate(1/sech(2*log(c*x))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} c x \log\left(\frac{c^{5} x^{5} + 2 \, c x - 2 \, {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{c x^{5}}\right) + 2 \, \sqrt{2} {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{8 \, c^{2} x}"," ",0,"1/8*(sqrt(2)*c*x*log((c^5*x^5 + 2*c*x - 2*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c*x^5)) + 2*sqrt(2)*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c^2*x)","B",0
164,0,0,0,0.412114," ","integrate(sech(2*log(c*x))^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}{x}, x\right)"," ",0,"integral(sqrt(sech(2*log(c*x)))/x, x)","F",0
165,1,57,0,0.427088," ","integrate(sech(2*log(c*x))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} c \log\left(\frac{c^{5} x^{5} + 2 \, c x - 2 \, {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{c x^{5}}\right)"," ",0,"1/4*sqrt(2)*c*log((c^5*x^5 + 2*c*x - 2*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c*x^5))","A",0
166,0,0,0,0.414004," ","integrate(sech(2*log(c*x))^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(sech(2*log(c*x)))/x^3, x)","F",0
167,1,37,0,0.433221," ","integrate(sech(2*log(c*x))^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{2 \, x^{3}}"," ",0,"-1/2*sqrt(2)*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1))/x^3","A",0
168,0,0,0,0.430176," ","integrate(sech(2*log(c*x))^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)}}{x^{5}}, x\right)"," ",0,"integral(sqrt(sech(2*log(c*x)))/x^5, x)","F",0
169,1,109,0,0.440887," ","integrate(x^8/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(8 \, c^{13} x^{13} + 22 \, c^{9} x^{9} + 17 \, c^{5} x^{5} + 3 \, c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} + 3 \, \sqrt{2} \log\left(-2 \, c^{4} x^{4} + 2 \, {\left(c^{5} x^{5} + c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} - 1\right)}{768 \, c^{9}}"," ",0,"1/768*(2*sqrt(2)*(8*c^13*x^13 + 22*c^9*x^9 + 17*c^5*x^5 + 3*c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) + 3*sqrt(2)*log(-2*c^4*x^4 + 2*(c^5*x^5 + c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) - 1))/c^9","A",0
170,0,0,0,0.441875," ","integrate(x^7/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^7/sech(2*log(c*x))^(3/2), x)","F",0
171,1,56,0,0.419672," ","integrate(x^6/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(c^{12} x^{12} + 3 \, c^{8} x^{8} + 3 \, c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{40 \, c^{8} x}"," ",0,"1/40*sqrt(2)*(c^12*x^12 + 3*c^8*x^8 + 3*c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1))/(c^8*x)","B",0
172,0,0,0,0.432372," ","integrate(x^5/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^5/sech(2*log(c*x))^(3/2), x)","F",0
173,1,101,0,0.437297," ","integrate(x^4/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(2 \, c^{9} x^{9} + 7 \, c^{5} x^{5} + 5 \, c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} + 3 \, \sqrt{2} \log\left(-2 \, c^{4} x^{4} - 2 \, {\left(c^{5} x^{5} + c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} - 1\right)}{128 \, c^{5}}"," ",0,"1/128*(2*sqrt(2)*(2*c^9*x^9 + 7*c^5*x^5 + 5*c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) + 3*sqrt(2)*log(-2*c^4*x^4 - 2*(c^5*x^5 + c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) - 1))/c^5","A",0
174,0,0,0,0.428826," ","integrate(x^3/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^3/sech(2*log(c*x))^(3/2), x)","F",0
175,1,109,0,0.418322," ","integrate(x^2/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c x \log\left(\frac{c^{5} x^{5} + 2 \, c x - 2 \, {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{c x^{5}}\right) + 2 \, \sqrt{2} {\left(c^{8} x^{8} + 5 \, c^{4} x^{4} + 4\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{48 \, c^{4} x}"," ",0,"1/48*(3*sqrt(2)*c*x*log((c^5*x^5 + 2*c*x - 2*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c*x^5)) + 2*sqrt(2)*(c^8*x^8 + 5*c^4*x^4 + 4)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c^4*x)","A",0
176,0,0,0,0.481888," ","integrate(x/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x/sech(2*log(c*x))^(3/2), x)","F",0
177,1,106,0,0.427380," ","integrate(1/sech(2*log(c*x))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c^{3} x^{3} \log\left(-2 \, c^{4} x^{4} - 2 \, {\left(c^{5} x^{5} + c x\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} - 1\right) + 2 \, \sqrt{2} {\left(c^{8} x^{8} - c^{4} x^{4} - 2\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{32 \, c^{4} x^{3}}"," ",0,"1/32*(3*sqrt(2)*c^3*x^3*log(-2*c^4*x^4 - 2*(c^5*x^5 + c*x)*sqrt(c^2*x^2/(c^4*x^4 + 1)) - 1) + 2*sqrt(2)*(c^8*x^8 - c^4*x^4 - 2)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c^4*x^3)","A",0
178,0,0,0,0.431776," ","integrate(sech(2*log(c*x))^(3/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}{x}, x\right)"," ",0,"integral(sech(2*log(c*x))^(3/2)/x, x)","F",0
179,1,28,0,0.414660," ","integrate(sech(2*log(c*x))^(3/2)/x^2,x, algorithm=""fricas"")","\sqrt{2} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} c^{2} x"," ",0,"sqrt(2)*sqrt(c^2*x^2/(c^4*x^4 + 1))*c^2*x","A",0
180,0,0,0,0.440403," ","integrate(sech(2*log(c*x))^(3/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(2 \, \log\left(c x\right)\right)^{\frac{3}{2}}}{x^{3}}, x\right)"," ",0,"integral(sech(2*log(c*x))^(3/2)/x^3, x)","F",0
181,1,93,0,0.436153," ","integrate(sech(2*log(c*x))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{\sqrt{2} c^{3} x \log\left(\frac{c^{5} x^{5} + 2 \, c x - 2 \, {\left(c^{4} x^{4} + 1\right)} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}}}{c x^{5}}\right) + 2 \, \sqrt{2} \sqrt{\frac{c^{2} x^{2}}{c^{4} x^{4} + 1}} c^{2}}{2 \, x}"," ",0,"1/2*(sqrt(2)*c^3*x*log((c^5*x^5 + 2*c*x - 2*(c^4*x^4 + 1)*sqrt(c^2*x^2/(c^4*x^4 + 1)))/(c*x^5)) + 2*sqrt(2)*sqrt(c^2*x^2/(c^4*x^4 + 1))*c^2)/x","A",0
182,0,0,0,0.424059," ","integrate(sech(a+b*log(c*x^n)),x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right), x\right)"," ",0,"integral(sech(b*log(c*x^n) + a), x)","F",0
183,0,0,0,0.407013," ","integrate(sech(a+b*log(c*x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{2}, x\right)"," ",0,"integral(sech(b*log(c*x^n) + a)^2, x)","F",0
184,0,0,0,0.425159," ","integrate(sech(a+b*log(c*x^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{3}, x\right)"," ",0,"integral(sech(b*log(c*x^n) + a)^3, x)","F",0
185,0,0,0,0.438509," ","integrate(sech(a+b*log(c*x^n))^4,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{4}, x\right)"," ",0,"integral(sech(b*log(c*x^n) + a)^4, x)","F",0
186,1,189,0,0.429542," ","integrate((-b^2*n^2+1)*sech(a+b*log(c*x^n))+2*b^2*n^2*sech(a+b*log(c*x^n))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b n + 1\right)} x \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 2 \, {\left(b n + 1\right)} x \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) + {\left(b n + 1\right)} x \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - {\left(b n - 1\right)} x\right)}}{\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) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + {\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) + 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}"," ",0,"2*((b*n + 1)*x*cosh(b*n*log(x) + b*log(c) + a)^2 + 2*(b*n + 1)*x*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a) + (b*n + 1)*x*sinh(b*n*log(x) + b*log(c) + a)^2 - (b*n - 1)*x)/(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)^2 + sinh(b*n*log(x) + b*log(c) + a)^3 + (3*cosh(b*n*log(x) + b*log(c) + a)^2 + 1)*sinh(b*n*log(x) + b*log(c) + a) + 3*cosh(b*n*log(x) + b*log(c) + a))","B",0
187,1,48,0,0.412044," ","integrate(sech(a+2*log(c*x^(1/2)))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, c^{4} x^{2} e^{\left(2 \, a\right)} + 1\right)}}{c^{10} x^{4} e^{\left(5 \, a\right)} + 2 \, c^{6} x^{2} e^{\left(3 \, a\right)} + c^{2} e^{a}}"," ",0,"-2*(2*c^4*x^2*e^(2*a) + 1)/(c^10*x^4*e^(5*a) + 2*c^6*x^2*e^(3*a) + c^2*e^a)","B",0
188,1,49,0,0.401241," ","integrate(sech(a+2*log(c/x^(1/2)))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(c^{10} e^{\left(5 \, a\right)} + 2 \, c^{6} x^{2} e^{\left(3 \, a\right)}\right)}}{c^{8} e^{\left(4 \, a\right)} + 2 \, c^{4} x^{2} e^{\left(2 \, a\right)} + x^{4}}"," ",0,"-2*(c^10*e^(5*a) + 2*c^6*x^2*e^(3*a))/(c^8*e^(4*a) + 2*c^4*x^2*e^(2*a) + x^4)","B",0
189,1,474,0,0.445300," ","integrate(sech(a+log(c*x^n)/n/(-2+p))^p,x, algorithm=""fricas"")","\frac{{\left(p - 2\right)} x \cosh\left(p \log\left(\frac{2 \, {\left(\cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)\right)}}{\cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 2 \, \cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 1}\right)\right) \cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) + {\left(p - 2\right)} x \cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(p \log\left(\frac{2 \, {\left(\cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)\right)}}{\cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 2 \, \cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 1}\right)\right)}{{\left(p - 1\right)} \cosh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right) - {\left(p - 1\right)} \sinh\left(\frac{a n p - 2 \, a n + n \log\left(x\right) + \log\left(c\right)}{n p - 2 \, n}\right)}"," ",0,"((p - 2)*x*cosh(p*log(2*(cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) + sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)))/(cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))^2 + 2*cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))*sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) + sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))^2 + 1)))*cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) + (p - 2)*x*cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))*sinh(p*log(2*(cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) + sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)))/(cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))^2 + 2*cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))*sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) + sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n))^2 + 1))))/((p - 1)*cosh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)) - (p - 1)*sinh((a*n*p - 2*a*n + n*log(x) + log(c))/(n*p - 2*n)))","B",0
190,1,538,0,0.445734," ","integrate(sech(a-log(c*x^n)/n/(-2+p))^p,x, algorithm=""fricas"")","\frac{{\left(p - 2\right)} x \cosh\left(p \log\left(\frac{2 \, {\left(\cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)\right)}}{\cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 2 \, \cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 1}\right)\right) \cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) + {\left(p - 2\right)} x \cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(p \log\left(\frac{2 \, {\left(\cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)\right)}}{\cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 2 \, \cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) + \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)^{2} + 1}\right)\right)}{{\left(p - 1\right)} \cosh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right) - {\left(p - 1\right)} \sinh\left(-\frac{a n p - 2 \, a n - n \log\left(x\right) - \log\left(c\right)}{n p - 2 \, n}\right)}"," ",0,"((p - 2)*x*cosh(p*log(2*(cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) + sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)))/(cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))^2 + 2*cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))*sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) + sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))^2 + 1)))*cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) + (p - 2)*x*cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))*sinh(p*log(2*(cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) + sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)))/(cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))^2 + 2*cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))*sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) + sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n))^2 + 1))))/((p - 1)*cosh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)) - (p - 1)*sinh(-(a*n*p - 2*a*n - n*log(x) - log(c))/(n*p - 2*n)))","B",0
191,1,34,0,0.422853," ","integrate(sech(a+b*log(c*x^n))/x,x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\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)}{b n}"," ",0,"2*arctan(cosh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a))/(b*n)","A",0
192,1,70,0,0.415009," ","integrate(sech(a+b*log(c*x^n))^2/x,x, algorithm=""fricas"")","-\frac{2}{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}"," ",0,"-2/(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
193,1,452,0,0.428498," ","integrate(sech(a+b*log(c*x^n))^3/x,x, algorithm=""fricas"")","\frac{\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) \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{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)} \arctan\left(\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) + {\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) - \cosh\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,"(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)^2 + sinh(b*n*log(x) + b*log(c) + a)^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)*arctan(cosh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)) + (3*cosh(b*n*log(x) + b*log(c) + a)^2 - 1)*sinh(b*n*log(x) + b*log(c) + a) - cosh(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
194,1,272,0,0.434739," ","integrate(sech(a+b*log(c*x^n))^4/x,x, algorithm=""fricas"")","-\frac{8 \, {\left(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)\right)}}{3 \, {\left(b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 5 \, 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)^{4} + b n \sinh\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} + {\left(10 \, 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)^{3} + 4 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right) + {\left(10 \, b n \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 9 \, 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)^{2} + {\left(5 \, 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} + 2 \, b n\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)\right)}}"," ",0,"-8/3*(2*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)^5 + 5*b*n*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^4 + b*n*sinh(b*n*log(x) + b*log(c) + a)^5 + 3*b*n*cosh(b*n*log(x) + b*log(c) + a)^3 + (10*b*n*cosh(b*n*log(x) + b*log(c) + a)^2 + 3*b*n)*sinh(b*n*log(x) + b*log(c) + a)^3 + 4*b*n*cosh(b*n*log(x) + b*log(c) + a) + (10*b*n*cosh(b*n*log(x) + b*log(c) + a)^3 + 9*b*n*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^2 + (5*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 + 2*b*n)*sinh(b*n*log(x) + b*log(c) + a))","B",0
195,1,1326,0,0.447985," ","integrate(sech(a+b*log(c*x^n))^5/x,x, algorithm=""fricas"")","\frac{3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} + 21 \, \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)^{6} + 3 \, \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{7} + {\left(63 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} + 11\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 11 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 5 \, {\left(21 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + 11 \, \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(105 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} + 110 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{2} - 11\right)} \sinh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 11 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} + {\left(63 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{5} + 110 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{3} - 33 \, \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)^{2} + 3 \, {\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)} \arctan\left(\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) + {\left(21 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{6} + 55 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)^{4} - 33 \, \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) - 3 \, \cosh\left(b n \log\left(x\right) + b \log\left(c\right) + a\right)}{4 \, {\left(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)\right)}}"," ",0,"1/4*(3*cosh(b*n*log(x) + b*log(c) + a)^7 + 21*cosh(b*n*log(x) + b*log(c) + a)*sinh(b*n*log(x) + b*log(c) + a)^6 + 3*sinh(b*n*log(x) + b*log(c) + a)^7 + (63*cosh(b*n*log(x) + b*log(c) + a)^2 + 11)*sinh(b*n*log(x) + b*log(c) + a)^5 + 11*cosh(b*n*log(x) + b*log(c) + a)^5 + 5*(21*cosh(b*n*log(x) + b*log(c) + a)^3 + 11*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^4 + (105*cosh(b*n*log(x) + b*log(c) + a)^4 + 110*cosh(b*n*log(x) + b*log(c) + a)^2 - 11)*sinh(b*n*log(x) + b*log(c) + a)^3 - 11*cosh(b*n*log(x) + b*log(c) + a)^3 + (63*cosh(b*n*log(x) + b*log(c) + a)^5 + 110*cosh(b*n*log(x) + b*log(c) + a)^3 - 33*cosh(b*n*log(x) + b*log(c) + a))*sinh(b*n*log(x) + b*log(c) + a)^2 + 3*(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)*arctan(cosh(b*n*log(x) + b*log(c) + a) + sinh(b*n*log(x) + b*log(c) + a)) + (21*cosh(b*n*log(x) + b*log(c) + a)^6 + 55*cosh(b*n*log(x) + b*log(c) + a)^4 - 33*cosh(b*n*log(x) + b*log(c) + a)^2 - 3)*sinh(b*n*log(x) + b*log(c) + a) - 3*cosh(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
196,0,0,0,0.428869," ","integrate(sech(a+b*log(c*x^n))^(5/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{\frac{5}{2}}}{x}, x\right)"," ",0,"integral(sech(b*log(c*x^n) + a)^(5/2)/x, x)","F",0
197,0,0,0,0.440626," ","integrate(sech(a+b*log(c*x^n))^(3/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{\frac{3}{2}}}{x}, x\right)"," ",0,"integral(sech(b*log(c*x^n) + a)^(3/2)/x, x)","F",0
198,0,0,0,0.431420," ","integrate(sech(a+b*log(c*x^n))^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)}}{x}, x\right)"," ",0,"integral(sqrt(sech(b*log(c*x^n) + a))/x, x)","F",0
199,0,0,0,0.420319," ","integrate(1/x/sech(a+b*log(c*x^n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \sqrt{\operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)}}, x\right)"," ",0,"integral(1/(x*sqrt(sech(b*log(c*x^n) + a))), x)","F",0
200,0,0,0,0.428425," ","integrate(1/x/sech(a+b*log(c*x^n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/(x*sech(b*log(c*x^n) + a)^(3/2)), x)","F",0
201,0,0,0,0.435054," ","integrate(1/x/sech(a+b*log(c*x^n))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \operatorname{sech}\left(b \log\left(c x^{n}\right) + a\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(1/(x*sech(b*log(c*x^n) + a)^(5/2)), x)","F",0
