1,1,14,0,0.506461," ","integrate(sinh(x)^4/(a-a*cosh(x)^2),x, algorithm=""fricas"")","-\frac{\cosh\left(x\right) \sinh\left(x\right) - x}{2 \, a}"," ",0,"-1/2*(cosh(x)*sinh(x) - x)/a","A",0
2,1,7,0,0.496546," ","integrate(sinh(x)^3/(a-a*cosh(x)^2),x, algorithm=""fricas"")","-\frac{\cosh\left(x\right)}{a}"," ",0,"-cosh(x)/a","A",0
3,1,6,0,0.450069," ","integrate(sinh(x)^2/(a-a*cosh(x)^2),x, algorithm=""fricas"")","-\frac{x}{a}"," ",0,"-x/a","A",0
4,1,100,0,0.427666," ","integrate(csch(x)^2/(a-a*cosh(x)^2),x, algorithm=""fricas"")","\frac{8 \, {\left(\cosh\left(x\right) + 2 \, \sinh\left(x\right)\right)}}{3 \, {\left(a \cosh\left(x\right)^{5} + 5 \, a \cosh\left(x\right) \sinh\left(x\right)^{4} + a \sinh\left(x\right)^{5} - 3 \, a \cosh\left(x\right)^{3} + {\left(10 \, a \cosh\left(x\right)^{2} - 3 \, a\right)} \sinh\left(x\right)^{3} + {\left(10 \, a \cosh\left(x\right)^{3} - 9 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) + {\left(5 \, a \cosh\left(x\right)^{4} - 9 \, a \cosh\left(x\right)^{2} + 4 \, a\right)} \sinh\left(x\right)\right)}}"," ",0,"8/3*(cosh(x) + 2*sinh(x))/(a*cosh(x)^5 + 5*a*cosh(x)*sinh(x)^4 + a*sinh(x)^5 - 3*a*cosh(x)^3 + (10*a*cosh(x)^2 - 3*a)*sinh(x)^3 + (10*a*cosh(x)^3 - 9*a*cosh(x))*sinh(x)^2 + 2*a*cosh(x) + (5*a*cosh(x)^4 - 9*a*cosh(x)^2 + 4*a)*sinh(x))","B",0
5,1,216,0,0.389161," ","integrate(csch(x)^4/(a-a*cosh(x)^2),x, algorithm=""fricas"")","\frac{16 \, {\left(11 \, \cosh\left(x\right)^{2} + 18 \, \cosh\left(x\right) \sinh\left(x\right) + 11 \, \sinh\left(x\right)^{2} - 5\right)}}{15 \, {\left(a \cosh\left(x\right)^{8} + 8 \, a \cosh\left(x\right) \sinh\left(x\right)^{7} + a \sinh\left(x\right)^{8} - 5 \, a \cosh\left(x\right)^{6} + {\left(28 \, a \cosh\left(x\right)^{2} - 5 \, a\right)} \sinh\left(x\right)^{6} + 2 \, {\left(28 \, a \cosh\left(x\right)^{3} - 15 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, a \cosh\left(x\right)^{4} + 5 \, {\left(14 \, a \cosh\left(x\right)^{4} - 15 \, a \cosh\left(x\right)^{2} + 2 \, a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, a \cosh\left(x\right)^{5} - 25 \, a \cosh\left(x\right)^{3} + 10 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 11 \, a \cosh\left(x\right)^{2} + {\left(28 \, a \cosh\left(x\right)^{6} - 75 \, a \cosh\left(x\right)^{4} + 60 \, a \cosh\left(x\right)^{2} - 11 \, a\right)} \sinh\left(x\right)^{2} + 2 \, {\left(4 \, a \cosh\left(x\right)^{7} - 15 \, a \cosh\left(x\right)^{5} + 20 \, a \cosh\left(x\right)^{3} - 9 \, a \cosh\left(x\right)\right)} \sinh\left(x\right) + 5 \, a\right)}}"," ",0,"16/15*(11*cosh(x)^2 + 18*cosh(x)*sinh(x) + 11*sinh(x)^2 - 5)/(a*cosh(x)^8 + 8*a*cosh(x)*sinh(x)^7 + a*sinh(x)^8 - 5*a*cosh(x)^6 + (28*a*cosh(x)^2 - 5*a)*sinh(x)^6 + 2*(28*a*cosh(x)^3 - 15*a*cosh(x))*sinh(x)^5 + 10*a*cosh(x)^4 + 5*(14*a*cosh(x)^4 - 15*a*cosh(x)^2 + 2*a)*sinh(x)^4 + 4*(14*a*cosh(x)^5 - 25*a*cosh(x)^3 + 10*a*cosh(x))*sinh(x)^3 - 11*a*cosh(x)^2 + (28*a*cosh(x)^6 - 75*a*cosh(x)^4 + 60*a*cosh(x)^2 - 11*a)*sinh(x)^2 + 2*(4*a*cosh(x)^7 - 15*a*cosh(x)^5 + 20*a*cosh(x)^3 - 9*a*cosh(x))*sinh(x) + 5*a)","B",0
6,1,2346,0,0.452764," ","integrate(sinh(x)^7/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{3 \, a b^{3} \cosh\left(x\right)^{10} + 30 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{9} + 3 \, a b^{3} \sinh\left(x\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(27 \, a b^{3} \cosh\left(x\right)^{2} - 4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(9 \, a b^{3} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 30 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(63 \, a b^{3} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 66 \, a^{2} b^{2} + 57 \, a b^{3} - 14 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(189 \, a b^{3} \cosh\left(x\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 45 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 30 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(63 \, a b^{3} \cosh\left(x\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 66 \, a^{2} b^{2} + 57 \, a b^{3} + 45 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 3 \, a b^{3} + 40 \, {\left(9 \, a b^{3} \cosh\left(x\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 15 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 5 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(27 \, a b^{3} \cosh\left(x\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 90 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, a^{2} b^{2} - 9 \, a b^{3} + 36 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 240 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{5}\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right) + \cosh\left(x\right)\right)} \sqrt{-a b} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 10 \, {\left(3 \, a b^{3} \cosh\left(x\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{7} + 18 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{480 \, {\left(a b^{4} \cosh\left(x\right)^{5} + 5 \, a b^{4} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, a b^{4} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, a b^{4} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, a b^{4} \cosh\left(x\right) \sinh\left(x\right)^{4} + a b^{4} \sinh\left(x\right)^{5}\right)}}, \frac{3 \, a b^{3} \cosh\left(x\right)^{10} + 30 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{9} + 3 \, a b^{3} \sinh\left(x\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(27 \, a b^{3} \cosh\left(x\right)^{2} - 4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(9 \, a b^{3} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 30 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(63 \, a b^{3} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 66 \, a^{2} b^{2} + 57 \, a b^{3} - 14 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(189 \, a b^{3} \cosh\left(x\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 45 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 30 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(63 \, a b^{3} \cosh\left(x\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 66 \, a^{2} b^{2} + 57 \, a b^{3} + 45 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 3 \, a b^{3} + 40 \, {\left(9 \, a b^{3} \cosh\left(x\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 15 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 5 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(27 \, a b^{3} \cosh\left(x\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 90 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, a^{2} b^{2} - 9 \, a b^{3} + 36 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 480 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, a}\right) + 480 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{5}\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 10 \, {\left(3 \, a b^{3} \cosh\left(x\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)^{7} + 18 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 12 \, {\left(8 \, a^{3} b + 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{480 \, {\left(a b^{4} \cosh\left(x\right)^{5} + 5 \, a b^{4} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, a b^{4} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, a b^{4} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, a b^{4} \cosh\left(x\right) \sinh\left(x\right)^{4} + a b^{4} \sinh\left(x\right)^{5}\right)}}\right]"," ",0,"[1/480*(3*a*b^3*cosh(x)^10 + 30*a*b^3*cosh(x)*sinh(x)^9 + 3*a*b^3*sinh(x)^10 - 5*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^8 + 5*(27*a*b^3*cosh(x)^2 - 4*a^2*b^2 - 9*a*b^3)*sinh(x)^8 + 40*(9*a*b^3*cosh(x)^3 - (4*a^2*b^2 + 9*a*b^3)*cosh(x))*sinh(x)^7 + 30*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^6 + 10*(63*a*b^3*cosh(x)^4 + 24*a^3*b + 66*a^2*b^2 + 57*a*b^3 - 14*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^2)*sinh(x)^6 + 4*(189*a*b^3*cosh(x)^5 - 70*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^3 + 45*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x))*sinh(x)^5 + 30*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^4 + 10*(63*a*b^3*cosh(x)^6 - 35*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^4 + 24*a^3*b + 66*a^2*b^2 + 57*a*b^3 + 45*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^2)*sinh(x)^4 + 3*a*b^3 + 40*(9*a*b^3*cosh(x)^7 - 7*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^5 + 15*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^3 + 3*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x))*sinh(x)^3 - 5*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^2 + 5*(27*a*b^3*cosh(x)^8 - 28*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^6 + 90*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^4 - 4*a^2*b^2 - 9*a*b^3 + 36*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^2)*sinh(x)^2 - 240*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4*sinh(x) + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3*sinh(x)^2 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2*sinh(x)^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^4 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^5)*sqrt(-a*b)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 + 1)*sinh(x) + cosh(x))*sqrt(-a*b) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 10*(3*a*b^3*cosh(x)^9 - 4*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^7 + 18*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^5 + 12*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^3 - (4*a^2*b^2 + 9*a*b^3)*cosh(x))*sinh(x))/(a*b^4*cosh(x)^5 + 5*a*b^4*cosh(x)^4*sinh(x) + 10*a*b^4*cosh(x)^3*sinh(x)^2 + 10*a*b^4*cosh(x)^2*sinh(x)^3 + 5*a*b^4*cosh(x)*sinh(x)^4 + a*b^4*sinh(x)^5), 1/480*(3*a*b^3*cosh(x)^10 + 30*a*b^3*cosh(x)*sinh(x)^9 + 3*a*b^3*sinh(x)^10 - 5*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^8 + 5*(27*a*b^3*cosh(x)^2 - 4*a^2*b^2 - 9*a*b^3)*sinh(x)^8 + 40*(9*a*b^3*cosh(x)^3 - (4*a^2*b^2 + 9*a*b^3)*cosh(x))*sinh(x)^7 + 30*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^6 + 10*(63*a*b^3*cosh(x)^4 + 24*a^3*b + 66*a^2*b^2 + 57*a*b^3 - 14*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^2)*sinh(x)^6 + 4*(189*a*b^3*cosh(x)^5 - 70*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^3 + 45*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x))*sinh(x)^5 + 30*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^4 + 10*(63*a*b^3*cosh(x)^6 - 35*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^4 + 24*a^3*b + 66*a^2*b^2 + 57*a*b^3 + 45*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^2)*sinh(x)^4 + 3*a*b^3 + 40*(9*a*b^3*cosh(x)^7 - 7*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^5 + 15*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^3 + 3*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x))*sinh(x)^3 - 5*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^2 + 5*(27*a*b^3*cosh(x)^8 - 28*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^6 + 90*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^4 - 4*a^2*b^2 - 9*a*b^3 + 36*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^2)*sinh(x)^2 - 480*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4*sinh(x) + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3*sinh(x)^2 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2*sinh(x)^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^4 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^5)*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(x) + sinh(x))/a) + 480*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4*sinh(x) + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3*sinh(x)^2 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2*sinh(x)^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^4 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^5)*sqrt(a*b)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(a*b)/(a*b)) + 10*(3*a*b^3*cosh(x)^9 - 4*(4*a^2*b^2 + 9*a*b^3)*cosh(x)^7 + 18*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^5 + 12*(8*a^3*b + 22*a^2*b^2 + 19*a*b^3)*cosh(x)^3 - (4*a^2*b^2 + 9*a*b^3)*cosh(x))*sinh(x))/(a*b^4*cosh(x)^5 + 5*a*b^4*cosh(x)^4*sinh(x) + 10*a*b^4*cosh(x)^3*sinh(x)^2 + 10*a*b^4*cosh(x)^2*sinh(x)^3 + 5*a*b^4*cosh(x)*sinh(x)^4 + a*b^4*sinh(x)^5)]","B",0
7,1,1064,0,0.544409," ","integrate(sinh(x)^5/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{2} - 4 \, a^{2} b - 7 \, a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{4} - 4 \, a^{2} b - 7 \, a b^{2} - 6 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 12 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{3}\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right) + \cosh\left(x\right)\right)} \sqrt{-a b} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 6 \, {\left(a b^{2} \cosh\left(x\right)^{5} - 2 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left(a b^{3} \cosh\left(x\right)^{3} + 3 \, a b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{2} + a b^{3} \sinh\left(x\right)^{3}\right)}}, \frac{a b^{2} \cosh\left(x\right)^{6} + 6 \, a b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a b^{2} \sinh\left(x\right)^{6} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{2} - 4 \, a^{2} b - 7 \, a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{3} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} - 3 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(x\right)^{4} - 4 \, a^{2} b - 7 \, a b^{2} - 6 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 24 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, a}\right) - 24 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{3}\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 6 \, {\left(a b^{2} \cosh\left(x\right)^{5} - 2 \, {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left(a b^{3} \cosh\left(x\right)^{3} + 3 \, a b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a b^{3} \cosh\left(x\right) \sinh\left(x\right)^{2} + a b^{3} \sinh\left(x\right)^{3}\right)}}\right]"," ",0,"[1/24*(a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 - 3*(4*a^2*b + 7*a*b^2)*cosh(x)^4 + 3*(5*a*b^2*cosh(x)^2 - 4*a^2*b - 7*a*b^2)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 - 3*(4*a^2*b + 7*a*b^2)*cosh(x))*sinh(x)^3 + a*b^2 - 3*(4*a^2*b + 7*a*b^2)*cosh(x)^2 + 3*(5*a*b^2*cosh(x)^4 - 4*a^2*b - 7*a*b^2 - 6*(4*a^2*b + 7*a*b^2)*cosh(x)^2)*sinh(x)^2 - 12*((a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^2*sinh(x) + 3*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^2 + (a^2 + 2*a*b + b^2)*sinh(x)^3)*sqrt(-a*b)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) - 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 + 1)*sinh(x) + cosh(x))*sqrt(-a*b) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 6*(a*b^2*cosh(x)^5 - 2*(4*a^2*b + 7*a*b^2)*cosh(x)^3 - (4*a^2*b + 7*a*b^2)*cosh(x))*sinh(x))/(a*b^3*cosh(x)^3 + 3*a*b^3*cosh(x)^2*sinh(x) + 3*a*b^3*cosh(x)*sinh(x)^2 + a*b^3*sinh(x)^3), 1/24*(a*b^2*cosh(x)^6 + 6*a*b^2*cosh(x)*sinh(x)^5 + a*b^2*sinh(x)^6 - 3*(4*a^2*b + 7*a*b^2)*cosh(x)^4 + 3*(5*a*b^2*cosh(x)^2 - 4*a^2*b - 7*a*b^2)*sinh(x)^4 + 4*(5*a*b^2*cosh(x)^3 - 3*(4*a^2*b + 7*a*b^2)*cosh(x))*sinh(x)^3 + a*b^2 - 3*(4*a^2*b + 7*a*b^2)*cosh(x)^2 + 3*(5*a*b^2*cosh(x)^4 - 4*a^2*b - 7*a*b^2 - 6*(4*a^2*b + 7*a*b^2)*cosh(x)^2)*sinh(x)^2 + 24*((a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^2*sinh(x) + 3*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^2 + (a^2 + 2*a*b + b^2)*sinh(x)^3)*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(x) + sinh(x))/a) - 24*((a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^2*sinh(x) + 3*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^2 + (a^2 + 2*a*b + b^2)*sinh(x)^3)*sqrt(a*b)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(a*b)/(a*b)) + 6*(a*b^2*cosh(x)^5 - 2*(4*a^2*b + 7*a*b^2)*cosh(x)^3 - (4*a^2*b + 7*a*b^2)*cosh(x))*sinh(x))/(a*b^3*cosh(x)^3 + 3*a*b^3*cosh(x)^2*sinh(x) + 3*a*b^3*cosh(x)*sinh(x)^2 + a*b^3*sinh(x)^3)]","B",0
8,1,416,0,0.487979," ","integrate(sinh(x)^3/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{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} - \sqrt{-a b} {\left({\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)\right)} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right) + \cosh\left(x\right)\right)} \sqrt{-a b} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + a b}{2 \, {\left(a b^{2} \cosh\left(x\right) + a b^{2} \sinh\left(x\right)\right)}}, \frac{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} - 2 \, \sqrt{a b} {\left({\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)\right)} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, a}\right) + 2 \, \sqrt{a b} {\left({\left(a + b\right)} \cosh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)\right)} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{a b}}{2 \, a b}\right) + a b}{2 \, {\left(a b^{2} \cosh\left(x\right) + a b^{2} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/2*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - sqrt(-a*b)*((a + b)*cosh(x) + (a + b)*sinh(x))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 + 1)*sinh(x) + cosh(x))*sqrt(-a*b) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + a*b)/(a*b^2*cosh(x) + a*b^2*sinh(x)), 1/2*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 - 2*sqrt(a*b)*((a + b)*cosh(x) + (a + b)*sinh(x))*arctan(1/2*sqrt(a*b)*(cosh(x) + sinh(x))/a) + 2*sqrt(a*b)*((a + b)*cosh(x) + (a + b)*sinh(x))*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(a*b)/(a*b)) + a*b)/(a*b^2*cosh(x) + a*b^2*sinh(x))]","B",0
9,1,300,0,0.516131," ","integrate(sinh(x)/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right) + \cosh\left(x\right)\right)} \sqrt{-a b} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right)}{2 \, a b}, \frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, a}\right) - \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{a b}}{2 \, a b}\right)}{a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) - 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 + 1)*sinh(x) + cosh(x))*sqrt(-a*b) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b))/(a*b), (sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(x) + sinh(x))/a) - sqrt(a*b)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(a*b)/(a*b)))/(a*b)]","B",0
10,1,349,0,0.637226," ","integrate(csch(x)/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right) \sinh\left(x\right)^{2} + a \sinh\left(x\right)^{3} + a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) - 2 \, \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + 2 \, \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)}{2 \, {\left(a + b\right)}}, -\frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) - \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) - \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)}{a + b}\right]"," ",0,"[1/2*(sqrt(-b/a)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) - 4*(a*cosh(x)^3 + 3*a*cosh(x)*sinh(x)^2 + a*sinh(x)^3 + a*cosh(x) + (3*a*cosh(x)^2 + a)*sinh(x))*sqrt(-b/a) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) - 2*log(cosh(x) + sinh(x) + 1) + 2*log(cosh(x) + sinh(x) - 1))/(a + b), -(sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(x) + sinh(x))) - sqrt(b/a)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(b/a)/b) + log(cosh(x) + sinh(x) + 1) - log(cosh(x) + sinh(x) - 1))/(a + b)]","B",0
11,1,1332,0,0.489172," ","integrate(csch(x)^3/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \sinh\left(x\right)^{3} - {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right) \sinh\left(x\right)^{2} + a \sinh\left(x\right)^{3} + a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 2 \, {\left(a + b\right)} \cosh\left(x\right) - {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} - a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 3 \, b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} - a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 3 \, b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)}{2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \sinh\left(x\right)^{3} - 2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) + 2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(a + b\right)} \cosh\left(x\right) - {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} - a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 3 \, b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 3 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 3 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 3 \, b\right)} \cosh\left(x\right)^{2} - a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 3 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 3 \, b\right)} \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right) + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)}{2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/2*(2*(a + b)*cosh(x)^3 + 6*(a + b)*cosh(x)*sinh(x)^2 + 2*(a + b)*sinh(x)^3 - (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(-b/a)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 4*(a*cosh(x)^3 + 3*a*cosh(x)*sinh(x)^2 + a*sinh(x)^3 + a*cosh(x) + (3*a*cosh(x)^2 + a)*sinh(x))*sqrt(-b/a) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 2*(a + b)*cosh(x) - ((a + 3*b)*cosh(x)^4 + 4*(a + 3*b)*cosh(x)*sinh(x)^3 + (a + 3*b)*sinh(x)^4 - 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a + 3*b)*cosh(x)^2 - a - 3*b)*sinh(x)^2 + 4*((a + 3*b)*cosh(x)^3 - (a + 3*b)*cosh(x))*sinh(x) + a + 3*b)*log(cosh(x) + sinh(x) + 1) + ((a + 3*b)*cosh(x)^4 + 4*(a + 3*b)*cosh(x)*sinh(x)^3 + (a + 3*b)*sinh(x)^4 - 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a + 3*b)*cosh(x)^2 - a - 3*b)*sinh(x)^2 + 4*((a + 3*b)*cosh(x)^3 - (a + 3*b)*cosh(x))*sinh(x) + a + 3*b)*log(cosh(x) + sinh(x) - 1) + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x))/((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)), -1/2*(2*(a + b)*cosh(x)^3 + 6*(a + b)*cosh(x)*sinh(x)^2 + 2*(a + b)*sinh(x)^3 - 2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(x) + sinh(x))) + 2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(b/a)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(b/a)/b) + 2*(a + b)*cosh(x) - ((a + 3*b)*cosh(x)^4 + 4*(a + 3*b)*cosh(x)*sinh(x)^3 + (a + 3*b)*sinh(x)^4 - 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a + 3*b)*cosh(x)^2 - a - 3*b)*sinh(x)^2 + 4*((a + 3*b)*cosh(x)^3 - (a + 3*b)*cosh(x))*sinh(x) + a + 3*b)*log(cosh(x) + sinh(x) + 1) + ((a + 3*b)*cosh(x)^4 + 4*(a + 3*b)*cosh(x)*sinh(x)^3 + (a + 3*b)*sinh(x)^4 - 2*(a + 3*b)*cosh(x)^2 + 2*(3*(a + 3*b)*cosh(x)^2 - a - 3*b)*sinh(x)^2 + 4*((a + 3*b)*cosh(x)^3 - (a + 3*b)*cosh(x))*sinh(x) + a + 3*b)*log(cosh(x) + sinh(x) - 1) + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x))/((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))]","B",0
12,1,5326,0,0.598625," ","integrate(csch(x)^5/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{7} + 14 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{6} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{7} - 2 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} - 26 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{5} + 10 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 2 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} - 10 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} - 26 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{3} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} - 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} - b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right) \sinh\left(x\right)^{2} + a \sinh\left(x\right)^{3} + a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right) - {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 30 \, a b + 45 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 10 \, a b + 15 \, 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(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 30 \, a b + 45 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 10 \, a b + 15 \, 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(7 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{6} - 5 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{7} + 14 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{6} + 2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)^{7} - 2 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} - 26 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{5} + 10 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - 2 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{4} - 10 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} - 26 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{3} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} - 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} - b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) + 8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} - 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} - b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right) - {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 30 \, a b + 45 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 10 \, a b + 15 \, 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(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 30 \, a b + 45 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 10 \, a b - 15 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 10 \, a b + 15 \, 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(7 \, {\left(3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \cosh\left(x\right)^{6} - 5 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(11 \, a^{2} + 26 \, a b + 15 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 10 \, a b + 7 \, b^{2}\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/8*(2*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^7 + 14*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)*sinh(x)^6 + 2*(3*a^2 + 10*a*b + 7*b^2)*sinh(x)^7 - 2*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^5 + 2*(21*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^2 - 11*a^2 - 26*a*b - 15*b^2)*sinh(x)^5 + 10*(7*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^3 - (11*a^2 + 26*a*b + 15*b^2)*cosh(x))*sinh(x)^4 - 2*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^3 + 2*(35*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^4 - 10*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^2 - 11*a^2 - 26*a*b - 15*b^2)*sinh(x)^3 + 2*(21*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^5 - 10*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^3 - 3*(11*a^2 + 26*a*b + 15*b^2)*cosh(x))*sinh(x)^2 + 4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 - 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 - 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 - 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 - b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 - 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 - b^2*cosh(x))*sinh(x))*sqrt(-b/a)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) - 4*(a*cosh(x)^3 + 3*a*cosh(x)*sinh(x)^2 + a*sinh(x)^3 + a*cosh(x) + (3*a*cosh(x)^2 + a)*sinh(x))*sqrt(-b/a) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 2*(3*a^2 + 10*a*b + 7*b^2)*cosh(x) - ((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 10*a*b + 15*b^2)*sinh(x)^8 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 - 30*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 9*a^2 + 30*a*b + 45*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 - 10*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 - 15*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 9*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^2 + 3*a^2 + 10*a*b + 15*b^2 + 8*((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^7 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - (3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) + 1) + ((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 10*a*b + 15*b^2)*sinh(x)^8 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 - 30*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 9*a^2 + 30*a*b + 45*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 - 10*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 - 15*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 9*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^2 + 3*a^2 + 10*a*b + 15*b^2 + 8*((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^7 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - (3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) - 1) + 2*(7*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^6 - 5*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^4 - 3*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^2 + 3*a^2 + 10*a*b + 7*b^2)*sinh(x))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^8 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^6 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 3*a^3 + 9*a^2*b + 9*a*b^2 + 3*b^3 - 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 - 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2 + 4*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^6 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^7 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x)), 1/8*(2*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^7 + 14*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)*sinh(x)^6 + 2*(3*a^2 + 10*a*b + 7*b^2)*sinh(x)^7 - 2*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^5 + 2*(21*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^2 - 11*a^2 - 26*a*b - 15*b^2)*sinh(x)^5 + 10*(7*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^3 - (11*a^2 + 26*a*b + 15*b^2)*cosh(x))*sinh(x)^4 - 2*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^3 + 2*(35*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^4 - 10*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^2 - 11*a^2 - 26*a*b - 15*b^2)*sinh(x)^3 + 2*(21*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^5 - 10*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^3 - 3*(11*a^2 + 26*a*b + 15*b^2)*cosh(x))*sinh(x)^2 - 8*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 - 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 - 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 - 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 - b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 - 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 - b^2*cosh(x))*sinh(x))*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(x) + sinh(x))) + 8*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 - 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 - 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 - 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 - b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 - 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 - b^2*cosh(x))*sinh(x))*sqrt(b/a)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + b)*sinh(x))*sqrt(b/a)/b) + 2*(3*a^2 + 10*a*b + 7*b^2)*cosh(x) - ((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 10*a*b + 15*b^2)*sinh(x)^8 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 - 30*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 9*a^2 + 30*a*b + 45*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 - 10*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 - 15*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 9*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^2 + 3*a^2 + 10*a*b + 15*b^2 + 8*((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^7 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - (3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) + 1) + ((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 10*a*b + 15*b^2)*sinh(x)^8 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 - 30*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 9*a^2 + 30*a*b + 45*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 - 10*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^6 - 15*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^4 + 9*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^2 - 3*a^2 - 10*a*b - 15*b^2)*sinh(x)^2 + 3*a^2 + 10*a*b + 15*b^2 + 8*((3*a^2 + 10*a*b + 15*b^2)*cosh(x)^7 - 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^5 + 3*(3*a^2 + 10*a*b + 15*b^2)*cosh(x)^3 - (3*a^2 + 10*a*b + 15*b^2)*cosh(x))*sinh(x))*log(cosh(x) + sinh(x) - 1) + 2*(7*(3*a^2 + 10*a*b + 7*b^2)*cosh(x)^6 - 5*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^4 - 3*(11*a^2 + 26*a*b + 15*b^2)*cosh(x)^2 + 3*a^2 + 10*a*b + 7*b^2)*sinh(x))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^8 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^6 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x)^5 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 3*a^3 + 9*a^2*b + 9*a*b^2 + 3*b^3 - 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 - 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2 + 4*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^6 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^7 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^5 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x))*sinh(x))]","B",0
13,1,1308,0,0.514149," ","integrate(sinh(x)^6/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 8 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - 2 \, a b - 4 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 6 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 60 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 20 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 30 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 2 \, a b + 4 \, b^{2}\right)} \sinh\left(x\right)^{2} + 32 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4}\right)} \sqrt{\frac{a + b}{a}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} + 2 \, a^{2} + a b\right)} \sqrt{\frac{a + b}{a}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 6 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{3} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left(b^{3} \cosh\left(x\right)^{4} + 4 \, b^{3} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{3} \sinh\left(x\right)^{4}\right)}}, \frac{b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 8 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - 2 \, a b - 4 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 6 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 60 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 20 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 30 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 2 \, a b + 4 \, b^{2}\right)} \sinh\left(x\right)^{2} - 64 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4}\right)} \sqrt{-\frac{a + b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 6 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x \cosh\left(x\right)^{3} + 2 \, {\left(a b + 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left(b^{3} \cosh\left(x\right)^{4} + 4 \, b^{3} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{3} \sinh\left(x\right)^{4}\right)}}\right]"," ",0,"[1/64*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 8*(a*b + 2*b^2)*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - 2*a*b - 4*b^2)*sinh(x)^6 + 8*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 6*(a*b + 2*b^2)*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 60*(a*b + 2*b^2)*cosh(x)^2 + 4*(8*a^2 + 20*a*b + 15*b^2)*x)*sinh(x)^4 + 8*(7*b^2*cosh(x)^5 - 20*(a*b + 2*b^2)*cosh(x)^3 + 4*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x))*sinh(x)^3 + 8*(a*b + 2*b^2)*cosh(x)^2 + 4*(7*b^2*cosh(x)^6 - 30*(a*b + 2*b^2)*cosh(x)^4 + 12*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^2 + 2*a*b + 4*b^2)*sinh(x)^2 + 32*((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)^3*sinh(x) + 6*(a^2 + 2*a*b + b^2)*cosh(x)^2*sinh(x)^2 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4)*sqrt((a + b)/a)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 + 2*a^2 + a*b)*sqrt((a + b)/a))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) - b^2 + 8*(b^2*cosh(x)^7 - 6*(a*b + 2*b^2)*cosh(x)^5 + 4*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^3 + 2*(a*b + 2*b^2)*cosh(x))*sinh(x))/(b^3*cosh(x)^4 + 4*b^3*cosh(x)^3*sinh(x) + 6*b^3*cosh(x)^2*sinh(x)^2 + 4*b^3*cosh(x)*sinh(x)^3 + b^3*sinh(x)^4), 1/64*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 8*(a*b + 2*b^2)*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - 2*a*b - 4*b^2)*sinh(x)^6 + 8*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 6*(a*b + 2*b^2)*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 60*(a*b + 2*b^2)*cosh(x)^2 + 4*(8*a^2 + 20*a*b + 15*b^2)*x)*sinh(x)^4 + 8*(7*b^2*cosh(x)^5 - 20*(a*b + 2*b^2)*cosh(x)^3 + 4*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x))*sinh(x)^3 + 8*(a*b + 2*b^2)*cosh(x)^2 + 4*(7*b^2*cosh(x)^6 - 30*(a*b + 2*b^2)*cosh(x)^4 + 12*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^2 + 2*a*b + 4*b^2)*sinh(x)^2 - 64*((a^2 + 2*a*b + b^2)*cosh(x)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(x)^3*sinh(x) + 6*(a^2 + 2*a*b + b^2)*cosh(x)^2*sinh(x)^2 + 4*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^3 + (a^2 + 2*a*b + b^2)*sinh(x)^4)*sqrt(-(a + b)/a)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-(a + b)/a)/(a + b)) - b^2 + 8*(b^2*cosh(x)^7 - 6*(a*b + 2*b^2)*cosh(x)^5 + 4*(8*a^2 + 20*a*b + 15*b^2)*x*cosh(x)^3 + 2*(a*b + 2*b^2)*cosh(x))*sinh(x))/(b^3*cosh(x)^4 + 4*b^3*cosh(x)^3*sinh(x) + 6*b^3*cosh(x)^2*sinh(x)^2 + 4*b^3*cosh(x)*sinh(x)^3 + b^3*sinh(x)^4)]","B",0
14,1,568,0,0.483971," ","integrate(sinh(x)^4/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 4 \, {\left(2 \, a + 3 \, b\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a + 3 \, b\right)} x\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{a + b}{a}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} + 2 \, a^{2} + a b\right)} \sqrt{\frac{a + b}{a}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 4 \, {\left(b \cosh\left(x\right)^{3} - 2 \, {\left(2 \, a + 3 \, b\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right) - b}{8 \, {\left(b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2}\right)}}, \frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 4 \, {\left(2 \, a + 3 \, b\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a + 3 \, b\right)} x\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2}\right)} \sqrt{-\frac{a + b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) + 4 \, {\left(b \cosh\left(x\right)^{3} - 2 \, {\left(2 \, a + 3 \, b\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right) - b}{8 \, {\left(b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2}\right)}}\right]"," ",0,"[1/8*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 4*(2*a + 3*b)*x*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*(2*a + 3*b)*x)*sinh(x)^2 + 4*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2)*sqrt((a + b)/a)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 + 2*a^2 + a*b)*sqrt((a + b)/a))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 4*(b*cosh(x)^3 - 2*(2*a + 3*b)*x*cosh(x))*sinh(x) - b)/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2), 1/8*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 4*(2*a + 3*b)*x*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*(2*a + 3*b)*x)*sinh(x)^2 + 8*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2)*sqrt(-(a + b)/a)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-(a + b)/a)/(a + b)) + 4*(b*cosh(x)^3 - 2*(2*a + 3*b)*x*cosh(x))*sinh(x) - b)/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2)]","B",0
15,1,300,0,0.551318," ","integrate(sinh(x)^2/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a + b}{a}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(a b \cosh\left(x\right)^{2} + 2 \, a b \cosh\left(x\right) \sinh\left(x\right) + a b \sinh\left(x\right)^{2} + 2 \, a^{2} + a b\right)} \sqrt{\frac{a + b}{a}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 2 \, x}{2 \, b}, -\frac{\sqrt{-\frac{a + b}{a}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) - x}{b}\right]"," ",0,"[1/2*(sqrt((a + b)/a)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*(a*b*cosh(x)^2 + 2*a*b*cosh(x)*sinh(x) + a*b*sinh(x)^2 + 2*a^2 + a*b)*sqrt((a + b)/a))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 2*x)/b, -(sqrt(-(a + b)/a)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-(a + b)/a)/(a + b)) - x)/b]","A",0
16,1,293,0,0.458650," ","integrate(1/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right)}{2 \, \sqrt{a^{2} + a b}}, \frac{\sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right)}{a^{2} + a b}\right]"," ",0,"[1/2*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b))/sqrt(a^2 + a*b), sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b))/(a^2 + a*b)]","B",0
17,1,1875,0,0.544456," ","integrate(csch(x)^4/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 48 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 12 \, {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, a^{3} + 28 \, a^{2} b + 20 \, a b^{2} - 24 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} - 24 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} - 3 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} - 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} - b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} - 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{6 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - 5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - a b^{3} + 4 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{6 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 24 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, a^{3} + 14 \, a^{2} b + 10 \, a b^{2} - 12 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)^{2} - 12 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2} - 3 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} - 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} - b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} - 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right) + 24 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - 5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - a b^{3} + 4 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/6*(12*(a^2*b + a*b^2)*cosh(x)^4 + 48*(a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + 12*(a^2*b + a*b^2)*sinh(x)^4 + 8*a^3 + 28*a^2*b + 20*a*b^2 - 24*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 - 24*(a^3 + 3*a^2*b + 2*a*b^2 - 3*(a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 - 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 - b^2 + 6*(b^2*cosh(x)^5 - 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 48*((a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^5 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^6 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - 5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^4 - a^4 - 3*a^3*b - 3*a^2*b^2 - a*b^3 + 4*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2 + 3*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 - 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)), 1/3*(6*(a^2*b + a*b^2)*cosh(x)^4 + 24*(a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + 6*(a^2*b + a*b^2)*sinh(x)^4 + 4*a^3 + 14*a^2*b + 10*a*b^2 - 12*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(x)^2 - 12*(a^3 + 3*a^2*b + 2*a*b^2 - 3*(a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 - 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 - b^2 + 6*(b^2*cosh(x)^5 - 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)) + 24*((a^2*b + a*b^2)*cosh(x)^3 - (a^3 + 3*a^2*b + 2*a*b^2)*cosh(x))*sinh(x))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^5 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^6 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - 5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^4 - a^4 - 3*a^3*b - 3*a^2*b^2 - a*b^3 + 4*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2 + 3*(5*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 - 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x))]","B",0
18,1,4977,0,0.529233," ","integrate(csch(x)^6/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[-\frac{60 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 480 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + 60 \, {\left(a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} - 120 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{6} - 120 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3} - 14 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 240 \, {\left(14 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 40 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 40 \, {\left(105 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3} - 45 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 32 \, a^{4} + 136 \, a^{3} b + 236 \, a^{2} b^{2} + 132 \, a b^{3} + 160 \, {\left(21 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 15 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 40 \, {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 40 \, {\left(42 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} - 45 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, a^{4} - 17 \, a^{3} b - 28 \, a^{2} b^{2} - 15 \, a b^{3} + 6 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 15 \, {\left(b^{3} \cosh\left(x\right)^{10} + 10 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{3} \sinh\left(x\right)^{10} - 5 \, b^{3} \cosh\left(x\right)^{8} + 10 \, b^{3} \cosh\left(x\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(x\right)^{2} - b^{3}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(x\right)^{3} - b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} - 10 \, b^{3} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(x\right)^{4} - 14 \, b^{3} \cosh\left(x\right)^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(x\right)^{5} - 70 \, b^{3} \cosh\left(x\right)^{3} + 15 \, b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, b^{3} \cosh\left(x\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(x\right)^{6} - 35 \, b^{3} \cosh\left(x\right)^{4} + 15 \, b^{3} \cosh\left(x\right)^{2} - b^{3}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(x\right)^{7} - 7 \, b^{3} \cosh\left(x\right)^{5} + 5 \, b^{3} \cosh\left(x\right)^{3} - b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(x\right)^{8} - 28 \, b^{3} \cosh\left(x\right)^{6} + 30 \, b^{3} \cosh\left(x\right)^{4} - 12 \, b^{3} \cosh\left(x\right)^{2} + b^{3}\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b^{3} \cosh\left(x\right)^{9} - 4 \, b^{3} \cosh\left(x\right)^{7} + 6 \, b^{3} \cosh\left(x\right)^{5} - 4 \, b^{3} \cosh\left(x\right)^{3} + b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 80 \, {\left(6 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} - 9 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{30 \, {\left({\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{8} - 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 9 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 21 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 4 \, a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} - 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} - a^{5} - 4 \, a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} - 35 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} + a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 30 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 10 \, {\left({\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{30 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 240 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + 30 \, {\left(a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} - 60 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{6} - 60 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3} - 14 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 120 \, {\left(14 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 20 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{4} + 20 \, {\left(105 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3} - 45 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 16 \, a^{4} + 68 \, a^{3} b + 118 \, a^{2} b^{2} + 66 \, a b^{3} + 80 \, {\left(21 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 15 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 20 \, {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cosh\left(x\right)^{2} + 20 \, {\left(42 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} - 45 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} - 4 \, a^{4} - 17 \, a^{3} b - 28 \, a^{2} b^{2} - 15 \, a b^{3} + 6 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 15 \, {\left(b^{3} \cosh\left(x\right)^{10} + 10 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{3} \sinh\left(x\right)^{10} - 5 \, b^{3} \cosh\left(x\right)^{8} + 10 \, b^{3} \cosh\left(x\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(x\right)^{2} - b^{3}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(x\right)^{3} - b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} - 10 \, b^{3} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(x\right)^{4} - 14 \, b^{3} \cosh\left(x\right)^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(x\right)^{5} - 70 \, b^{3} \cosh\left(x\right)^{3} + 15 \, b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, b^{3} \cosh\left(x\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(x\right)^{6} - 35 \, b^{3} \cosh\left(x\right)^{4} + 15 \, b^{3} \cosh\left(x\right)^{2} - b^{3}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(x\right)^{7} - 7 \, b^{3} \cosh\left(x\right)^{5} + 5 \, b^{3} \cosh\left(x\right)^{3} - b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(x\right)^{8} - 28 \, b^{3} \cosh\left(x\right)^{6} + 30 \, b^{3} \cosh\left(x\right)^{4} - 12 \, b^{3} \cosh\left(x\right)^{2} + b^{3}\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b^{3} \cosh\left(x\right)^{9} - 4 \, b^{3} \cosh\left(x\right)^{7} + 6 \, b^{3} \cosh\left(x\right)^{5} - 4 \, b^{3} \cosh\left(x\right)^{3} + b^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right) + 40 \, {\left(6 \, {\left(a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} - 9 \, {\left(a^{3} b + 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(8 \, a^{4} + 31 \, a^{3} b + 47 \, a^{2} b^{2} + 24 \, a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{4} + 17 \, a^{3} b + 28 \, a^{2} b^{2} + 15 \, a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{15 \, {\left({\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{8} - 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 9 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 21 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 4 \, a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} - 10 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} - a^{5} - 4 \, a^{4} b - 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} - 35 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{6} + a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 30 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 10 \, {\left({\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[-1/30*(60*(a^2*b^2 + a*b^3)*cosh(x)^8 + 480*(a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + 60*(a^2*b^2 + a*b^3)*sinh(x)^8 - 120*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^6 - 120*(a^3*b + 4*a^2*b^2 + 3*a*b^3 - 14*(a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 240*(14*(a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x))*sinh(x)^5 + 40*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^4 + 40*(105*(a^2*b^2 + a*b^3)*cosh(x)^4 + 8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3 - 45*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^2)*sinh(x)^4 + 32*a^4 + 136*a^3*b + 236*a^2*b^2 + 132*a*b^3 + 160*(21*(a^2*b^2 + a*b^3)*cosh(x)^5 - 15*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^3 + (8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x))*sinh(x)^3 - 40*(4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cosh(x)^2 + 40*(42*(a^2*b^2 + a*b^3)*cosh(x)^6 - 45*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^4 - 4*a^4 - 17*a^3*b - 28*a^2*b^2 - 15*a*b^3 + 6*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^2)*sinh(x)^2 - 15*(b^3*cosh(x)^10 + 10*b^3*cosh(x)*sinh(x)^9 + b^3*sinh(x)^10 - 5*b^3*cosh(x)^8 + 10*b^3*cosh(x)^6 + 5*(9*b^3*cosh(x)^2 - b^3)*sinh(x)^8 + 40*(3*b^3*cosh(x)^3 - b^3*cosh(x))*sinh(x)^7 - 10*b^3*cosh(x)^4 + 10*(21*b^3*cosh(x)^4 - 14*b^3*cosh(x)^2 + b^3)*sinh(x)^6 + 4*(63*b^3*cosh(x)^5 - 70*b^3*cosh(x)^3 + 15*b^3*cosh(x))*sinh(x)^5 + 5*b^3*cosh(x)^2 + 10*(21*b^3*cosh(x)^6 - 35*b^3*cosh(x)^4 + 15*b^3*cosh(x)^2 - b^3)*sinh(x)^4 + 40*(3*b^3*cosh(x)^7 - 7*b^3*cosh(x)^5 + 5*b^3*cosh(x)^3 - b^3*cosh(x))*sinh(x)^3 - b^3 + 5*(9*b^3*cosh(x)^8 - 28*b^3*cosh(x)^6 + 30*b^3*cosh(x)^4 - 12*b^3*cosh(x)^2 + b^3)*sinh(x)^2 + 10*(b^3*cosh(x)^9 - 4*b^3*cosh(x)^7 + 6*b^3*cosh(x)^5 - 4*b^3*cosh(x)^3 + b^3*cosh(x))*sinh(x))*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 80*(6*(a^2*b^2 + a*b^3)*cosh(x)^7 - 9*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^5 + 2*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^3 - (4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cosh(x))*sinh(x))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^10 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)*sinh(x)^9 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sinh(x)^10 - 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^8 - 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 9*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^8 + 40*(3*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 - (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^7 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 21*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 - 14*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 - 70*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 + 15*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^5 - a^5 - 4*a^4*b - 6*a^3*b^2 - 4*a^2*b^3 - a*b^4 - 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 + 10*(21*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 - a^5 - 4*a^4*b - 6*a^3*b^2 - 4*a^2*b^3 - a*b^4 - 35*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 + 15*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^4 + 40*(3*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^7 - 7*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 + 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 - (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^3 + 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2 + 5*(9*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^8 - 28*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 + a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 30*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 - 12*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^2 + 10*((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^9 - 4*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^7 + 6*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 - 4*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)), -1/15*(30*(a^2*b^2 + a*b^3)*cosh(x)^8 + 240*(a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + 30*(a^2*b^2 + a*b^3)*sinh(x)^8 - 60*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^6 - 60*(a^3*b + 4*a^2*b^2 + 3*a*b^3 - 14*(a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 120*(14*(a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x))*sinh(x)^5 + 20*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^4 + 20*(105*(a^2*b^2 + a*b^3)*cosh(x)^4 + 8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3 - 45*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^2)*sinh(x)^4 + 16*a^4 + 68*a^3*b + 118*a^2*b^2 + 66*a*b^3 + 80*(21*(a^2*b^2 + a*b^3)*cosh(x)^5 - 15*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^3 + (8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x))*sinh(x)^3 - 20*(4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cosh(x)^2 + 20*(42*(a^2*b^2 + a*b^3)*cosh(x)^6 - 45*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^4 - 4*a^4 - 17*a^3*b - 28*a^2*b^2 - 15*a*b^3 + 6*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^2)*sinh(x)^2 + 15*(b^3*cosh(x)^10 + 10*b^3*cosh(x)*sinh(x)^9 + b^3*sinh(x)^10 - 5*b^3*cosh(x)^8 + 10*b^3*cosh(x)^6 + 5*(9*b^3*cosh(x)^2 - b^3)*sinh(x)^8 + 40*(3*b^3*cosh(x)^3 - b^3*cosh(x))*sinh(x)^7 - 10*b^3*cosh(x)^4 + 10*(21*b^3*cosh(x)^4 - 14*b^3*cosh(x)^2 + b^3)*sinh(x)^6 + 4*(63*b^3*cosh(x)^5 - 70*b^3*cosh(x)^3 + 15*b^3*cosh(x))*sinh(x)^5 + 5*b^3*cosh(x)^2 + 10*(21*b^3*cosh(x)^6 - 35*b^3*cosh(x)^4 + 15*b^3*cosh(x)^2 - b^3)*sinh(x)^4 + 40*(3*b^3*cosh(x)^7 - 7*b^3*cosh(x)^5 + 5*b^3*cosh(x)^3 - b^3*cosh(x))*sinh(x)^3 - b^3 + 5*(9*b^3*cosh(x)^8 - 28*b^3*cosh(x)^6 + 30*b^3*cosh(x)^4 - 12*b^3*cosh(x)^2 + b^3)*sinh(x)^2 + 10*(b^3*cosh(x)^9 - 4*b^3*cosh(x)^7 + 6*b^3*cosh(x)^5 - 4*b^3*cosh(x)^3 + b^3*cosh(x))*sinh(x))*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)) + 40*(6*(a^2*b^2 + a*b^3)*cosh(x)^7 - 9*(a^3*b + 4*a^2*b^2 + 3*a*b^3)*cosh(x)^5 + 2*(8*a^4 + 31*a^3*b + 47*a^2*b^2 + 24*a*b^3)*cosh(x)^3 - (4*a^4 + 17*a^3*b + 28*a^2*b^2 + 15*a*b^3)*cosh(x))*sinh(x))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^10 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)*sinh(x)^9 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sinh(x)^10 - 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^8 - 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 9*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^8 + 40*(3*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 - (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^7 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 + 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 21*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 - 14*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 - 70*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 + 15*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^5 - a^5 - 4*a^4*b - 6*a^3*b^2 - 4*a^2*b^3 - a*b^4 - 10*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 + 10*(21*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 - a^5 - 4*a^4*b - 6*a^3*b^2 - 4*a^2*b^3 - a*b^4 - 35*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 + 15*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^4 + 40*(3*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^7 - 7*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 + 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 - (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x)^3 + 5*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2 + 5*(9*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^8 - 28*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^6 + a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 30*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^4 - 12*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^2)*sinh(x)^2 + 10*((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^9 - 4*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^7 + 6*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^5 - 4*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x)^3 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*cosh(x))*sinh(x))]","B",0
19,1,305,0,0.519932," ","integrate(sinh(x)/(4-3*cosh(x)^3),x, algorithm=""fricas"")","\frac{1}{12} \cdot 6^{\frac{1}{6}} \sqrt{2} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{12} \cdot 6^{\frac{1}{6}} {\left(6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \cosh\left(x\right)^{3} + 6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \sinh\left(x\right)^{3} + {\left(3 \cdot 6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \cosh\left(x\right) + 4 \cdot 6^{\frac{1}{3}} \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \cdot 6^{\frac{1}{3}} \sqrt{2} \cosh\left(x\right)^{2} + {\left(6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} - 16 \, \sqrt{2} \left(-1\right)^{\frac{1}{3}}\right)} \cosh\left(x\right) + {\left(3 \cdot 6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \cosh\left(x\right)^{2} + 6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} + 8 \cdot 6^{\frac{1}{3}} \sqrt{2} \cosh\left(x\right) - 16 \, \sqrt{2} \left(-1\right)^{\frac{1}{3}}\right)} \sinh\left(x\right) + 2 \cdot 6^{\frac{1}{3}} \sqrt{2}\right)}\right) - \frac{1}{12} \cdot 6^{\frac{1}{6}} \sqrt{2} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{12} \cdot 6^{\frac{1}{6}} {\left(6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \cosh\left(x\right) + 6^{\frac{2}{3}} \sqrt{2} \left(-1\right)^{\frac{2}{3}} \sinh\left(x\right) + 2 \cdot 6^{\frac{1}{3}} \sqrt{2}\right)}\right) - \frac{1}{72} \cdot 6^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{2 \, {\left(2 \cdot 6^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \cosh\left(x\right) - 3 \, \cosh\left(x\right)^{2} - 3 \, \sinh\left(x\right)^{2} - 4 \cdot 6^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} - 3\right)}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \frac{1}{36} \cdot 6^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(\frac{2 \, {\left(6^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 3 \, \cosh\left(x\right)\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"1/12*6^(1/6)*sqrt(2)*(-1)^(1/3)*arctan(1/12*6^(1/6)*(6^(2/3)*sqrt(2)*(-1)^(2/3)*cosh(x)^3 + 6^(2/3)*sqrt(2)*(-1)^(2/3)*sinh(x)^3 + (3*6^(2/3)*sqrt(2)*(-1)^(2/3)*cosh(x) + 4*6^(1/3)*sqrt(2))*sinh(x)^2 + 4*6^(1/3)*sqrt(2)*cosh(x)^2 + (6^(2/3)*sqrt(2)*(-1)^(2/3) - 16*sqrt(2)*(-1)^(1/3))*cosh(x) + (3*6^(2/3)*sqrt(2)*(-1)^(2/3)*cosh(x)^2 + 6^(2/3)*sqrt(2)*(-1)^(2/3) + 8*6^(1/3)*sqrt(2)*cosh(x) - 16*sqrt(2)*(-1)^(1/3))*sinh(x) + 2*6^(1/3)*sqrt(2))) - 1/12*6^(1/6)*sqrt(2)*(-1)^(1/3)*arctan(1/12*6^(1/6)*(6^(2/3)*sqrt(2)*(-1)^(2/3)*cosh(x) + 6^(2/3)*sqrt(2)*(-1)^(2/3)*sinh(x) + 2*6^(1/3)*sqrt(2))) - 1/72*6^(2/3)*(-1)^(1/3)*log(-2*(2*6^(2/3)*(-1)^(1/3)*cosh(x) - 3*cosh(x)^2 - 3*sinh(x)^2 - 4*6^(1/3)*(-1)^(2/3) - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1/36*6^(2/3)*(-1)^(1/3)*log(2*(6^(2/3)*(-1)^(1/3) + 3*cosh(x))/(cosh(x) - sinh(x)))","B",0
20,1,2508,0,0.518544," ","integrate(cosh(x)^7/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{10} + 30 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + 3 \, {\left(a b^{3} + b^{4}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{8} - 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4} - 27 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(9 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 30 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(63 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 6 \, a^{2} b^{2} - 3 \, a b^{3} + 15 \, b^{4} - 14 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(189 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{3} + 45 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 30 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(63 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{4} - 24 \, a^{3} b - 6 \, a^{2} b^{2} + 3 \, a b^{3} - 15 \, b^{4} + 45 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a b^{3} - 3 \, b^{4} + 40 \, {\left(9 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{5} + 15 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(27 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{6} + 90 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4} - 36 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 240 \, {\left(a^{3} \cosh\left(x\right)^{5} + 5 \, a^{3} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, a^{3} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, a^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{4} + a^{3} \sinh\left(x\right)^{5}\right)} \sqrt{-a b - b^{2}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)\right)} \sqrt{-a b - b^{2}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 10 \, {\left(3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{7} + 18 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{5} - 12 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{480 \, {\left({\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + {\left(a b^{4} + b^{5}\right)} \sinh\left(x\right)^{5}\right)}}, \frac{3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{10} + 30 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + 3 \, {\left(a b^{3} + b^{4}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{8} - 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4} - 27 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(9 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} - {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 30 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(63 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 24 \, a^{3} b + 6 \, a^{2} b^{2} - 3 \, a b^{3} + 15 \, b^{4} - 14 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(189 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{3} + 45 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 30 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(63 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{4} - 24 \, a^{3} b - 6 \, a^{2} b^{2} + 3 \, a b^{3} - 15 \, b^{4} + 45 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a b^{3} - 3 \, b^{4} + 40 \, {\left(9 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{5} + 15 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(27 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{6} + 90 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4} - 36 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 480 \, {\left(a^{3} \cosh\left(x\right)^{5} + 5 \, a^{3} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, a^{3} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, a^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{4} + a^{3} \sinh\left(x\right)^{5}\right)} \sqrt{a b + b^{2}} \arctan\left(\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)}{2 \, \sqrt{a b + b^{2}}}\right) - 480 \, {\left(a^{3} \cosh\left(x\right)^{5} + 5 \, a^{3} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, a^{3} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, a^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{4} + a^{3} \sinh\left(x\right)^{5}\right)} \sqrt{a b + b^{2}} \arctan\left(\frac{\sqrt{a b + b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, {\left(a + b\right)}}\right) + 10 \, {\left(3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)^{7} + 18 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{5} - 12 \, {\left(8 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{480 \, {\left({\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} \sinh\left(x\right) + 10 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} \sinh\left(x\right)^{2} + 10 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right)^{3} + 5 \, {\left(a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{4} + {\left(a b^{4} + b^{5}\right)} \sinh\left(x\right)^{5}\right)}}\right]"," ",0,"[1/480*(3*(a*b^3 + b^4)*cosh(x)^10 + 30*(a*b^3 + b^4)*cosh(x)*sinh(x)^9 + 3*(a*b^3 + b^4)*sinh(x)^10 - 5*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^8 - 5*(4*a^2*b^2 - a*b^3 - 5*b^4 - 27*(a*b^3 + b^4)*cosh(x)^2)*sinh(x)^8 + 40*(9*(a*b^3 + b^4)*cosh(x)^3 - (4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x))*sinh(x)^7 + 30*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^6 + 10*(63*(a*b^3 + b^4)*cosh(x)^4 + 24*a^3*b + 6*a^2*b^2 - 3*a*b^3 + 15*b^4 - 14*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(189*(a*b^3 + b^4)*cosh(x)^5 - 70*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^3 + 45*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x))*sinh(x)^5 - 30*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^4 + 10*(63*(a*b^3 + b^4)*cosh(x)^6 - 35*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^4 - 24*a^3*b - 6*a^2*b^2 + 3*a*b^3 - 15*b^4 + 45*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^2)*sinh(x)^4 - 3*a*b^3 - 3*b^4 + 40*(9*(a*b^3 + b^4)*cosh(x)^7 - 7*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^5 + 15*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^3 - 3*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x))*sinh(x)^3 + 5*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^2 + 5*(27*(a*b^3 + b^4)*cosh(x)^8 - 28*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^6 + 90*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^4 + 4*a^2*b^2 - a*b^3 - 5*b^4 - 36*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^2)*sinh(x)^2 - 240*(a^3*cosh(x)^5 + 5*a^3*cosh(x)^4*sinh(x) + 10*a^3*cosh(x)^3*sinh(x)^2 + 10*a^3*cosh(x)^2*sinh(x)^3 + 5*a^3*cosh(x)*sinh(x)^4 + a^3*sinh(x)^5)*sqrt(-a*b - b^2)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) + 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))*sqrt(-a*b - b^2) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 10*(3*(a*b^3 + b^4)*cosh(x)^9 - 4*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^7 + 18*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^5 - 12*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^3 + (4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x))*sinh(x))/((a*b^4 + b^5)*cosh(x)^5 + 5*(a*b^4 + b^5)*cosh(x)^4*sinh(x) + 10*(a*b^4 + b^5)*cosh(x)^3*sinh(x)^2 + 10*(a*b^4 + b^5)*cosh(x)^2*sinh(x)^3 + 5*(a*b^4 + b^5)*cosh(x)*sinh(x)^4 + (a*b^4 + b^5)*sinh(x)^5), 1/480*(3*(a*b^3 + b^4)*cosh(x)^10 + 30*(a*b^3 + b^4)*cosh(x)*sinh(x)^9 + 3*(a*b^3 + b^4)*sinh(x)^10 - 5*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^8 - 5*(4*a^2*b^2 - a*b^3 - 5*b^4 - 27*(a*b^3 + b^4)*cosh(x)^2)*sinh(x)^8 + 40*(9*(a*b^3 + b^4)*cosh(x)^3 - (4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x))*sinh(x)^7 + 30*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^6 + 10*(63*(a*b^3 + b^4)*cosh(x)^4 + 24*a^3*b + 6*a^2*b^2 - 3*a*b^3 + 15*b^4 - 14*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^2)*sinh(x)^6 + 4*(189*(a*b^3 + b^4)*cosh(x)^5 - 70*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^3 + 45*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x))*sinh(x)^5 - 30*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^4 + 10*(63*(a*b^3 + b^4)*cosh(x)^6 - 35*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^4 - 24*a^3*b - 6*a^2*b^2 + 3*a*b^3 - 15*b^4 + 45*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^2)*sinh(x)^4 - 3*a*b^3 - 3*b^4 + 40*(9*(a*b^3 + b^4)*cosh(x)^7 - 7*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^5 + 15*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^3 - 3*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x))*sinh(x)^3 + 5*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^2 + 5*(27*(a*b^3 + b^4)*cosh(x)^8 - 28*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^6 + 90*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^4 + 4*a^2*b^2 - a*b^3 - 5*b^4 - 36*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^2)*sinh(x)^2 - 480*(a^3*cosh(x)^5 + 5*a^3*cosh(x)^4*sinh(x) + 10*a^3*cosh(x)^3*sinh(x)^2 + 10*a^3*cosh(x)^2*sinh(x)^3 + 5*a^3*cosh(x)*sinh(x)^4 + a^3*sinh(x)^5)*sqrt(a*b + b^2)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))/sqrt(a*b + b^2)) - 480*(a^3*cosh(x)^5 + 5*a^3*cosh(x)^4*sinh(x) + 10*a^3*cosh(x)^3*sinh(x)^2 + 10*a^3*cosh(x)^2*sinh(x)^3 + 5*a^3*cosh(x)*sinh(x)^4 + a^3*sinh(x)^5)*sqrt(a*b + b^2)*arctan(1/2*sqrt(a*b + b^2)*(cosh(x) + sinh(x))/(a + b)) + 10*(3*(a*b^3 + b^4)*cosh(x)^9 - 4*(4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x)^7 + 18*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^5 - 12*(8*a^3*b + 2*a^2*b^2 - a*b^3 + 5*b^4)*cosh(x)^3 + (4*a^2*b^2 - a*b^3 - 5*b^4)*cosh(x))*sinh(x))/((a*b^4 + b^5)*cosh(x)^5 + 5*(a*b^4 + b^5)*cosh(x)^4*sinh(x) + 10*(a*b^4 + b^5)*cosh(x)^3*sinh(x)^2 + 10*(a*b^4 + b^5)*cosh(x)^2*sinh(x)^3 + 5*(a*b^4 + b^5)*cosh(x)*sinh(x)^4 + (a*b^4 + b^5)*sinh(x)^5)]","B",0
21,1,1245,0,0.481962," ","integrate(cosh(x)^6/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 8 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - 2 \, a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 6 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 60 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 20 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 30 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 2 \, a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + 32 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, a^{2} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4}\right)} \sqrt{\frac{a}{a + b}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a + b}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 6 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{3} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left(b^{3} \cosh\left(x\right)^{4} + 4 \, b^{3} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{3} \sinh\left(x\right)^{4}\right)}}, \frac{b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} - 8 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} - 2 \, a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} - 6 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} - 60 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} - 20 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{3} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} - 30 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{2} + 2 \, a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} - 64 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, a^{2} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4}\right)} \sqrt{-\frac{a}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a}{a + b}}}{2 \, a}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} - 6 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} x \cosh\left(x\right)^{3} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{64 \, {\left(b^{3} \cosh\left(x\right)^{4} + 4 \, b^{3} \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, b^{3} \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, b^{3} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{3} \sinh\left(x\right)^{4}\right)}}\right]"," ",0,"[1/64*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 8*(a*b - b^2)*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - 2*a*b + 2*b^2)*sinh(x)^6 + 8*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 6*(a*b - b^2)*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 60*(a*b - b^2)*cosh(x)^2 + 4*(8*a^2 - 4*a*b + 3*b^2)*x)*sinh(x)^4 + 8*(7*b^2*cosh(x)^5 - 20*(a*b - b^2)*cosh(x)^3 + 4*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x))*sinh(x)^3 + 8*(a*b - b^2)*cosh(x)^2 + 4*(7*b^2*cosh(x)^6 - 30*(a*b - b^2)*cosh(x)^4 + 12*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^2 + 2*a*b - 2*b^2)*sinh(x)^2 + 32*(a^2*cosh(x)^4 + 4*a^2*cosh(x)^3*sinh(x) + 6*a^2*cosh(x)^2*sinh(x)^2 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4)*sqrt(a/(a + b))*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 + 2*a^2 + 3*a*b + b^2)*sqrt(a/(a + b)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) - b^2 + 8*(b^2*cosh(x)^7 - 6*(a*b - b^2)*cosh(x)^5 + 4*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^3 + 2*(a*b - b^2)*cosh(x))*sinh(x))/(b^3*cosh(x)^4 + 4*b^3*cosh(x)^3*sinh(x) + 6*b^3*cosh(x)^2*sinh(x)^2 + 4*b^3*cosh(x)*sinh(x)^3 + b^3*sinh(x)^4), 1/64*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 - 8*(a*b - b^2)*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 - 2*a*b + 2*b^2)*sinh(x)^6 + 8*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 - 6*(a*b - b^2)*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 - 60*(a*b - b^2)*cosh(x)^2 + 4*(8*a^2 - 4*a*b + 3*b^2)*x)*sinh(x)^4 + 8*(7*b^2*cosh(x)^5 - 20*(a*b - b^2)*cosh(x)^3 + 4*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x))*sinh(x)^3 + 8*(a*b - b^2)*cosh(x)^2 + 4*(7*b^2*cosh(x)^6 - 30*(a*b - b^2)*cosh(x)^4 + 12*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^2 + 2*a*b - 2*b^2)*sinh(x)^2 - 64*(a^2*cosh(x)^4 + 4*a^2*cosh(x)^3*sinh(x) + 6*a^2*cosh(x)^2*sinh(x)^2 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4)*sqrt(-a/(a + b))*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a/(a + b))/a) - b^2 + 8*(b^2*cosh(x)^7 - 6*(a*b - b^2)*cosh(x)^5 + 4*(8*a^2 - 4*a*b + 3*b^2)*x*cosh(x)^3 + 2*(a*b - b^2)*cosh(x))*sinh(x))/(b^3*cosh(x)^4 + 4*b^3*cosh(x)^3*sinh(x) + 6*b^3*cosh(x)^2*sinh(x)^2 + 4*b^3*cosh(x)*sinh(x)^3 + b^3*sinh(x)^4)]","B",0
22,1,1184,0,0.526026," ","integrate(cosh(x)^5/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3} - 5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a b^{2} - b^{3} + 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, a^{2} b + a b^{2} - 3 \, b^{3} - 6 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} - 12 \, {\left(a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{3}\right)} \sqrt{-a b - b^{2}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)\right)} \sqrt{-a b - b^{2}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 6 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a b^{3} + b^{4}\right)} \sinh\left(x\right)^{3}\right)}}, \frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3} - 5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a b^{2} - b^{3} + 3 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, a^{2} b + a b^{2} - 3 \, b^{3} - 6 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 24 \, {\left(a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{3}\right)} \sqrt{a b + b^{2}} \arctan\left(\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)}{2 \, \sqrt{a b + b^{2}}}\right) + 24 \, {\left(a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{2} + a^{2} \sinh\left(x\right)^{3}\right)} \sqrt{a b + b^{2}} \arctan\left(\frac{\sqrt{a b + b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, {\left(a + b\right)}}\right) + 6 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{24 \, {\left({\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2} \sinh\left(x\right) + 3 \, {\left(a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a b^{3} + b^{4}\right)} \sinh\left(x\right)^{3}\right)}}\right]"," ",0,"[1/24*((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 - 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^4 - 3*(4*a^2*b + a*b^2 - 3*b^3 - 5*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 - 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x))*sinh(x)^3 - a*b^2 - b^3 + 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^2 + 3*(5*(a*b^2 + b^3)*cosh(x)^4 + 4*a^2*b + a*b^2 - 3*b^3 - 6*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^2 - 12*(a^2*cosh(x)^3 + 3*a^2*cosh(x)^2*sinh(x) + 3*a^2*cosh(x)*sinh(x)^2 + a^2*sinh(x)^3)*sqrt(-a*b - b^2)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) - 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))*sqrt(-a*b - b^2) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 6*((a*b^2 + b^3)*cosh(x)^5 - 2*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^3 + (4*a^2*b + a*b^2 - 3*b^3)*cosh(x))*sinh(x))/((a*b^3 + b^4)*cosh(x)^3 + 3*(a*b^3 + b^4)*cosh(x)^2*sinh(x) + 3*(a*b^3 + b^4)*cosh(x)*sinh(x)^2 + (a*b^3 + b^4)*sinh(x)^3), 1/24*((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 - 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^4 - 3*(4*a^2*b + a*b^2 - 3*b^3 - 5*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 - 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x))*sinh(x)^3 - a*b^2 - b^3 + 3*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^2 + 3*(5*(a*b^2 + b^3)*cosh(x)^4 + 4*a^2*b + a*b^2 - 3*b^3 - 6*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^2 + 24*(a^2*cosh(x)^3 + 3*a^2*cosh(x)^2*sinh(x) + 3*a^2*cosh(x)*sinh(x)^2 + a^2*sinh(x)^3)*sqrt(a*b + b^2)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))/sqrt(a*b + b^2)) + 24*(a^2*cosh(x)^3 + 3*a^2*cosh(x)^2*sinh(x) + 3*a^2*cosh(x)*sinh(x)^2 + a^2*sinh(x)^3)*sqrt(a*b + b^2)*arctan(1/2*sqrt(a*b + b^2)*(cosh(x) + sinh(x))/(a + b)) + 6*((a*b^2 + b^3)*cosh(x)^5 - 2*(4*a^2*b + a*b^2 - 3*b^3)*cosh(x)^3 + (4*a^2*b + a*b^2 - 3*b^3)*cosh(x))*sinh(x))/((a*b^3 + b^4)*cosh(x)^3 + 3*(a*b^3 + b^4)*cosh(x)^2*sinh(x) + 3*(a*b^3 + b^4)*cosh(x)*sinh(x)^2 + (a*b^3 + b^4)*sinh(x)^3)]","B",0
23,1,573,0,0.584413," ","integrate(cosh(x)^4/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 4 \, {\left(2 \, a - b\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a - b\right)} x\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2}\right)} \sqrt{\frac{a}{a + b}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a + b}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 4 \, {\left(b \cosh\left(x\right)^{3} - 2 \, {\left(2 \, a - b\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right) - b}{8 \, {\left(b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2}\right)}}, \frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 4 \, {\left(2 \, a - b\right)} x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, {\left(2 \, a - b\right)} x\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2}\right)} \sqrt{-\frac{a}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a}{a + b}}}{2 \, a}\right) + 4 \, {\left(b \cosh\left(x\right)^{3} - 2 \, {\left(2 \, a - b\right)} x \cosh\left(x\right)\right)} \sinh\left(x\right) - b}{8 \, {\left(b^{2} \cosh\left(x\right)^{2} + 2 \, b^{2} \cosh\left(x\right) \sinh\left(x\right) + b^{2} \sinh\left(x\right)^{2}\right)}}\right]"," ",0,"[1/8*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 4*(2*a - b)*x*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*(2*a - b)*x)*sinh(x)^2 + 4*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2)*sqrt(a/(a + b))*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 + 2*a^2 + 3*a*b + b^2)*sqrt(a/(a + b)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 4*(b*cosh(x)^3 - 2*(2*a - b)*x*cosh(x))*sinh(x) - b)/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2), 1/8*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 4*(2*a - b)*x*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*(2*a - b)*x)*sinh(x)^2 + 8*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2)*sqrt(-a/(a + b))*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a/(a + b))/a) + 4*(b*cosh(x)^3 - 2*(2*a - b)*x*cosh(x))*sinh(x) - b)/(b^2*cosh(x)^2 + 2*b^2*cosh(x)*sinh(x) + b^2*sinh(x)^2)]","B",0
24,1,498,0,0.453168," ","integrate(cosh(x)^3/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - \sqrt{-a b - b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)\right)} \sqrt{-a b - b^{2}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) - a b - b^{2}}{2 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)\right)}}, \frac{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{a b + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)} \arctan\left(\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)}{2 \, \sqrt{a b + b^{2}}}\right) - 2 \, \sqrt{a b + b^{2}} {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)} \arctan\left(\frac{\sqrt{a b + b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, {\left(a + b\right)}}\right) - a b - b^{2}}{2 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/2*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - sqrt(-a*b - b^2)*(a*cosh(x) + a*sinh(x))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) + 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))*sqrt(-a*b - b^2) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) - a*b - b^2)/((a*b^2 + b^3)*cosh(x) + (a*b^2 + b^3)*sinh(x)), 1/2*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - 2*sqrt(a*b + b^2)*(a*cosh(x) + a*sinh(x))*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))/sqrt(a*b + b^2)) - 2*sqrt(a*b + b^2)*(a*cosh(x) + a*sinh(x))*arctan(1/2*sqrt(a*b + b^2)*(cosh(x) + sinh(x))/(a + b)) - a*b - b^2)/((a*b^2 + b^3)*cosh(x) + (a*b^2 + b^3)*sinh(x))]","B",0
25,1,317,0,0.491245," ","integrate(cosh(x)^2/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a}{a + b}} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a + b}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 2 \, x}{2 \, b}, -\frac{\sqrt{-\frac{a}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-\frac{a}{a + b}}}{2 \, a}\right) - x}{b}\right]"," ",0,"[1/2*(sqrt(a/(a + b))*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 + 2*a^2 + 3*a*b + b^2)*sqrt(a/(a + b)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 2*x)/b, -(sqrt(-a/(a + b))*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a/(a + b))/a) - x)/b]","A",0
26,1,337,0,0.457332," ","integrate(cosh(x)/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b - b^{2}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)\right)} \sqrt{-a b - b^{2}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right)}{2 \, {\left(a b + b^{2}\right)}}, \frac{\sqrt{a b + b^{2}} \arctan\left(\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)}{2 \, \sqrt{a b + b^{2}}}\right) + \sqrt{a b + b^{2}} \arctan\left(\frac{\sqrt{a b + b^{2}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}{2 \, {\left(a + b\right)}}\right)}{a b + b^{2}}\right]"," ",0,"[-1/2*sqrt(-a*b - b^2)*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) - 4*(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))*sqrt(-a*b - b^2) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b))/(a*b + b^2), (sqrt(a*b + b^2)*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))/sqrt(a*b + b^2)) + sqrt(a*b + b^2)*arctan(1/2*sqrt(a*b + b^2)*(cosh(x) + sinh(x))/(a + b)))/(a*b + b^2)]","B",0
27,1,293,0,0.559790," ","integrate(1/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right)}{2 \, \sqrt{a^{2} + a b}}, \frac{\sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right)}{a^{2} + a b}\right]"," ",0,"[1/2*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b))/sqrt(a^2 + a*b), sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b))/(a^2 + a*b)]","B",0
28,1,360,0,0.471176," ","integrate(sech(x)/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a + b}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a + b}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 4 \, \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{2 \, a}, -\frac{\sqrt{\frac{b}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a + b}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) + \sqrt{\frac{b}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a + b}}}{2 \, b}\right) - 2 \, \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{a}\right]"," ",0,"[1/2*(sqrt(-b/(a + b))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) - 4*((a + b)*cosh(x)^3 + 3*(a + b)*cosh(x)*sinh(x)^2 + (a + b)*sinh(x)^3 - (a + b)*cosh(x) + (3*(a + b)*cosh(x)^2 - a - b)*sinh(x))*sqrt(-b/(a + b)) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 4*arctan(cosh(x) + sinh(x)))/a, -(sqrt(b/(a + b))*arctan(1/2*sqrt(b/(a + b))*(cosh(x) + sinh(x))) + sqrt(b/(a + b))*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))*sqrt(b/(a + b))/b) - 2*arctan(cosh(x) + sinh(x)))/a]","B",0
29,1,457,0,0.451554," ","integrate(sech(x)^2/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) - 4 \, a^{2} - 4 \, a b}{2 \, {\left(a^{3} + a^{2} b + {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{2}\right)}}, -\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right) + 2 \, a^{2} + 2 \, a b}{a^{3} + a^{2} b + {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{2}}\right]"," ",0,"[1/2*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) + 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) - 4*a^2 - 4*a*b)/(a^3 + a^2*b + (a^3 + a^2*b)*cosh(x)^2 + 2*(a^3 + a^2*b)*cosh(x)*sinh(x) + (a^3 + a^2*b)*sinh(x)^2), -((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)) + 2*a^2 + 2*a*b)/(a^3 + a^2*b + (a^3 + a^2*b)*cosh(x)^2 + 2*(a^3 + a^2*b)*cosh(x)*sinh(x) + (a^3 + a^2*b)*sinh(x)^2)]","B",0
30,1,963,0,0.527618," ","integrate(sech(x)^3/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a \cosh\left(x\right)^{3} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{2} + 2 \, a \sinh\left(x\right)^{3} + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-\frac{b}{a + b}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a + b}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 2 \, {\left({\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a - 2 \, b\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - 2 \, a \cosh\left(x\right) + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)}{2 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right) \sinh\left(x\right)^{2} + a \sinh\left(x\right)^{3} + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{\frac{b}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a + b}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{\frac{b}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a + b}}}{2 \, b}\right) + {\left({\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a - 2 \, b\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - a \cosh\left(x\right) + {\left(3 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)}{a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} + 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} + a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right]"," ",0,"[1/2*(2*a*cosh(x)^3 + 6*a*cosh(x)*sinh(x)^2 + 2*a*sinh(x)^3 + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-b/(a + b))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) + 4*((a + b)*cosh(x)^3 + 3*(a + b)*cosh(x)*sinh(x)^2 + (a + b)*sinh(x)^3 - (a + b)*cosh(x) + (3*(a + b)*cosh(x)^2 - a - b)*sinh(x))*sqrt(-b/(a + b)) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 2*((a - 2*b)*cosh(x)^4 + 4*(a - 2*b)*cosh(x)*sinh(x)^3 + (a - 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a - 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 + 4*((a - 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a - 2*b)*arctan(cosh(x) + sinh(x)) - 2*a*cosh(x) + 2*(3*a*cosh(x)^2 - a)*sinh(x))/(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x)), (a*cosh(x)^3 + 3*a*cosh(x)*sinh(x)^2 + a*sinh(x)^3 + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(b/(a + b))*arctan(1/2*sqrt(b/(a + b))*(cosh(x) + sinh(x))) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(b/(a + b))*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))*sqrt(b/(a + b))/b) + ((a - 2*b)*cosh(x)^4 + 4*(a - 2*b)*cosh(x)*sinh(x)^3 + (a - 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a - 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 + 4*((a - 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a - 2*b)*arctan(cosh(x) + sinh(x)) - a*cosh(x) + (3*a*cosh(x)^2 - a)*sinh(x))/(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 + 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 + a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 + a^2*cosh(x))*sinh(x))]","B",0
31,1,1377,0,0.444666," ","integrate(sech(x)^4/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 48 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 12 \, {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} - 8 \, a^{3} + 4 \, a^{2} b + 12 \, a b^{2} - 24 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - 24 \, {\left(a^{3} - a b^{2} - 3 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{6 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + a^{3} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + a^{3} b + 5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + a^{3} b + 4 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b + 6 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{6 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 24 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{3} + 2 \, a^{2} b + 6 \, a b^{2} - 12 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} - 12 \, {\left(a^{3} - a b^{2} - 3 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right) + 24 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{3 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + a^{3} b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + a^{3} b + 5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + a^{3} b + 4 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b + 6 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/6*(12*(a^2*b + a*b^2)*cosh(x)^4 + 48*(a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + 12*(a^2*b + a*b^2)*sinh(x)^4 - 8*a^3 + 4*a^2*b + 12*a*b^2 - 24*(a^3 - a*b^2)*cosh(x)^2 - 24*(a^3 - a*b^2 - 3*(a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 48*((a^2*b + a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))/((a^4 + a^3*b)*cosh(x)^6 + 6*(a^4 + a^3*b)*cosh(x)*sinh(x)^5 + (a^4 + a^3*b)*sinh(x)^6 + 3*(a^4 + a^3*b)*cosh(x)^4 + 3*(a^4 + a^3*b + 5*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^4 + a^4 + a^3*b + 4*(5*(a^4 + a^3*b)*cosh(x)^3 + 3*(a^4 + a^3*b)*cosh(x))*sinh(x)^3 + 3*(a^4 + a^3*b)*cosh(x)^2 + 3*(5*(a^4 + a^3*b)*cosh(x)^4 + a^4 + a^3*b + 6*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + a^3*b)*cosh(x)^5 + 2*(a^4 + a^3*b)*cosh(x)^3 + (a^4 + a^3*b)*cosh(x))*sinh(x)), 1/3*(6*(a^2*b + a*b^2)*cosh(x)^4 + 24*(a^2*b + a*b^2)*cosh(x)*sinh(x)^3 + 6*(a^2*b + a*b^2)*sinh(x)^4 - 4*a^3 + 2*a^2*b + 6*a*b^2 - 12*(a^3 - a*b^2)*cosh(x)^2 - 12*(a^3 - a*b^2 - 3*(a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^2 + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)) + 24*((a^2*b + a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))/((a^4 + a^3*b)*cosh(x)^6 + 6*(a^4 + a^3*b)*cosh(x)*sinh(x)^5 + (a^4 + a^3*b)*sinh(x)^6 + 3*(a^4 + a^3*b)*cosh(x)^4 + 3*(a^4 + a^3*b + 5*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^4 + a^4 + a^3*b + 4*(5*(a^4 + a^3*b)*cosh(x)^3 + 3*(a^4 + a^3*b)*cosh(x))*sinh(x)^3 + 3*(a^4 + a^3*b)*cosh(x)^2 + 3*(5*(a^4 + a^3*b)*cosh(x)^4 + a^4 + a^3*b + 6*(a^4 + a^3*b)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + a^3*b)*cosh(x)^5 + 2*(a^4 + a^3*b)*cosh(x)^3 + (a^4 + a^3*b)*cosh(x))*sinh(x))]","B",0
32,1,3239,0,0.582700," ","integrate(sech(x)^5/(a+b*cosh(x)^2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{6} + {\left(3 \, a^{2} - 4 \, a b\right)} \sinh\left(x\right)^{7} + {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{5} + {\left(21 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} + 11 \, a^{2} - 4 \, a b\right)} \sinh\left(x\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} + {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} + {\left(35 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{4} + 10 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{3} + {\left(21 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 2 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a + b}} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)\right)} \sqrt{-\frac{b}{a + b}} + b}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + {\left({\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 12 \, a b + 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right) + {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{6} + 5 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{4} - 3 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)}{4 \, {\left(a^{3} \cosh\left(x\right)^{8} + 8 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{3} \sinh\left(x\right)^{8} + 4 \, a^{3} \cosh\left(x\right)^{6} + 6 \, a^{3} \cosh\left(x\right)^{4} + 4 \, {\left(7 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 4 \, a^{3} \cosh\left(x\right)^{2} + 2 \, {\left(35 \, a^{3} \cosh\left(x\right)^{4} + 30 \, a^{3} \cosh\left(x\right)^{2} + 3 \, a^{3}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{3} \cosh\left(x\right)^{5} + 10 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 4 \, {\left(7 \, a^{3} \cosh\left(x\right)^{6} + 15 \, a^{3} \cosh\left(x\right)^{4} + 9 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{3} \cosh\left(x\right)^{7} + 3 \, a^{3} \cosh\left(x\right)^{5} + 3 \, a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{6} + {\left(3 \, a^{2} - 4 \, a b\right)} \sinh\left(x\right)^{7} + {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{5} + {\left(21 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} + 11 \, a^{2} - 4 \, a b\right)} \sinh\left(x\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} + {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} - {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} + {\left(35 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{4} + 10 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} - 11 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)^{3} + {\left(21 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} - 4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a + b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a + b}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}\right) - 4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a + b}} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + b \sinh\left(x\right)^{3} + {\left(4 \, a + 3 \, b\right)} \cosh\left(x\right) + {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + 3 \, b\right)} \sinh\left(x\right)\right)} \sqrt{\frac{b}{a + b}}}{2 \, b}\right) + {\left({\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} - 12 \, a b + 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 4 \, a b + 8 \, 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(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right) + {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{6} + 5 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{4} - 3 \, {\left(11 \, a^{2} - 4 \, a b\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} + 4 \, a b\right)} \sinh\left(x\right)}{4 \, {\left(a^{3} \cosh\left(x\right)^{8} + 8 \, a^{3} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{3} \sinh\left(x\right)^{8} + 4 \, a^{3} \cosh\left(x\right)^{6} + 6 \, a^{3} \cosh\left(x\right)^{4} + 4 \, {\left(7 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 4 \, a^{3} \cosh\left(x\right)^{2} + 2 \, {\left(35 \, a^{3} \cosh\left(x\right)^{4} + 30 \, a^{3} \cosh\left(x\right)^{2} + 3 \, a^{3}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a^{3} \cosh\left(x\right)^{5} + 10 \, a^{3} \cosh\left(x\right)^{3} + 3 \, a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 4 \, {\left(7 \, a^{3} \cosh\left(x\right)^{6} + 15 \, a^{3} \cosh\left(x\right)^{4} + 9 \, a^{3} \cosh\left(x\right)^{2} + a^{3}\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a^{3} \cosh\left(x\right)^{7} + 3 \, a^{3} \cosh\left(x\right)^{5} + 3 \, a^{3} \cosh\left(x\right)^{3} + a^{3} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((3*a^2 - 4*a*b)*cosh(x)^7 + 7*(3*a^2 - 4*a*b)*cosh(x)*sinh(x)^6 + (3*a^2 - 4*a*b)*sinh(x)^7 + (11*a^2 - 4*a*b)*cosh(x)^5 + (21*(3*a^2 - 4*a*b)*cosh(x)^2 + 11*a^2 - 4*a*b)*sinh(x)^5 + 5*(7*(3*a^2 - 4*a*b)*cosh(x)^3 + (11*a^2 - 4*a*b)*cosh(x))*sinh(x)^4 - (11*a^2 - 4*a*b)*cosh(x)^3 + (35*(3*a^2 - 4*a*b)*cosh(x)^4 + 10*(11*a^2 - 4*a*b)*cosh(x)^2 - 11*a^2 + 4*a*b)*sinh(x)^3 + (21*(3*a^2 - 4*a*b)*cosh(x)^5 + 10*(11*a^2 - 4*a*b)*cosh(x)^3 - 3*(11*a^2 - 4*a*b)*cosh(x))*sinh(x)^2 + 2*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-b/(a + b))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*(2*a + 3*b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 - 2*a - 3*b)*sinh(x)^2 + 4*(b*cosh(x)^3 - (2*a + 3*b)*cosh(x))*sinh(x) - 4*((a + b)*cosh(x)^3 + 3*(a + b)*cosh(x)*sinh(x)^2 + (a + b)*sinh(x)^3 - (a + b)*cosh(x) + (3*(a + b)*cosh(x)^2 - a - b)*sinh(x))*sqrt(-b/(a + b)) + b)/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + ((3*a^2 - 4*a*b + 8*b^2)*cosh(x)^8 + 8*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 4*a*b + 8*b^2)*sinh(x)^8 + 4*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 3*a^2 - 4*a*b + 8*b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 30*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 9*a^2 - 12*a*b + 24*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^5 + 10*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^6 + 15*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 9*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 3*a^2 - 4*a*b + 8*b^2)*sinh(x)^2 + 3*a^2 - 4*a*b + 8*b^2 + 8*((3*a^2 - 4*a*b + 8*b^2)*cosh(x)^7 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^5 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + (3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (3*a^2 - 4*a*b)*cosh(x) + (7*(3*a^2 - 4*a*b)*cosh(x)^6 + 5*(11*a^2 - 4*a*b)*cosh(x)^4 - 3*(11*a^2 - 4*a*b)*cosh(x)^2 - 3*a^2 + 4*a*b)*sinh(x))/(a^3*cosh(x)^8 + 8*a^3*cosh(x)*sinh(x)^7 + a^3*sinh(x)^8 + 4*a^3*cosh(x)^6 + 6*a^3*cosh(x)^4 + 4*(7*a^3*cosh(x)^2 + a^3)*sinh(x)^6 + 8*(7*a^3*cosh(x)^3 + 3*a^3*cosh(x))*sinh(x)^5 + 4*a^3*cosh(x)^2 + 2*(35*a^3*cosh(x)^4 + 30*a^3*cosh(x)^2 + 3*a^3)*sinh(x)^4 + 8*(7*a^3*cosh(x)^5 + 10*a^3*cosh(x)^3 + 3*a^3*cosh(x))*sinh(x)^3 + a^3 + 4*(7*a^3*cosh(x)^6 + 15*a^3*cosh(x)^4 + 9*a^3*cosh(x)^2 + a^3)*sinh(x)^2 + 8*(a^3*cosh(x)^7 + 3*a^3*cosh(x)^5 + 3*a^3*cosh(x)^3 + a^3*cosh(x))*sinh(x)), 1/4*((3*a^2 - 4*a*b)*cosh(x)^7 + 7*(3*a^2 - 4*a*b)*cosh(x)*sinh(x)^6 + (3*a^2 - 4*a*b)*sinh(x)^7 + (11*a^2 - 4*a*b)*cosh(x)^5 + (21*(3*a^2 - 4*a*b)*cosh(x)^2 + 11*a^2 - 4*a*b)*sinh(x)^5 + 5*(7*(3*a^2 - 4*a*b)*cosh(x)^3 + (11*a^2 - 4*a*b)*cosh(x))*sinh(x)^4 - (11*a^2 - 4*a*b)*cosh(x)^3 + (35*(3*a^2 - 4*a*b)*cosh(x)^4 + 10*(11*a^2 - 4*a*b)*cosh(x)^2 - 11*a^2 + 4*a*b)*sinh(x)^3 + (21*(3*a^2 - 4*a*b)*cosh(x)^5 + 10*(11*a^2 - 4*a*b)*cosh(x)^3 - 3*(11*a^2 - 4*a*b)*cosh(x))*sinh(x)^2 - 4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(b/(a + b))*arctan(1/2*sqrt(b/(a + b))*(cosh(x) + sinh(x))) - 4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(b/(a + b))*arctan(1/2*(b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + b*sinh(x)^3 + (4*a + 3*b)*cosh(x) + (3*b*cosh(x)^2 + 4*a + 3*b)*sinh(x))*sqrt(b/(a + b))/b) + ((3*a^2 - 4*a*b + 8*b^2)*cosh(x)^8 + 8*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 - 4*a*b + 8*b^2)*sinh(x)^8 + 4*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^6 + 4*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 3*a^2 - 4*a*b + 8*b^2)*sinh(x)^6 + 8*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x)^5 + 6*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 2*(35*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 30*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 9*a^2 - 12*a*b + 24*b^2)*sinh(x)^4 + 8*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^5 + 10*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 4*(7*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^6 + 15*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^4 + 9*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^2 + 3*a^2 - 4*a*b + 8*b^2)*sinh(x)^2 + 3*a^2 - 4*a*b + 8*b^2 + 8*((3*a^2 - 4*a*b + 8*b^2)*cosh(x)^7 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^5 + 3*(3*a^2 - 4*a*b + 8*b^2)*cosh(x)^3 + (3*a^2 - 4*a*b + 8*b^2)*cosh(x))*sinh(x))*arctan(cosh(x) + sinh(x)) - (3*a^2 - 4*a*b)*cosh(x) + (7*(3*a^2 - 4*a*b)*cosh(x)^6 + 5*(11*a^2 - 4*a*b)*cosh(x)^4 - 3*(11*a^2 - 4*a*b)*cosh(x)^2 - 3*a^2 + 4*a*b)*sinh(x))/(a^3*cosh(x)^8 + 8*a^3*cosh(x)*sinh(x)^7 + a^3*sinh(x)^8 + 4*a^3*cosh(x)^6 + 6*a^3*cosh(x)^4 + 4*(7*a^3*cosh(x)^2 + a^3)*sinh(x)^6 + 8*(7*a^3*cosh(x)^3 + 3*a^3*cosh(x))*sinh(x)^5 + 4*a^3*cosh(x)^2 + 2*(35*a^3*cosh(x)^4 + 30*a^3*cosh(x)^2 + 3*a^3)*sinh(x)^4 + 8*(7*a^3*cosh(x)^5 + 10*a^3*cosh(x)^3 + 3*a^3*cosh(x))*sinh(x)^3 + a^3 + 4*(7*a^3*cosh(x)^6 + 15*a^3*cosh(x)^4 + 9*a^3*cosh(x)^2 + a^3)*sinh(x)^2 + 8*(a^3*cosh(x)^7 + 3*a^3*cosh(x)^5 + 3*a^3*cosh(x)^3 + a^3*cosh(x))*sinh(x))]","B",0
33,1,1239,0,0.465764," ","integrate(1/(a+b*cosh(x)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 8 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2} + {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(4 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right)}{4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2} + {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(4 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(4 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right)}{2 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{5} + 5 \, a^{4} b + 4 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(4*a^2*b + 4*a*b^2 + 4*(2*a^3 + 3*a^2*b + a*b^2)*cosh(x)^2 + 8*(2*a^3 + 3*a^2*b + a*b^2)*cosh(x)*sinh(x) + 4*(2*a^3 + 3*a^2*b + a*b^2)*sinh(x)^2 + ((2*a*b + b^2)*cosh(x)^4 + 4*(2*a*b + b^2)*cosh(x)*sinh(x)^3 + (2*a*b + b^2)*sinh(x)^4 + 2*(4*a^2 + 4*a*b + b^2)*cosh(x)^2 + 2*(3*(2*a*b + b^2)*cosh(x)^2 + 4*a^2 + 4*a*b + b^2)*sinh(x)^2 + 2*a*b + b^2 + 4*((2*a*b + b^2)*cosh(x)^3 + (4*a^2 + 4*a*b + b^2)*cosh(x))*sinh(x))*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)))/(a^4*b + 2*a^3*b^2 + a^2*b^3 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3)*cosh(x)^2 + 2*(2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3 + 3*(a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3)*cosh(x))*sinh(x)), 1/2*(2*a^2*b + 2*a*b^2 + 2*(2*a^3 + 3*a^2*b + a*b^2)*cosh(x)^2 + 4*(2*a^3 + 3*a^2*b + a*b^2)*cosh(x)*sinh(x) + 2*(2*a^3 + 3*a^2*b + a*b^2)*sinh(x)^2 + ((2*a*b + b^2)*cosh(x)^4 + 4*(2*a*b + b^2)*cosh(x)*sinh(x)^3 + (2*a*b + b^2)*sinh(x)^4 + 2*(4*a^2 + 4*a*b + b^2)*cosh(x)^2 + 2*(3*(2*a*b + b^2)*cosh(x)^2 + 4*a^2 + 4*a*b + b^2)*sinh(x)^2 + 2*a*b + b^2 + 4*((2*a*b + b^2)*cosh(x)^3 + (4*a^2 + 4*a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)))/(a^4*b + 2*a^3*b^2 + a^2*b^3 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^4*b + 2*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3)*cosh(x)^2 + 2*(2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3 + 3*(a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^4*b + 2*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (2*a^5 + 5*a^4*b + 4*a^3*b^2 + a^2*b^3)*cosh(x))*sinh(x))]","B",0
34,1,5117,0,0.601146," ","integrate(1/(a+b*cosh(x)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 24 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + 4 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(x\right)^{6} + 24 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 12 \, a b^{4} + 12 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 16 \, {\left(5 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + {\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{5} + {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a^{2} + a b} \log\left(\frac{b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + {\left(2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{a^{2} + a b}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + 8 \, {\left(3 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{16 \, {\left({\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{8} + a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + 35 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{6} + 12 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + 2 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(x\right)^{6} + 12 \, a^{3} b^{2} + 18 \, a^{2} b^{3} + 6 \, a b^{4} + 6 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(5 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 2 \, {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{4} + 18 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + {\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{5} + {\left(64 \, a^{4} + 128 \, a^{3} b + 112 \, a^{2} b^{2} + 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(16 \, a^{3} b + 24 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a^{2} - a b} \arctan\left(\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, a + b\right)} \sqrt{-a^{2} - a b}}{2 \, {\left(a^{2} + a b\right)}}\right) + 4 \, {\left(3 \, {\left(8 \, a^{4} b + 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{5} + 6 \, {\left(16 \, a^{5} + 40 \, a^{4} b + 38 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(x\right)^{3} + {\left(40 \, a^{4} b + 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{8 \, {\left({\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{8} + a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + 35 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 7 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + {\left(8 \, a^{8} + 32 \, a^{7} b + 51 \, a^{6} b^{2} + 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{7} b + 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/16*(4*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^6 + 24*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)*sinh(x)^5 + 4*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*sinh(x)^6 + 24*a^3*b^2 + 36*a^2*b^3 + 12*a*b^4 + 12*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 12*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4 + 5*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^4 + 16*(5*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + 3*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x)^3 + 4*(40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4)*cosh(x)^2 + 4*(40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4 + 15*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 18*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^2 + ((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^8 + 8*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)*sinh(x)^7 + (8*a^2*b^2 + 8*a*b^3 + 3*b^4)*sinh(x)^8 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^6 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4 + 7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^3 + 3*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^5 + 2*(64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^4 + 2*(35*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^4 + 64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4 + 30*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^4 + 8*a^2*b^2 + 8*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^5 + 10*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^3 + (64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x))*sinh(x)^3 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^2 + 4*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^6 + 15*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^4 + 16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4 + 3*(64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^7 + 3*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^5 + (64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^3 + (16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x))*sinh(x))*sqrt(a^2 + a*b)*log((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*(2*a*b + b^2)*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + 2*a*b + b^2)*sinh(x)^2 + 8*a^2 + 8*a*b + b^2 + 4*(b^2*cosh(x)^3 + (2*a*b + b^2)*cosh(x))*sinh(x) - 4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(a^2 + a*b))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(2*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + b)) + 8*(3*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^5 + 6*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + (40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4)*cosh(x))*sinh(x))/((a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^8 + 8*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^7 + (a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*sinh(x)^8 + a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^3 + 3*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x))*sinh(x)^5 + 2*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^4 + 2*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5 + 35*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 30*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^5 + 10*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 + (8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x))*sinh(x)^3 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^6 + 15*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 3*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^7 + 3*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 + (8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^3 + (2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x))*sinh(x)), 1/8*(2*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^6 + 12*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)*sinh(x)^5 + 2*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*sinh(x)^6 + 12*a^3*b^2 + 18*a^2*b^3 + 6*a*b^4 + 6*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 6*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4 + 5*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^4 + 8*(5*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + 3*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x))*sinh(x)^3 + 2*(40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4)*cosh(x)^2 + 2*(40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4 + 15*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^4 + 18*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^2)*sinh(x)^2 + ((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^8 + 8*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)*sinh(x)^7 + (8*a^2*b^2 + 8*a*b^3 + 3*b^4)*sinh(x)^8 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^6 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4 + 7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^3 + 3*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^5 + 2*(64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^4 + 2*(35*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^4 + 64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4 + 30*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^4 + 8*a^2*b^2 + 8*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^5 + 10*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^3 + (64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x))*sinh(x)^3 + 4*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^2 + 4*(7*(8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^6 + 15*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^4 + 16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4 + 3*(64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((8*a^2*b^2 + 8*a*b^3 + 3*b^4)*cosh(x)^7 + 3*(16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x)^5 + (64*a^4 + 128*a^3*b + 112*a^2*b^2 + 48*a*b^3 + 9*b^4)*cosh(x)^3 + (16*a^3*b + 24*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(x))*sinh(x))*sqrt(-a^2 - a*b)*arctan(1/2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*a + b)*sqrt(-a^2 - a*b)/(a^2 + a*b)) + 4*(3*(8*a^4*b + 16*a^3*b^2 + 11*a^2*b^3 + 3*a*b^4)*cosh(x)^5 + 6*(16*a^5 + 40*a^4*b + 38*a^3*b^2 + 17*a^2*b^3 + 3*a*b^4)*cosh(x)^3 + (40*a^4*b + 80*a^3*b^2 + 49*a^2*b^3 + 9*a*b^4)*cosh(x))*sinh(x))/((a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^8 + 8*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^7 + (a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*sinh(x)^8 + a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^3 + 3*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x))*sinh(x)^5 + 2*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^4 + 2*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5 + 35*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 30*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^5 + 10*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 + (8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x))*sinh(x)^3 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2 + 4*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 7*(a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^6 + 15*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 3*(8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 + a^3*b^5)*cosh(x)^7 + 3*(2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 + (8*a^8 + 32*a^7*b + 51*a^6*b^2 + 41*a^5*b^3 + 17*a^4*b^4 + 3*a^3*b^5)*cosh(x)^3 + (2*a^7*b + 7*a^6*b^2 + 9*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x))*sinh(x))]","B",0
35,1,66,0,0.400300," ","integrate(1/(1+cosh(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} - 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}\right)"," ",0,"1/4*sqrt(2)*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 + 2*sqrt(2) - 3)/(cosh(x)^2 + sinh(x)^2 + 3))","B",0
36,1,214,0,0.534457," ","integrate(1/(1+cosh(x)^2)^2,x, algorithm=""fricas"")","\frac{24 \, \cosh\left(x\right)^{2} + 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 6 \, {\left(\sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{2} + 6 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} - 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}\right) + 48 \, \cosh\left(x\right) \sinh\left(x\right) + 24 \, \sinh\left(x\right)^{2} + 8}{16 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 6 \, {\left(\cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 6 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"1/16*(24*cosh(x)^2 + 3*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 6*(sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^2 + 6*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 + 2*sqrt(2) - 3)/(cosh(x)^2 + sinh(x)^2 + 3)) + 48*cosh(x)*sinh(x) + 24*sinh(x)^2 + 8)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 6*(cosh(x)^2 + 1)*sinh(x)^2 + 6*cosh(x)^2 + 4*(cosh(x)^3 + 3*cosh(x))*sinh(x) + 1)","B",0
37,1,575,0,0.555839," ","integrate(1/(1+cosh(x)^2)^3,x, algorithm=""fricas"")","\frac{152 \, \cosh\left(x\right)^{6} + 912 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + 152 \, \sinh\left(x\right)^{6} + 456 \, {\left(5 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 1368 \, \cosh\left(x\right)^{4} + 608 \, {\left(5 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(285 \, \cosh\left(x\right)^{4} + 1026 \, \cosh\left(x\right)^{2} + 89\right)} \sinh\left(x\right)^{2} + 712 \, \cosh\left(x\right)^{2} + 19 \, {\left(\sqrt{2} \cosh\left(x\right)^{8} + 8 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + \sqrt{2} \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{2} + 3 \, \sqrt{2}\right)} \sinh\left(x\right)^{6} + 12 \, \sqrt{2} \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{3} + 9 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \sqrt{2} \cosh\left(x\right)^{4} + 90 \, \sqrt{2} \cosh\left(x\right)^{2} + 19 \, \sqrt{2}\right)} \sinh\left(x\right)^{4} + 38 \, \sqrt{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{5} + 30 \, \sqrt{2} \cosh\left(x\right)^{3} + 19 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{6} + 45 \, \sqrt{2} \cosh\left(x\right)^{4} + 57 \, \sqrt{2} \cosh\left(x\right)^{2} + 3 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 12 \, \sqrt{2} \cosh\left(x\right)^{2} + 8 \, {\left(\sqrt{2} \cosh\left(x\right)^{7} + 9 \, \sqrt{2} \cosh\left(x\right)^{5} + 19 \, \sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} - 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}\right) + 16 \, {\left(57 \, \cosh\left(x\right)^{5} + 342 \, \cosh\left(x\right)^{3} + 89 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 72}{128 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 12 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 90 \, \cosh\left(x\right)^{2} + 19\right)} \sinh\left(x\right)^{4} + 38 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 30 \, \cosh\left(x\right)^{3} + 19 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 57 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{2} + 12 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 19 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"1/128*(152*cosh(x)^6 + 912*cosh(x)*sinh(x)^5 + 152*sinh(x)^6 + 456*(5*cosh(x)^2 + 3)*sinh(x)^4 + 1368*cosh(x)^4 + 608*(5*cosh(x)^3 + 9*cosh(x))*sinh(x)^3 + 8*(285*cosh(x)^4 + 1026*cosh(x)^2 + 89)*sinh(x)^2 + 712*cosh(x)^2 + 19*(sqrt(2)*cosh(x)^8 + 8*sqrt(2)*cosh(x)*sinh(x)^7 + sqrt(2)*sinh(x)^8 + 4*(7*sqrt(2)*cosh(x)^2 + 3*sqrt(2))*sinh(x)^6 + 12*sqrt(2)*cosh(x)^6 + 8*(7*sqrt(2)*cosh(x)^3 + 9*sqrt(2)*cosh(x))*sinh(x)^5 + 2*(35*sqrt(2)*cosh(x)^4 + 90*sqrt(2)*cosh(x)^2 + 19*sqrt(2))*sinh(x)^4 + 38*sqrt(2)*cosh(x)^4 + 8*(7*sqrt(2)*cosh(x)^5 + 30*sqrt(2)*cosh(x)^3 + 19*sqrt(2)*cosh(x))*sinh(x)^3 + 4*(7*sqrt(2)*cosh(x)^6 + 45*sqrt(2)*cosh(x)^4 + 57*sqrt(2)*cosh(x)^2 + 3*sqrt(2))*sinh(x)^2 + 12*sqrt(2)*cosh(x)^2 + 8*(sqrt(2)*cosh(x)^7 + 9*sqrt(2)*cosh(x)^5 + 19*sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 + 2*sqrt(2) - 3)/(cosh(x)^2 + sinh(x)^2 + 3)) + 16*(57*cosh(x)^5 + 342*cosh(x)^3 + 89*cosh(x))*sinh(x) + 72)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 3)*sinh(x)^6 + 12*cosh(x)^6 + 8*(7*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 90*cosh(x)^2 + 19)*sinh(x)^4 + 38*cosh(x)^4 + 8*(7*cosh(x)^5 + 30*cosh(x)^3 + 19*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 45*cosh(x)^4 + 57*cosh(x)^2 + 3)*sinh(x)^2 + 12*cosh(x)^2 + 8*(cosh(x)^7 + 9*cosh(x)^5 + 19*cosh(x)^3 + 3*cosh(x))*sinh(x) + 1)","B",0
38,1,20,0,0.503036," ","integrate(1/(1-cosh(x)^2),x, algorithm=""fricas"")","\frac{2}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1}"," ",0,"2/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
39,1,84,0,0.424576," ","integrate(1/(1-cosh(x)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(\cosh\left(x\right) + 2 \, \sinh\left(x\right)\right)}}{3 \, {\left(\cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + {\left(10 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{3} - 3 \, \cosh\left(x\right)^{3} + {\left(10 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} + 4\right)} \sinh\left(x\right) + 2 \, \cosh\left(x\right)\right)}}"," ",0,"-8/3*(cosh(x) + 2*sinh(x))/(cosh(x)^5 + 5*cosh(x)*sinh(x)^4 + sinh(x)^5 + (10*cosh(x)^2 - 3)*sinh(x)^3 - 3*cosh(x)^3 + (10*cosh(x)^3 - 9*cosh(x))*sinh(x)^2 + (5*cosh(x)^4 - 9*cosh(x)^2 + 4)*sinh(x) + 2*cosh(x))","B",0
40,1,185,0,0.482383," ","integrate(1/(1-cosh(x)^2)^3,x, algorithm=""fricas"")","\frac{16 \, {\left(11 \, \cosh\left(x\right)^{2} + 18 \, \cosh\left(x\right) \sinh\left(x\right) + 11 \, \sinh\left(x\right)^{2} - 5\right)}}{15 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} - 5\right)} \sinh\left(x\right)^{6} - 5 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} - 15 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} - 15 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right)^{4} + 10 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} - 25 \, \cosh\left(x\right)^{3} + 10 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} - 75 \, \cosh\left(x\right)^{4} + 60 \, \cosh\left(x\right)^{2} - 11\right)} \sinh\left(x\right)^{2} - 11 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} - 15 \, \cosh\left(x\right)^{5} + 20 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 5\right)}}"," ",0,"16/15*(11*cosh(x)^2 + 18*cosh(x)*sinh(x) + 11*sinh(x)^2 - 5)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 - 5)*sinh(x)^6 - 5*cosh(x)^6 + 2*(28*cosh(x)^3 - 15*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 - 15*cosh(x)^2 + 2)*sinh(x)^4 + 10*cosh(x)^4 + 4*(14*cosh(x)^5 - 25*cosh(x)^3 + 10*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 - 75*cosh(x)^4 + 60*cosh(x)^2 - 11)*sinh(x)^2 - 11*cosh(x)^2 + 2*(4*cosh(x)^7 - 15*cosh(x)^5 + 20*cosh(x)^3 - 9*cosh(x))*sinh(x) + 5)","B",0
41,0,0,0,0.418750," ","integrate((a+b*cosh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cosh\left(x\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*cosh(x)^2 + a), x)","F",0
42,0,0,0,0.460897," ","integrate((1+cosh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\cosh\left(x\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(cosh(x)^2 + 1), x)","F",0
43,1,1,0,0.573204," ","integrate((1-cosh(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
44,1,2,0,0.391920," ","integrate((-1+cosh(x)^2)^(1/2),x, algorithm=""fricas"")","\cosh\left(x\right)"," ",0,"cosh(x)","A",0
45,0,0,0,0.683774," ","integrate((-1-cosh(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{\left(2 \, x\right)} - e^{x}\right)} {\rm integral}\left(\frac{4 \, \sqrt{-e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} - 1} {\left(e^{\left(2 \, x\right)} + 1\right)}}{e^{\left(6 \, x\right)} - 2 \, e^{\left(5 \, x\right)} + 7 \, e^{\left(4 \, x\right)} - 12 \, e^{\left(3 \, x\right)} + 7 \, e^{\left(2 \, x\right)} - 2 \, e^{x} + 1}, x\right) + \sqrt{-e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} - 1} {\left(e^{x} + 1\right)}}{2 \, {\left(e^{\left(2 \, x\right)} - e^{x}\right)}}"," ",0,"1/2*(2*(e^(2*x) - e^x)*integral(4*sqrt(-e^(4*x) - 6*e^(2*x) - 1)*(e^(2*x) + 1)/(e^(6*x) - 2*e^(5*x) + 7*e^(4*x) - 12*e^(3*x) + 7*e^(2*x) - 2*e^x + 1), x) + sqrt(-e^(4*x) - 6*e^(2*x) - 1)*(e^x + 1))/(e^(2*x) - e^x)","F",0
46,0,0,0,0.581255," ","integrate((a+b*cosh(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cosh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cosh(x)^2 + a)^(3/2), x)","F",0
47,0,0,0,0.475016," ","integrate((1+cosh(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\cosh\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((cosh(x)^2 + 1)^(3/2), x)","F",0
48,1,1,0,0.570868," ","integrate((1-cosh(x)^2)^(3/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
49,1,19,0,0.483174," ","integrate((-1+cosh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{12} \, \cosh\left(x\right)^{3} + \frac{1}{4} \, \cosh\left(x\right) \sinh\left(x\right)^{2} - \frac{3}{4} \, \cosh\left(x\right)"," ",0,"1/12*cosh(x)^3 + 1/4*cosh(x)*sinh(x)^2 - 3/4*cosh(x)","A",0
50,0,0,0,0.806204," ","integrate((-1-cosh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{24 \, {\left(e^{\left(4 \, x\right)} - e^{\left(3 \, x\right)}\right)} {\rm integral}\left(-\frac{4 \, \sqrt{-e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} - 1} {\left(5 \, e^{\left(2 \, x\right)} + 2 \, e^{x} + 5\right)}}{3 \, {\left(e^{\left(6 \, x\right)} - 2 \, e^{\left(5 \, x\right)} + 7 \, e^{\left(4 \, x\right)} - 12 \, e^{\left(3 \, x\right)} + 7 \, e^{\left(2 \, x\right)} - 2 \, e^{x} + 1\right)}}, x\right) - {\left(e^{\left(5 \, x\right)} - e^{\left(4 \, x\right)} + 24 \, e^{\left(3 \, x\right)} + 24 \, e^{\left(2 \, x\right)} - e^{x} + 1\right)} \sqrt{-e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} - 1}}{24 \, {\left(e^{\left(4 \, x\right)} - e^{\left(3 \, x\right)}\right)}}"," ",0,"1/24*(24*(e^(4*x) - e^(3*x))*integral(-4/3*sqrt(-e^(4*x) - 6*e^(2*x) - 1)*(5*e^(2*x) + 2*e^x + 5)/(e^(6*x) - 2*e^(5*x) + 7*e^(4*x) - 12*e^(3*x) + 7*e^(2*x) - 2*e^x + 1), x) - (e^(5*x) - e^(4*x) + 24*e^(3*x) + 24*e^(2*x) - e^x + 1)*sqrt(-e^(4*x) - 6*e^(2*x) - 1))/(e^(4*x) - e^(3*x))","F",0
51,0,0,0,0.503561," ","integrate(1/(a+b*cosh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cosh\left(x\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*cosh(x)^2 + a), x)","F",0
52,0,0,0,0.475419," ","integrate(1/(1+cosh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\cosh\left(x\right)^{2} + 1}}, x\right)"," ",0,"integral(1/sqrt(cosh(x)^2 + 1), x)","F",0
53,1,1,0,0.486354," ","integrate(1/(1-cosh(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
54,1,17,0,0.778184," ","integrate(1/(-1+cosh(x)^2)^(1/2),x, algorithm=""fricas"")","-\log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)"," ",0,"-log(cosh(x) + sinh(x) + 1) + log(cosh(x) + sinh(x) - 1)","A",0
55,0,0,0,0.653574," ","integrate(1/(-1-cosh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, \sqrt{-e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} - 1}}{e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} + 1}, x\right)"," ",0,"integral(-2*sqrt(-e^(4*x) - 6*e^(2*x) - 1)/(e^(4*x) + 6*e^(2*x) + 1), x)","F",0
56,-1,0,0,0.000000," ","integrate(1/(a+b*cosh(x)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(1/(a-b*cosh(x)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,1,602,0,0.537524," ","integrate(1/(1+cosh(x)^3),x, algorithm=""fricas"")","\frac{4 \, {\left(3^{\frac{3}{4}} e^{x} + 3^{\frac{3}{4}}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, {\left(\sqrt{3} {\left(\sqrt{3} + 3\right)} - 3 \, \sqrt{3} + 9\right)} e^{x} - \frac{1}{48} \, {\left(2 \, \sqrt{3} {\left(\sqrt{3} + 3\right)} - {\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 6 \, \sqrt{3} + 18\right)} \sqrt{2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} - 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} - 4 \, e^{x} + 4} + \frac{1}{12} \, \sqrt{3} {\left(\sqrt{3} - 3\right)} - \frac{1}{24} \, {\left({\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} e^{x} - 3^{\frac{3}{4}} {\left(\sqrt{3} + 1\right)} - 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} - 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{4} \, \sqrt{3} - \frac{1}{4}\right) + 4 \, {\left(3^{\frac{3}{4}} e^{x} + 3^{\frac{3}{4}}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{12} \, {\left(\sqrt{3} {\left(\sqrt{3} + 3\right)} - 3 \, \sqrt{3} + 9\right)} e^{x} + \frac{1}{48} \, {\left(2 \, \sqrt{3} {\left(\sqrt{3} + 3\right)} + {\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 6 \, \sqrt{3} + 18\right)} \sqrt{-2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} - 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} - 4 \, e^{x} + 4} - \frac{1}{12} \, \sqrt{3} {\left(\sqrt{3} - 3\right)} - \frac{1}{24} \, {\left({\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} e^{x} - 3^{\frac{3}{4}} {\left(\sqrt{3} + 1\right)} - 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} - 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{4} \, \sqrt{3} + \frac{1}{4}\right) - {\left(3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)} e^{x} + 3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} - 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} - 4 \, e^{x} + 4\right) + {\left(3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)} e^{x} + 3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} - 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} - 4 \, e^{x} + 4\right) - 24}{36 \, {\left(e^{x} + 1\right)}}"," ",0,"1/36*(4*(3^(3/4)*e^x + 3^(3/4))*sqrt(-4*sqrt(3) + 8)*arctan(1/12*(sqrt(3)*(sqrt(3) + 3) - 3*sqrt(3) + 9)*e^x - 1/48*(2*sqrt(3)*(sqrt(3) + 3) - (3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*sqrt(-4*sqrt(3) + 8) - 6*sqrt(3) + 18)*sqrt(2*(3^(1/4)*(sqrt(3) + 2) - 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) - 4*e^x + 4) + 1/12*sqrt(3)*(sqrt(3) - 3) - 1/24*((3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*e^x - 3^(3/4)*(sqrt(3) + 1) - 3*3^(1/4)*(sqrt(3) - 1))*sqrt(-4*sqrt(3) + 8) + 1/4*sqrt(3) - 1/4) + 4*(3^(3/4)*e^x + 3^(3/4))*sqrt(-4*sqrt(3) + 8)*arctan(-1/12*(sqrt(3)*(sqrt(3) + 3) - 3*sqrt(3) + 9)*e^x + 1/48*(2*sqrt(3)*(sqrt(3) + 3) + (3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*sqrt(-4*sqrt(3) + 8) - 6*sqrt(3) + 18)*sqrt(-2*(3^(1/4)*(sqrt(3) + 2) - 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) - 4*e^x + 4) - 1/12*sqrt(3)*(sqrt(3) - 3) - 1/24*((3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*e^x - 3^(3/4)*(sqrt(3) + 1) - 3*3^(1/4)*(sqrt(3) - 1))*sqrt(-4*sqrt(3) + 8) - 1/4*sqrt(3) + 1/4) - (3^(1/4)*(2*sqrt(3) + 3)*e^x + 3^(1/4)*(2*sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8)*log(2*(3^(1/4)*(sqrt(3) + 2) - 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) - 4*e^x + 4) + (3^(1/4)*(2*sqrt(3) + 3)*e^x + 3^(1/4)*(2*sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8)*log(-2*(3^(1/4)*(sqrt(3) + 2) - 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) - 4*e^x + 4) - 24)/(e^x + 1)","B",0
59,1,602,0,0.569400," ","integrate(1/(1-cosh(x)^3),x, algorithm=""fricas"")","-\frac{4 \, {\left(3^{\frac{3}{4}} e^{x} - 3^{\frac{3}{4}}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, {\left(\sqrt{3} {\left(\sqrt{3} + 3\right)} - 3 \, \sqrt{3} + 9\right)} e^{x} - \frac{1}{48} \, {\left(2 \, \sqrt{3} {\left(\sqrt{3} + 3\right)} - {\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 6 \, \sqrt{3} + 18\right)} \sqrt{2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} + 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 4 \, e^{x} + 4} - \frac{1}{12} \, \sqrt{3} {\left(\sqrt{3} - 3\right)} - \frac{1}{24} \, {\left({\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} e^{x} + 3^{\frac{3}{4}} {\left(\sqrt{3} + 1\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} - 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{4} \, \sqrt{3} + \frac{1}{4}\right) + 4 \, {\left(3^{\frac{3}{4}} e^{x} - 3^{\frac{3}{4}}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{12} \, {\left(\sqrt{3} {\left(\sqrt{3} + 3\right)} - 3 \, \sqrt{3} + 9\right)} e^{x} + \frac{1}{48} \, {\left(2 \, \sqrt{3} {\left(\sqrt{3} + 3\right)} + {\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 6 \, \sqrt{3} + 18\right)} \sqrt{-2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} + 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 4 \, e^{x} + 4} + \frac{1}{12} \, \sqrt{3} {\left(\sqrt{3} - 3\right)} - \frac{1}{24} \, {\left({\left(3^{\frac{3}{4}} {\left(3 \, \sqrt{3} + 5\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} + 1\right)}\right)} e^{x} + 3^{\frac{3}{4}} {\left(\sqrt{3} + 1\right)} + 3 \cdot 3^{\frac{1}{4}} {\left(\sqrt{3} - 1\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{4} \, \sqrt{3} - \frac{1}{4}\right) + {\left(3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)} e^{x} - 3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} + 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 4 \, e^{x} + 4\right) - {\left(3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)} e^{x} - 3^{\frac{1}{4}} {\left(2 \, \sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-2 \, {\left(3^{\frac{1}{4}} {\left(\sqrt{3} + 2\right)} + 3^{\frac{1}{4}} e^{x}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 4 \, e^{x} + 4\right) - 24}{36 \, {\left(e^{x} - 1\right)}}"," ",0,"-1/36*(4*(3^(3/4)*e^x - 3^(3/4))*sqrt(-4*sqrt(3) + 8)*arctan(1/12*(sqrt(3)*(sqrt(3) + 3) - 3*sqrt(3) + 9)*e^x - 1/48*(2*sqrt(3)*(sqrt(3) + 3) - (3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*sqrt(-4*sqrt(3) + 8) - 6*sqrt(3) + 18)*sqrt(2*(3^(1/4)*(sqrt(3) + 2) + 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) + 4*e^x + 4) - 1/12*sqrt(3)*(sqrt(3) - 3) - 1/24*((3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*e^x + 3^(3/4)*(sqrt(3) + 1) + 3*3^(1/4)*(sqrt(3) - 1))*sqrt(-4*sqrt(3) + 8) - 1/4*sqrt(3) + 1/4) + 4*(3^(3/4)*e^x - 3^(3/4))*sqrt(-4*sqrt(3) + 8)*arctan(-1/12*(sqrt(3)*(sqrt(3) + 3) - 3*sqrt(3) + 9)*e^x + 1/48*(2*sqrt(3)*(sqrt(3) + 3) + (3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*sqrt(-4*sqrt(3) + 8) - 6*sqrt(3) + 18)*sqrt(-2*(3^(1/4)*(sqrt(3) + 2) + 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) + 4*e^x + 4) + 1/12*sqrt(3)*(sqrt(3) - 3) - 1/24*((3^(3/4)*(3*sqrt(3) + 5) + 3*3^(1/4)*(sqrt(3) + 1))*e^x + 3^(3/4)*(sqrt(3) + 1) + 3*3^(1/4)*(sqrt(3) - 1))*sqrt(-4*sqrt(3) + 8) + 1/4*sqrt(3) - 1/4) + (3^(1/4)*(2*sqrt(3) + 3)*e^x - 3^(1/4)*(2*sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8)*log(2*(3^(1/4)*(sqrt(3) + 2) + 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) + 4*e^x + 4) - (3^(1/4)*(2*sqrt(3) + 3)*e^x - 3^(1/4)*(2*sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8)*log(-2*(3^(1/4)*(sqrt(3) + 2) + 3^(1/4)*e^x)*sqrt(-4*sqrt(3) + 8) + 4*sqrt(3) + 4*e^(2*x) + 4*e^x + 4) - 24)/(e^x - 1)","B",0
60,1,771,0,0.912935," ","integrate(1/(a+b*cosh(x)^4),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, {\left(a b + {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} + 2 \, {\left(a^{3} + a^{2} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + b\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - 2 \, {\left(a b + {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} + a b}} + 2 \, {\left(a^{3} + a^{2} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + b\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, {\left(a b - {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} - 2 \, {\left(a^{3} + a^{2} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + b\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - 2 \, {\left(a b - {\left(a^{4} + a^{3} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{-\frac{{\left(a^{2} + a b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} + a b}} - 2 \, {\left(a^{3} + a^{2} b\right)} \sqrt{-\frac{b}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}}} + b\right)"," ",0,"-1/4*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*(a*b + (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)))*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b)) + 2*(a^3 + a^2*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + b) + 1/4*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - 2*(a*b + (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)))*sqrt(((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + 1)/(a^2 + a*b)) + 2*(a^3 + a^2*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + b) - 1/4*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*(a*b - (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)))*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b)) - 2*(a^3 + a^2*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + b) + 1/4*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - 2*(a*b - (a^4 + a^3*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)))*sqrt(-((a^2 + a*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) - 1)/(a^2 + a*b)) - 2*(a^3 + a^2*b)*sqrt(-b/(a^5 + 2*a^4*b + a^3*b^2)) + b)","B",0
61,1,779,0,0.506140," ","integrate(1/(a-b*cosh(x)^4),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, {\left(a b - {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} - 2 \, {\left(a^{3} - a^{2} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + b\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - 2 \, {\left(a b - {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + 1}{a^{2} - a b}} - 2 \, {\left(a^{3} - a^{2} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + b\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + 2 \, {\left(a b + {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} + 2 \, {\left(a^{3} - a^{2} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + b\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} \log\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - 2 \, {\left(a b + {\left(a^{4} - a^{3} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}}\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} - 1}{a^{2} - a b}} + 2 \, {\left(a^{3} - a^{2} b\right)} \sqrt{\frac{b}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}}} + b\right)"," ",0,"-1/4*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*(a*b - (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)))*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b)) - 2*(a^3 - a^2*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + b) + 1/4*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - 2*(a*b - (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)))*sqrt(((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + 1)/(a^2 - a*b)) - 2*(a^3 - a^2*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + b) - 1/4*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + 2*(a*b + (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)))*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b)) + 2*(a^3 - a^2*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + b) + 1/4*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b))*log(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - 2*(a*b + (a^4 - a^3*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)))*sqrt(-((a^2 - a*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) - 1)/(a^2 - a*b)) + 2*(a^3 - a^2*b)*sqrt(b/(a^5 - 2*a^4*b + a^3*b^2)) + b)","B",0
62,1,590,0,0.477025," ","integrate(1/(1+cosh(x)^4),x, algorithm=""fricas"")","-\frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left({\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5\right) + \frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} - \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5} + \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} + 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{7} \, \sqrt{2} - \frac{3}{7}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} + \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5} - \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} + 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{7} \, \sqrt{2} + \frac{3}{7}\right)"," ",0,"-1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log((2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + 1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log(-(2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) - 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) - (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt((2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) + 2^(3/4)*(2*sqrt(2) + 1) + 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) + 1/7*sqrt(2) - 3/7) + 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(-1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) + 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) + (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt(-(2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) - 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) + 2^(3/4)*(2*sqrt(2) + 1) + 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) - 1/7*sqrt(2) + 3/7)","B",0
63,1,115,0,0.629246," ","integrate(1/(1-cosh(x)^4),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} - 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}\right) + 8}{8 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}"," ",0,"1/8*((sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 + 2*sqrt(2) - 3)/(cosh(x)^2 + sinh(x)^2 + 3)) + 8)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)","B",0
64,-2,0,0,0.000000," ","integrate(1/(a+b*cosh(x)^5),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
65,-1,0,0,0.000000," ","integrate(1/(a+b*cosh(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(1/(a+b*cosh(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-2,0,0,0.000000," ","integrate(1/(a-b*cosh(x)^5),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
68,-1,0,0,0.000000," ","integrate(1/(a-b*cosh(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(1/(a-b*cosh(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,1,3228,0,1.045201," ","integrate(1/(1+cosh(x)^5),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{10} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} - 1\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} \arctan\left(\frac{1}{40} \, \sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + \frac{1}{400} \, \sqrt{10} {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 5} - \frac{1}{64000} \, {\left(80 \, \sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 8 \, \sqrt{10} {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} \sqrt{\sqrt{5} + 5} - \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(3 \, \sqrt{5} - 7\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + 1600 \, \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} - 200 \, {\left(\sqrt{5} + 1\right)} e^{x} - 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} + 5 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{16000} \, \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} {\left(5 \, {\left(\sqrt{5} - 3\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} - 2\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 2 \, e^{x} + 1\right)}\right) + 8 \, \sqrt{10} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} - 1\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} \arctan\left(-\frac{1}{40} \, \sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} - \frac{1}{400} \, \sqrt{10} {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 5} + \frac{1}{64000} \, {\left(80 \, \sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 8 \, \sqrt{10} {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} \sqrt{\sqrt{5} + 5} + \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(3 \, \sqrt{5} - 7\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + 1600 \, \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} - 200 \, {\left(\sqrt{5} + 1\right)} e^{x} + 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} + 5 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{16000} \, \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} {\left(5 \, {\left(\sqrt{5} - 3\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} - 2\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 2 \, e^{x} + 1\right)}\right) + 4 \, {\left({\left(\sqrt{5} + 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{32000} \, {\left({\left(20 \, {\left(3 \, \sqrt{5} + 7\right)} e^{x} + {\left(5 \, {\left(\sqrt{5} + 3\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 40\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{128000} \, {\left({\left({\left({\left(\sqrt{5} + 3\right)} \sqrt{-40 \, \sqrt{5} + 200} + 12 \, \sqrt{5} + 28\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} - 4 \, {\left({\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 800\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{200 \, {\left(\sqrt{5} - 1\right)} e^{x} + {\left({\left(\sqrt{5} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 10 \, \sqrt{5} + 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400} + \frac{1}{1600} \, {\left(20 \, {\left({\left(\sqrt{5} + 5\right)} e^{x} + \sqrt{5} - 1\right)} \sqrt{-40 \, \sqrt{5} + 200} + {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} - 400 \, \sqrt{5} - 800 \, e^{x} + 400\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + 4 \, {\left({\left(\sqrt{5} + 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{32000} \, {\left({\left(20 \, {\left(3 \, \sqrt{5} + 7\right)} e^{x} + {\left(5 \, {\left(\sqrt{5} + 3\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 40\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{128000} \, {\left({\left({\left({\left(\sqrt{5} + 3\right)} \sqrt{-40 \, \sqrt{5} + 200} + 12 \, \sqrt{5} + 28\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + 4 \, {\left({\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 800\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{200 \, {\left(\sqrt{5} - 1\right)} e^{x} - {\left({\left(\sqrt{5} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 10 \, \sqrt{5} + 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{1600} \, {\left(20 \, {\left({\left(\sqrt{5} + 5\right)} e^{x} + \sqrt{5} - 1\right)} \sqrt{-40 \, \sqrt{5} + 200} + {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} + 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} - 400 \, \sqrt{5} - 800 \, e^{x} + 400\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + 2 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 40 \, e^{x} - 40\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} - 200 \, {\left(\sqrt{5} + 1\right)} e^{x} + 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} + 5 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400\right) - 2 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 40 \, e^{x} - 40\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} - 200 \, {\left(\sqrt{5} + 1\right)} e^{x} - 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} + \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} + 5 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400\right) + {\left({\left({\left(\sqrt{5} + 5\right)} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 80 \, e^{x} + 80\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(200 \, {\left(\sqrt{5} - 1\right)} e^{x} + {\left({\left(\sqrt{5} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 10 \, \sqrt{5} + 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400\right) - {\left({\left({\left(\sqrt{5} + 5\right)} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 80 \, e^{x} + 80\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(200 \, {\left(\sqrt{5} - 1\right)} e^{x} - {\left({\left(\sqrt{5} e^{x} + \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 10 \, \sqrt{5} + 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400\right) + 3200}{8000 \, {\left(e^{x} + 1\right)}}"," ",0,"-1/8000*(8*sqrt(10)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(5) - 1)*e^x + sqrt(5) - 1)*(40*sqrt(5) + 200)^(1/4)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*arctan(1/40*sqrt(10)*((sqrt(5) - 5)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 1/400*sqrt(10)*(sqrt(10)*((sqrt(5) - 5)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 5) - 1/64000*(80*sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 8*sqrt(10)*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*sqrt(sqrt(5) + 5) - sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 3) + 2*(3*sqrt(5) - 7)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 4*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*(40*sqrt(5) + 200)^(1/4)) + 1600*sqrt(2*sqrt(5) + 5))*sqrt(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) - 200*(sqrt(5) + 1)*e^x - 2*(sqrt(10)*(sqrt(5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) + 5*sqrt(5) - 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 1/16000*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*(5*(sqrt(5) - 3)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((3*sqrt(5) - 7)*e^x - 2)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 20*(sqrt(10)*((sqrt(5) - 5)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(1/4)) - 1/4*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 2*e^x + 1)) + 8*sqrt(10)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(5) - 1)*e^x + sqrt(5) - 1)*(40*sqrt(5) + 200)^(1/4)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*arctan(-1/40*sqrt(10)*((sqrt(5) - 5)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 1/400*sqrt(10)*(sqrt(10)*((sqrt(5) - 5)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 5) + 1/64000*(80*sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 8*sqrt(10)*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*sqrt(sqrt(5) + 5) + sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 3) + 2*(3*sqrt(5) - 7)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 4*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*(40*sqrt(5) + 200)^(1/4)) + 1600*sqrt(2*sqrt(5) + 5))*sqrt(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) - 200*(sqrt(5) + 1)*e^x + 2*(sqrt(10)*(sqrt(5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) + 5*sqrt(5) - 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 1/16000*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*(5*(sqrt(5) - 3)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((3*sqrt(5) - 7)*e^x - 2)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 20*(sqrt(10)*((sqrt(5) - 5)*e^x + 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(1/4)) + 1/4*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 2*e^x + 1)) + 4*((sqrt(5) + 1)*e^x + sqrt(5) + 1)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5)*(-40*sqrt(5) + 200)^(3/4)*arctan(-1/32000*((20*(3*sqrt(5) + 7)*e^x + (5*(sqrt(5) + 3)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 40)*(-40*sqrt(5) + 200)^(3/4) + 20*(20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 1/128000*((((sqrt(5) + 3)*sqrt(-40*sqrt(5) + 200) + 12*sqrt(5) + 28)*(-40*sqrt(5) + 200)^(3/4) + 4*((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) - 4*(((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) + 20*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) - 800)*sqrt(-2*sqrt(5) + 5))*sqrt(200*(sqrt(5) - 1)*e^x + ((sqrt(5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 10*sqrt(5) + 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) + 1/1600*(20*((sqrt(5) + 5)*e^x + sqrt(5) - 1)*sqrt(-40*sqrt(5) + 200) + (20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) - 400*sqrt(5) - 800*e^x + 400)*sqrt(-2*sqrt(5) + 5)) + 4*((sqrt(5) + 1)*e^x + sqrt(5) + 1)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5)*(-40*sqrt(5) + 200)^(3/4)*arctan(-1/32000*((20*(3*sqrt(5) + 7)*e^x + (5*(sqrt(5) + 3)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 40)*(-40*sqrt(5) + 200)^(3/4) + 20*(20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 1/128000*((((sqrt(5) + 3)*sqrt(-40*sqrt(5) + 200) + 12*sqrt(5) + 28)*(-40*sqrt(5) + 200)^(3/4) + 4*((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 4*(((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) + 20*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) - 800)*sqrt(-2*sqrt(5) + 5))*sqrt(200*(sqrt(5) - 1)*e^x - ((sqrt(5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 10*sqrt(5) + 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) - 1/1600*(20*((sqrt(5) + 5)*e^x + sqrt(5) - 1)*sqrt(-40*sqrt(5) + 200) + (20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x + 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) - 400*sqrt(5) - 800*e^x + 400)*sqrt(-2*sqrt(5) + 5)) + 2*(sqrt(10)*((sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 40*e^x - 40)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4)*log(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) - 200*(sqrt(5) + 1)*e^x + 2*(sqrt(10)*(sqrt(5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) + 5*sqrt(5) - 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 2*(sqrt(10)*((sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 40*e^x - 40)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4)*log(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) - 200*(sqrt(5) + 1)*e^x - 2*(sqrt(10)*(sqrt(5)*e^x + sqrt(5) - 5)*sqrt(sqrt(5) + 5) + 5*sqrt(5) - 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) + (((sqrt(5) + 5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 80*e^x + 80)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4)*log(200*(sqrt(5) - 1)*e^x + ((sqrt(5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 10*sqrt(5) + 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) - (((sqrt(5) + 5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 80*e^x + 80)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4)*log(200*(sqrt(5) - 1)*e^x - ((sqrt(5)*e^x + sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 10*sqrt(5) + 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) + 3200)/(e^x + 1)","B",0
71,1,158,0,1.592787," ","integrate(1/(1+cosh(x)^6),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \log\left(16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28\right) + \frac{1}{12} \, \sqrt{3} \log\left(-16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\frac{2 \, {\left(2 \, \sqrt{2} - 3\right)} e^{\left(2 \, x\right)} + 12 \, \sqrt{2} - e^{\left(4 \, x\right)} - 17}{e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} + 1}\right) + \frac{1}{3} \, \arctan\left(-{\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(\sqrt{3} + 2\right)} \sqrt{-16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28}\right) - \frac{1}{3} \, \arctan\left(-{\left(\sqrt{3} - 2\right)} e^{\left(2 \, x\right)} + \sqrt{4 \, \sqrt{3} + e^{\left(4 \, x\right)} + 7} {\left(\sqrt{3} - 2\right)}\right)"," ",0,"-1/12*sqrt(3)*log(16*sqrt(3) + 4*e^(4*x) + 28) + 1/12*sqrt(3)*log(-16*sqrt(3) + 4*e^(4*x) + 28) + 1/12*sqrt(2)*log(-(2*(2*sqrt(2) - 3)*e^(2*x) + 12*sqrt(2) - e^(4*x) - 17)/(e^(4*x) + 6*e^(2*x) + 1)) + 1/3*arctan(-(sqrt(3) + 2)*e^(2*x) + 1/2*(sqrt(3) + 2)*sqrt(-16*sqrt(3) + 4*e^(4*x) + 28)) - 1/3*arctan(-(sqrt(3) - 2)*e^(2*x) + sqrt(4*sqrt(3) + e^(4*x) + 7)*(sqrt(3) - 2))","B",0
72,1,3773,0,1.280643," ","integrate(1/(1+cosh(x)^8),x, algorithm=""fricas"")","-\frac{1}{16} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 3} {\left(\sqrt{2} - 1\right)} \arctan\left(\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} - 20\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} - 13\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left({\left({\left(355 \, \sqrt{2} - 508\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} - 86\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} - 119\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} - 126\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} - 105\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} - 72\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{-4 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 4 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} + \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} - 355\right)} e^{\left(2 \, x\right)} + 102 \, \sqrt{2} - 145\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} - 59\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} - 164\right)} e^{\left(2 \, x\right)} + 39 \, \sqrt{2} - 60\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} - 85\right)} e^{\left(2 \, x\right)} + 17 \, \sqrt{2} - 19\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} - 152\right)} e^{\left(2 \, x\right)} - 13 \, \sqrt{2} + 20\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} - 53\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} - 46\right)} e^{\left(2 \, x\right)} + 3 \, \sqrt{2} - 7\right)} \sqrt{2 \, \sqrt{2} + 3}\right) - \frac{1}{16} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 3} {\left(\sqrt{2} - 1\right)} \arctan\left(-\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} - 20\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} - \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} - 13\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} - {\left({\left({\left(355 \, \sqrt{2} - 508\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} - 86\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} - 119\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} - 126\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} - 105\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} - 72\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{-4 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} - {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 4 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} + \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} - 355\right)} e^{\left(2 \, x\right)} + 102 \, \sqrt{2} - 145\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} - 59\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} - 164\right)} e^{\left(2 \, x\right)} + 39 \, \sqrt{2} - 60\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} - 85\right)} e^{\left(2 \, x\right)} + 17 \, \sqrt{2} - 19\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} - \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} - 152\right)} e^{\left(2 \, x\right)} - 13 \, \sqrt{2} + 20\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} - 53\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} - 46\right)} e^{\left(2 \, x\right)} + 3 \, \sqrt{2} - 7\right)} \sqrt{2 \, \sqrt{2} + 3}\right) + \frac{1}{16} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(\sqrt{2} + 1\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 3} \arctan\left(\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} + 20\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} - \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} + 13\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} - {\left({\left({\left(355 \, \sqrt{2} + 508\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} + 86\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} + 119\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} + 126\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} + 105\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} + 72\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{4 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} + 6\right)} \sqrt{-2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} + 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 4 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} - \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} + 355\right)} e^{\left(2 \, x\right)} + 102 \, \sqrt{2} + 145\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} + 59\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} + 164\right)} e^{\left(2 \, x\right)} + 39 \, \sqrt{2} + 60\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} + 85\right)} e^{\left(2 \, x\right)} + 17 \, \sqrt{2} + 19\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} + 152\right)} e^{\left(2 \, x\right)} - 13 \, \sqrt{2} - 20\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} + 53\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} + 46\right)} e^{\left(2 \, x\right)} + 3 \, \sqrt{2} + 7\right)} \sqrt{-2 \, \sqrt{2} + 3}\right) + \frac{1}{16} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(\sqrt{2} + 1\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 3} \arctan\left(-\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} + 20\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} + 13\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left({\left({\left(355 \, \sqrt{2} + 508\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} + 86\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} + 119\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} + 126\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} + 105\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} + 72\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{4 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} + 6\right)} \sqrt{-2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} + 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 4 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} - \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} + 355\right)} e^{\left(2 \, x\right)} + 102 \, \sqrt{2} + 145\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} + 59\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} + 164\right)} e^{\left(2 \, x\right)} + 39 \, \sqrt{2} + 60\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} + 85\right)} e^{\left(2 \, x\right)} + 17 \, \sqrt{2} + 19\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} - \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} + 152\right)} e^{\left(2 \, x\right)} - 13 \, \sqrt{2} - 20\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} + 53\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} + 46\right)} e^{\left(2 \, x\right)} + 3 \, \sqrt{2} + 7\right)} \sqrt{-2 \, \sqrt{2} + 3}\right) - \frac{1}{64} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left({\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} + 6\right)} \sqrt{-2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} + 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) + \frac{1}{64} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left({\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} + 6\right)} \sqrt{-2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} + 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) - \frac{1}{64} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(\sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} + 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(-2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) + \frac{1}{64} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(\sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} + 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(-2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} - \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} + 5 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2} + 4} + 6 \, \sqrt{2} - 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right)"," ",0,"-1/16*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(3/4)*sqrt(2*sqrt(2) + 3)*(sqrt(2) - 1)*arctan(1/31*(2*(13*sqrt(2) - 20)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 1/496*(32*(10*sqrt(2) - 13)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (((355*sqrt(2) - 508)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 6*(59*sqrt(2) - 86)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) - 119)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (85*sqrt(2) - 126)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 4*((76*sqrt(2) - 105)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(53*sqrt(2) - 72)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 16*(23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(-4*(sqrt(2) - 1)*e^(2*x) + (2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) + 5*sqrt(2) - 6)*sqrt(2*sqrt(2) + 4) + 6*sqrt(2) - 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 4*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 4*sqrt(2) + 2*e^(4*x) + 10) + 1/248*((((254*sqrt(2) - 355)*e^(2*x) + 102*sqrt(2) - 145)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) - 59)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) - 164)*e^(2*x) + 39*sqrt(2) - 60)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*((63*sqrt(2) - 85)*e^(2*x) + 17*sqrt(2) - 19)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 1/124*(((105*sqrt(2) - 152)*e^(2*x) - 13*sqrt(2) + 20)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 4*((36*sqrt(2) - 53)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 1/31*((33*sqrt(2) - 46)*e^(2*x) + 3*sqrt(2) - 7)*sqrt(2*sqrt(2) + 3)) - 1/16*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(3/4)*sqrt(2*sqrt(2) + 3)*(sqrt(2) - 1)*arctan(-1/31*(2*(13*sqrt(2) - 20)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) - 1/496*(32*(10*sqrt(2) - 13)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) - (((355*sqrt(2) - 508)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 6*(59*sqrt(2) - 86)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) - 119)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (85*sqrt(2) - 126)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 4*((76*sqrt(2) - 105)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(53*sqrt(2) - 72)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 16*(23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(-4*(sqrt(2) - 1)*e^(2*x) - (2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) + 5*sqrt(2) - 6)*sqrt(2*sqrt(2) + 4) + 6*sqrt(2) - 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 4*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 4*sqrt(2) + 2*e^(4*x) + 10) + 1/248*((((254*sqrt(2) - 355)*e^(2*x) + 102*sqrt(2) - 145)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) - 59)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) - 164)*e^(2*x) + 39*sqrt(2) - 60)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*((63*sqrt(2) - 85)*e^(2*x) + 17*sqrt(2) - 19)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) - 1/124*(((105*sqrt(2) - 152)*e^(2*x) - 13*sqrt(2) + 20)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 4*((36*sqrt(2) - 53)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) - 1/31*((33*sqrt(2) - 46)*e^(2*x) + 3*sqrt(2) - 7)*sqrt(2*sqrt(2) + 3)) + 1/16*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(sqrt(2) + 1)*(-2*sqrt(2) + 4)^(3/4)*sqrt(-2*sqrt(2) + 3)*arctan(1/31*(2*(13*sqrt(2) + 20)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) - 1/496*(32*(10*sqrt(2) + 13)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) - (((355*sqrt(2) + 508)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 6*(59*sqrt(2) + 86)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) + 119)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (85*sqrt(2) + 126)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 4*((76*sqrt(2) + 105)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(53*sqrt(2) + 72)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 16*(23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(4*(sqrt(2) + 1)*e^(2*x) + (2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) + 5*sqrt(2) + 6)*sqrt(-2*sqrt(2) + 4) + 6*sqrt(2) + 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 4*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 2*e^(4*x) + 10) - 1/248*((((254*sqrt(2) + 355)*e^(2*x) + 102*sqrt(2) + 145)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) + 59)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) + 164)*e^(2*x) + 39*sqrt(2) + 60)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*((63*sqrt(2) + 85)*e^(2*x) + 17*sqrt(2) + 19)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 1/124*(((105*sqrt(2) + 152)*e^(2*x) - 13*sqrt(2) - 20)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 4*((36*sqrt(2) + 53)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 1/31*((33*sqrt(2) + 46)*e^(2*x) + 3*sqrt(2) + 7)*sqrt(-2*sqrt(2) + 3)) + 1/16*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(sqrt(2) + 1)*(-2*sqrt(2) + 4)^(3/4)*sqrt(-2*sqrt(2) + 3)*arctan(-1/31*(2*(13*sqrt(2) + 20)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 1/496*(32*(10*sqrt(2) + 13)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (((355*sqrt(2) + 508)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 6*(59*sqrt(2) + 86)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) + 119)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (85*sqrt(2) + 126)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 4*((76*sqrt(2) + 105)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(53*sqrt(2) + 72)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 16*(23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(4*(sqrt(2) + 1)*e^(2*x) - (2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) + 5*sqrt(2) + 6)*sqrt(-2*sqrt(2) + 4) + 6*sqrt(2) + 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 4*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 2*e^(4*x) + 10) - 1/248*((((254*sqrt(2) + 355)*e^(2*x) + 102*sqrt(2) + 145)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) + 59)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) + 164)*e^(2*x) + 39*sqrt(2) + 60)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*((63*sqrt(2) + 85)*e^(2*x) + 17*sqrt(2) + 19)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) - 1/124*(((105*sqrt(2) + 152)*e^(2*x) - 13*sqrt(2) - 20)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 4*((36*sqrt(2) + 53)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) - 1/31*((33*sqrt(2) + 46)*e^(2*x) + 3*sqrt(2) + 7)*sqrt(-2*sqrt(2) + 3)) - 1/64*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*((sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2))*(-2*sqrt(2) + 4)^(1/4)*log(2*(sqrt(2) + 1)*e^(2*x) + 1/2*(2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) + 5*sqrt(2) + 6)*sqrt(-2*sqrt(2) + 4) + 6*sqrt(2) + 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 2*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2) + e^(4*x) + 5) + 1/64*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*((sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2))*(-2*sqrt(2) + 4)^(1/4)*log(2*(sqrt(2) + 1)*e^(2*x) - 1/2*(2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) + 5*sqrt(2) + 6)*sqrt(-2*sqrt(2) + 4) + 6*sqrt(2) + 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 2*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2) + e^(4*x) + 5) - 1/64*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1) + 2*sqrt(2))*(2*sqrt(2) + 4)^(1/4)*log(-2*(sqrt(2) - 1)*e^(2*x) + 1/2*(2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) + 5*sqrt(2) - 6)*sqrt(2*sqrt(2) + 4) + 6*sqrt(2) - 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 2*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 2*sqrt(2) + e^(4*x) + 5) + 1/64*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1) + 2*sqrt(2))*(2*sqrt(2) + 4)^(1/4)*log(-2*(sqrt(2) - 1)*e^(2*x) - 1/2*(2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) + 5*sqrt(2) - 6)*sqrt(2*sqrt(2) + 4) + 6*sqrt(2) - 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 2*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 2*sqrt(2) + e^(4*x) + 5)","B",0
73,1,3260,0,2.122738," ","integrate(1/(1-cosh(x)^5),x, algorithm=""fricas"")","\frac{8 \, \sqrt{10} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} + 1\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} \arctan\left(\frac{1}{40} \, \sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + \frac{1}{400} \, \sqrt{10} {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 5} - \frac{1}{64000} \, {\left(80 \, \sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 8 \, \sqrt{10} {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} \sqrt{\sqrt{5} + 5} - \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(3 \, \sqrt{5} - 7\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + 1600 \, \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 200 \, {\left(\sqrt{5} + 1\right)} e^{x} + 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 5 \, \sqrt{5} + 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{16000} \, \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} {\left(5 \, {\left(\sqrt{5} - 3\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} + 2\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} + 2 \, e^{x} + 1\right)}\right) + 8 \, \sqrt{10} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{5} - 1\right)} e^{x} - \sqrt{5} + 1\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} \arctan\left(-\frac{1}{40} \, \sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} - \frac{1}{400} \, \sqrt{10} {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 5} + \frac{1}{64000} \, {\left(80 \, \sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 8 \, \sqrt{10} {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} \sqrt{\sqrt{5} + 5} + \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(3 \, \sqrt{5} - 7\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{10} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 10 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 1\right)}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} + 1600 \, \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 200 \, {\left(\sqrt{5} + 1\right)} e^{x} - 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 5 \, \sqrt{5} + 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{16000} \, \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left({\left(\sqrt{10} {\left(5 \, {\left(\sqrt{5} - 3\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} + 2\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 5} + 10 \, {\left({\left(\sqrt{5} - 1\right)} e^{x} + \sqrt{5} + 1\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} + 2 \, e^{x} + 1\right)}\right) + 4 \, {\left({\left(\sqrt{5} + 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{32000} \, {\left({\left(20 \, {\left(3 \, \sqrt{5} + 7\right)} e^{x} + {\left(5 \, {\left(\sqrt{5} + 3\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 40\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} - 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{128000} \, {\left({\left({\left({\left(\sqrt{5} + 3\right)} \sqrt{-40 \, \sqrt{5} + 200} + 12 \, \sqrt{5} + 28\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + 4 \, {\left({\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 800\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{-200 \, {\left(\sqrt{5} - 1\right)} e^{x} + {\left({\left(\sqrt{5} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 10 \, \sqrt{5} - 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400} - \frac{1}{1600} \, {\left(20 \, {\left({\left(\sqrt{5} + 5\right)} e^{x} - \sqrt{5} + 1\right)} \sqrt{-40 \, \sqrt{5} + 200} + {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} - 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, \sqrt{5} - 800 \, e^{x} - 400\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + 4 \, {\left({\left(\sqrt{5} + 1\right)} e^{x} - \sqrt{5} - 1\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{32000} \, {\left({\left(20 \, {\left(3 \, \sqrt{5} + 7\right)} e^{x} + {\left(5 \, {\left(\sqrt{5} + 3\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} - 40\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 20 \, {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} - 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{128000} \, {\left({\left({\left({\left(\sqrt{5} + 3\right)} \sqrt{-40 \, \sqrt{5} + 200} + 12 \, \sqrt{5} + 28\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{3}{4}} + 4 \, {\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} \sqrt{-2 \, \sqrt{5} + 5} - 4 \, {\left({\left({\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 800\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{-200 \, {\left(\sqrt{5} - 1\right)} e^{x} - {\left({\left(\sqrt{5} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 10 \, \sqrt{5} - 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400} + \frac{1}{1600} \, {\left(20 \, {\left({\left(\sqrt{5} + 5\right)} e^{x} - \sqrt{5} + 1\right)} \sqrt{-40 \, \sqrt{5} + 200} + {\left(20 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left({\left(\sqrt{5} + 5\right)} e^{x} - 2 \, \sqrt{5}\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} - 20\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, \sqrt{5} - 800 \, e^{x} - 400\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + 2 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 40 \, e^{x} + 40\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 200 \, {\left(\sqrt{5} + 1\right)} e^{x} + 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 5 \, \sqrt{5} + 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400\right) - 2 \, {\left(\sqrt{10} {\left({\left(\sqrt{5} - 5\right)} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 40 \, e^{x} + 40\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-20 \, \sqrt{10} \sqrt{\sqrt{5} + 5} {\left(\sqrt{5} - 5\right)} + 200 \, {\left(\sqrt{5} + 1\right)} e^{x} - 2 \, {\left(\sqrt{10} {\left(\sqrt{5} e^{x} - \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 5} - 5 \, \sqrt{5} + 25\right)} \sqrt{2 \, \sqrt{10} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 5} - 20 \, \sqrt{5} + 60} {\left(40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 400 \, e^{\left(2 \, x\right)} + 400\right) + {\left({\left({\left(\sqrt{5} + 5\right)} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 80 \, e^{x} - 80\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-200 \, {\left(\sqrt{5} - 1\right)} e^{x} + {\left({\left(\sqrt{5} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 10 \, \sqrt{5} - 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400\right) - {\left({\left({\left(\sqrt{5} + 5\right)} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 80 \, e^{x} - 80\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} \log\left(-200 \, {\left(\sqrt{5} - 1\right)} e^{x} - {\left({\left(\sqrt{5} e^{x} - \sqrt{5} - 5\right)} \sqrt{-40 \, \sqrt{5} + 200} - 10 \, \sqrt{5} - 50\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 20 \, \sqrt{5} + 60} {\left(-40 \, \sqrt{5} + 200\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 5\right)} \sqrt{-40 \, \sqrt{5} + 200} + 400 \, e^{\left(2 \, x\right)} + 400\right) + 3200}{8000 \, {\left(e^{x} - 1\right)}}"," ",0,"1/8000*(8*sqrt(10)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(5) - 1)*e^x - sqrt(5) + 1)*(40*sqrt(5) + 200)^(1/4)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*arctan(1/40*sqrt(10)*((sqrt(5) - 5)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 1/400*sqrt(10)*(sqrt(10)*((sqrt(5) - 5)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 5) - 1/64000*(80*sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 8*sqrt(10)*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*sqrt(sqrt(5) + 5) - sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 3) + 2*(3*sqrt(5) - 7)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 4*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*(40*sqrt(5) + 200)^(1/4)) + 1600*sqrt(2*sqrt(5) + 5))*sqrt(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 200*(sqrt(5) + 1)*e^x + 2*(sqrt(10)*(sqrt(5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 5*sqrt(5) + 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 1/16000*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*(5*(sqrt(5) - 3)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((3*sqrt(5) - 7)*e^x + 2)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 20*(sqrt(10)*((sqrt(5) - 5)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(1/4)) + 1/4*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2*e^x + 1)) + 8*sqrt(10)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(5) - 1)*e^x - sqrt(5) + 1)*(40*sqrt(5) + 200)^(1/4)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*arctan(-1/40*sqrt(10)*((sqrt(5) - 5)*e^x - sqrt(5) - 1)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 1/400*sqrt(10)*(sqrt(10)*((sqrt(5) - 5)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 5) + 1/64000*(80*sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 8*sqrt(10)*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*sqrt(sqrt(5) + 5) + sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 3) + 2*(3*sqrt(5) - 7)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 4*(sqrt(10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 10*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 1))*(40*sqrt(5) + 200)^(1/4)) + 1600*sqrt(2*sqrt(5) + 5))*sqrt(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 200*(sqrt(5) + 1)*e^x - 2*(sqrt(10)*(sqrt(5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 5*sqrt(5) + 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 1/16000*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*((sqrt(10)*(5*(sqrt(5) - 3)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((3*sqrt(5) - 7)*e^x + 2)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(3/4) + 20*(sqrt(10)*((sqrt(5) - 5)*e^x - 2*sqrt(5))*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 5) + 10*((sqrt(5) - 1)*e^x + sqrt(5) + 1)*sqrt(2*sqrt(5) + 5))*(40*sqrt(5) + 200)^(1/4)) - 1/4*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2*e^x + 1)) + 4*((sqrt(5) + 1)*e^x - sqrt(5) - 1)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5)*(-40*sqrt(5) + 200)^(3/4)*arctan(-1/32000*((20*(3*sqrt(5) + 7)*e^x + (5*(sqrt(5) + 3)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 40)*(-40*sqrt(5) + 200)^(3/4) + 20*(20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) - 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 1/128000*((((sqrt(5) + 3)*sqrt(-40*sqrt(5) + 200) + 12*sqrt(5) + 28)*(-40*sqrt(5) + 200)^(3/4) + 4*((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 4*(((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) + 20*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) - 800)*sqrt(-2*sqrt(5) + 5))*sqrt(-200*(sqrt(5) - 1)*e^x + ((sqrt(5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) - 10*sqrt(5) - 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) - 1/1600*(20*((sqrt(5) + 5)*e^x - sqrt(5) + 1)*sqrt(-40*sqrt(5) + 200) + (20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) - 20)*sqrt(-40*sqrt(5) + 200) + 400*sqrt(5) - 800*e^x - 400)*sqrt(-2*sqrt(5) + 5)) + 4*((sqrt(5) + 1)*e^x - sqrt(5) - 1)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5)*(-40*sqrt(5) + 200)^(3/4)*arctan(-1/32000*((20*(3*sqrt(5) + 7)*e^x + (5*(sqrt(5) + 3)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) - 40)*(-40*sqrt(5) + 200)^(3/4) + 20*(20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) - 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) + 1/128000*((((sqrt(5) + 3)*sqrt(-40*sqrt(5) + 200) + 12*sqrt(5) + 28)*(-40*sqrt(5) + 200)^(3/4) + 4*((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*(-40*sqrt(5) + 200)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*sqrt(-2*sqrt(5) + 5) - 4*(((sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 20)*sqrt(-40*sqrt(5) + 200) + 20*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) - 800)*sqrt(-2*sqrt(5) + 5))*sqrt(-200*(sqrt(5) - 1)*e^x - ((sqrt(5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) - 10*sqrt(5) - 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) + 1/1600*(20*((sqrt(5) + 5)*e^x - sqrt(5) + 1)*sqrt(-40*sqrt(5) + 200) + (20*(sqrt(5) + 1)*e^x + ((sqrt(5) + 5)*e^x - 2*sqrt(5))*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) - 20)*sqrt(-40*sqrt(5) + 200) + 400*sqrt(5) - 800*e^x - 400)*sqrt(-2*sqrt(5) + 5)) + 2*(sqrt(10)*((sqrt(5) - 5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 40*e^x + 40)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4)*log(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 200*(sqrt(5) + 1)*e^x + 2*(sqrt(10)*(sqrt(5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 5*sqrt(5) + 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) - 2*(sqrt(10)*((sqrt(5) - 5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 40*e^x + 40)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4)*log(-20*sqrt(10)*sqrt(sqrt(5) + 5)*(sqrt(5) - 5) + 200*(sqrt(5) + 1)*e^x - 2*(sqrt(10)*(sqrt(5)*e^x - sqrt(5) + 5)*sqrt(sqrt(5) + 5) - 5*sqrt(5) + 25)*sqrt(2*sqrt(10)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 5) - 20*sqrt(5) + 60)*(40*sqrt(5) + 200)^(1/4) + 400*e^(2*x) + 400) + (((sqrt(5) + 5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) + 80*e^x - 80)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4)*log(-200*(sqrt(5) - 1)*e^x + ((sqrt(5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) - 10*sqrt(5) - 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) - (((sqrt(5) + 5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) + 80*e^x - 80)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4)*log(-200*(sqrt(5) - 1)*e^x - ((sqrt(5)*e^x - sqrt(5) - 5)*sqrt(-40*sqrt(5) + 200) - 10*sqrt(5) - 50)*sqrt(-(2*sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 20*sqrt(5) + 60)*(-40*sqrt(5) + 200)^(1/4) + 10*(sqrt(5) + 5)*sqrt(-40*sqrt(5) + 200) + 400*e^(2*x) + 400) + 3200)/(e^x - 1)","B",0
74,1,694,0,1.665511," ","integrate(1/(1-cosh(x)^6),x, algorithm=""fricas"")","\frac{4 \, {\left(12^{\frac{1}{4}} \sqrt{6} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left({\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{216} \, \sqrt{6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} + 144 \, e^{\left(2 \, x\right)} + 252} {\left({\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 36 \, \sqrt{3} - 72\right)} + \frac{2}{3} \, \sqrt{3} {\left(2 \, \sqrt{3} - 3\right)} + \frac{1}{36} \, {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)} - {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} e^{\left(2 \, x\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 2 \, \sqrt{3} - 4\right) + 4 \, {\left(12^{\frac{1}{4}} \sqrt{6} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-{\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{216} \, \sqrt{-6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} + 144 \, e^{\left(2 \, x\right)} + 252} {\left({\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 36 \, \sqrt{3} + 72\right)} - \frac{2}{3} \, \sqrt{3} {\left(2 \, \sqrt{3} - 3\right)} + \frac{1}{36} \, {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)} - {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} e^{\left(2 \, x\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 2 \, \sqrt{3} + 4\right) - {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} + 144 \, e^{\left(2 \, x\right)} + 252\right) + {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} + 144 \, e^{\left(2 \, x\right)} + 252\right) + 96}{144 \, {\left(e^{\left(2 \, x\right)} - 1\right)}}"," ",0,"1/144*(4*(12^(1/4)*sqrt(6)*e^(2*x) - 12^(1/4)*sqrt(6))*sqrt(-4*sqrt(3) + 8)*arctan((sqrt(3) + 2)*e^(2*x) + 1/216*sqrt(6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) + 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) + 144*e^(2*x) + 252)*((12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8) - 36*sqrt(3) - 72) + 2/3*sqrt(3)*(2*sqrt(3) - 3) + 1/36*(12^(3/4)*sqrt(6)*(sqrt(3) - 3) - (12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*e^(2*x) + 3*12^(1/4)*sqrt(6)*(sqrt(3) - 3))*sqrt(-4*sqrt(3) + 8) + 2*sqrt(3) - 4) + 4*(12^(1/4)*sqrt(6)*e^(2*x) - 12^(1/4)*sqrt(6))*sqrt(-4*sqrt(3) + 8)*arctan(-(sqrt(3) + 2)*e^(2*x) + 1/216*sqrt(-6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) + 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) + 144*e^(2*x) + 252)*((12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8) + 36*sqrt(3) + 72) - 2/3*sqrt(3)*(2*sqrt(3) - 3) + 1/36*(12^(3/4)*sqrt(6)*(sqrt(3) - 3) - (12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*e^(2*x) + 3*12^(1/4)*sqrt(6)*(sqrt(3) - 3))*sqrt(-4*sqrt(3) + 8) - 2*sqrt(3) + 4) - (12^(1/4)*sqrt(6)*(sqrt(3) + 2)*e^(2*x) - 12^(1/4)*sqrt(6)*(sqrt(3) + 2))*sqrt(-4*sqrt(3) + 8)*log(6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) + 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) + 144*e^(2*x) + 252) + (12^(1/4)*sqrt(6)*(sqrt(3) + 2)*e^(2*x) - 12^(1/4)*sqrt(6)*(sqrt(3) + 2))*sqrt(-4*sqrt(3) + 8)*log(-6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) + 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) + 144*e^(2*x) + 252) + 96)/(e^(2*x) - 1)","B",0
75,1,713,0,1.873822," ","integrate(1/(1-cosh(x)^8),x, algorithm=""fricas"")","\frac{4 \, {\left(2^{\frac{1}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}}\right)} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} - \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5} + \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} + 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{7} \, \sqrt{2} - \frac{3}{7}\right) + 4 \, {\left(2^{\frac{1}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}}\right)} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} + \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5} - \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} + 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{7} \, \sqrt{2} + \frac{3}{7}\right) - {\left(2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left({\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5\right) + {\left(2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 5\right) + 2 \, {\left(\sqrt{2} e^{\left(2 \, x\right)} - \sqrt{2}\right)} \log\left(-\frac{2 \, {\left(2 \, \sqrt{2} - 3\right)} e^{\left(2 \, x\right)} + 12 \, \sqrt{2} - e^{\left(4 \, x\right)} - 17}{e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} + 1}\right) + 16}{32 \, {\left(e^{\left(2 \, x\right)} - 1\right)}}"," ",0,"1/32*(4*(2^(1/4)*e^(2*x) - 2^(1/4))*sqrt(-2*sqrt(2) + 4)*arctan(1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) - 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) - (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt((2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) + 2^(3/4)*(2*sqrt(2) + 1) + 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) + 1/7*sqrt(2) - 3/7) + 4*(2^(1/4)*e^(2*x) - 2^(1/4))*sqrt(-2*sqrt(2) + 4)*arctan(-1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) + 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) + (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt(-(2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) - 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) + 2^(3/4)*(2*sqrt(2) + 1) + 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) - 1/7*sqrt(2) + 3/7) - (2^(1/4)*(sqrt(2) + 1)*e^(2*x) - 2^(1/4)*(sqrt(2) + 1))*sqrt(-2*sqrt(2) + 4)*log((2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + (2^(1/4)*(sqrt(2) + 1)*e^(2*x) - 2^(1/4)*(sqrt(2) + 1))*sqrt(-2*sqrt(2) + 4)*log(-(2^(3/4)*e^(2*x) + 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) + 2*e^(2*x) + 5) + 2*(sqrt(2)*e^(2*x) - sqrt(2))*log(-(2*(2*sqrt(2) - 3)*e^(2*x) + 12*sqrt(2) - e^(4*x) - 17)/(e^(4*x) + 6*e^(2*x) + 1)) + 16)/(e^(2*x) - 1)","B",0
76,1,47,0,1.142751," ","integrate(tanh(x)/(1+cosh(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3\right)}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-1/2*log(2*(cosh(x)^2 + sinh(x)^2 + 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + log(2*cosh(x)/(cosh(x) - sinh(x)))","B",0
77,1,357,0,1.205222," ","integrate((a+b*cosh(x)^2)^(1/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(4 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \sqrt{2} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}, \frac{2 \, \sqrt{-a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)}}\right) + \sqrt{2} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}\right]"," ",0,"[1/2*(sqrt(a)*(cosh(x) + sinh(x))*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(4*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 4*a + b)*sinh(x)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))*(cosh(x) + sinh(x)) + 4*(b*cosh(x)^3 + (4*a + b)*cosh(x))*sinh(x) + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + sqrt(2)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x)), 1/2*(2*sqrt(-a)*(cosh(x) + sinh(x))*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x) + a*sinh(x))) + sqrt(2)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x))]","B",0
78,1,248,0,3.996001," ","integrate(tanh(x)/(a+b*cosh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, {\left(4 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + 4 \, a + b\right)} \sinh\left(x\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} + 4 \, {\left(b \cosh\left(x\right)^{3} + {\left(4 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right)}{2 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(x\right)^{2} + b \sinh\left(x\right)^{2} + 2 \, a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a \cosh\left(x\right) + a \sinh\left(x\right)\right)}}\right)}{a}\right]"," ",0,"[1/2*log((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*(4*a + b)*cosh(x)^2 + 2*(3*b*cosh(x)^2 + 4*a + b)*sinh(x)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))*(cosh(x) + sinh(x)) + 4*(b*cosh(x)^3 + (4*a + b)*cosh(x))*sinh(x) + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1))/sqrt(a), sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(x)^2 + b*sinh(x)^2 + 2*a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(a*cosh(x) + a*sinh(x)))/a]","B",0
79,1,63,0,0.486294," ","integrate(tanh(x)/(1+cosh(x)^2)^(1/2),x, algorithm=""fricas"")","\log\left(\frac{\sqrt{2} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 2 \, \cosh\left(x\right) - 2 \, \sinh\left(x\right)}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1}\right)"," ",0,"log((sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 + 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*cosh(x) - 2*sinh(x))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1))","B",0
80,1,1,0,0.457170," ","integrate(tanh(x)/(1-cosh(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
81,1,1138,0,1.444664," ","integrate(tanh(x)^3/(a+b*cosh(x)^3),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{\frac{1}{3}} {\left(a e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} + a\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{3}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} e^{\left(2 \, x\right)} + b^{2} e^{\left(4 \, x\right)} - 2 \, a b e^{\left(3 \, x\right)} - 2 \, a b e^{x} + {\left(a^{2} b e^{\left(3 \, x\right)} - 4 \, a^{3} e^{\left(2 \, x\right)} + a^{2} b e^{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + b^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} e^{\left(2 \, x\right)}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{3} - 2 \, a^{2}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} - \sqrt{\frac{1}{3}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{5} e^{x} - 4 \, a^{2} b e^{\left(2 \, x\right)} + 4 \, a^{3} e^{x} - 4 \, a^{2} b + 2 \, {\left(a^{3} b e^{\left(2 \, x\right)} - 2 \, a^{4} e^{x} + a^{3} b\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}}\right)} e^{\left(-x\right)}}{8 \, b^{2}}\right) + 2 \, {\left(a e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} + a\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} \log\left(-{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{2} e^{x} + b e^{\left(2 \, x\right)} + 2 \, a e^{x} + b\right) - {\left({\left(a e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} + a\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} - 6 \, e^{\left(4 \, x\right)} - 12 \, e^{\left(2 \, x\right)} - 6\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} e^{\left(2 \, x\right)} + b^{2} e^{\left(4 \, x\right)} - 2 \, a b e^{\left(3 \, x\right)} - 2 \, a b e^{x} + {\left(a^{2} b e^{\left(3 \, x\right)} - 4 \, a^{3} e^{\left(2 \, x\right)} + a^{2} b e^{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} - b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + b^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} e^{\left(2 \, x\right)}\right) - 12 \, {\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)} \log\left(e^{\left(2 \, x\right)} + 1\right) - 24 \, e^{\left(2 \, x\right)}}{12 \, {\left(a e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} + a\right)}}"," ",0,"-1/12*(12*sqrt(1/3)*(a*e^(4*x) + 2*a*e^(2*x) + a)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2)*arctan(-1/8*(2*sqrt(1/3)*sqrt(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4*e^(2*x) + b^2*e^(4*x) - 2*a*b*e^(3*x) - 2*a*b*e^x + (a^2*b*e^(3*x) - 4*a^3*e^(2*x) + a^2*b*e^x)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + b^2 + 2*(2*a^2 + b^2)*e^(2*x))*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a^3 - 2*a^2)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2) - sqrt(1/3)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^5*e^x - 4*a^2*b*e^(2*x) + 4*a^3*e^x - 4*a^2*b + 2*(a^3*b*e^(2*x) - 2*a^4*e^x + a^3*b)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a))*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2))*e^(-x)/b^2) + 2*(a*e^(4*x) + 2*a*e^(2*x) + a)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*log(-((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)*a^2*e^x + b*e^(2*x) + 2*a*e^x + b) - ((a*e^(4*x) + 2*a*e^(2*x) + a)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) - 6*e^(4*x) - 12*e^(2*x) - 6)*log(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a)^2*a^4*e^(2*x) + b^2*e^(4*x) - 2*a*b*e^(3*x) - 2*a*b*e^x + (a^2*b*e^(3*x) - 4*a^3*e^(2*x) + a^2*b*e^x)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 - b^2)/a^5)^(1/3) + 2/a) + b^2 + 2*(2*a^2 + b^2)*e^(2*x)) - 12*(e^(4*x) + 2*e^(2*x) + 1)*log(e^(2*x) + 1) - 24*e^(2*x))/(a*e^(4*x) + 2*a*e^(2*x) + a)","C",0
82,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*cosh(x)^3)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(Expression(Integer)),failed) cannot be coerced to mode SparseUnivariatePolynomial(Expression(Integer))","F(-2)",0
83,1,1648,0,1.427860," ","integrate((a+b*cosh(x)^3)^(1/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(-\frac{b^{2} \cosh\left(x\right)^{12} + 12 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{11} + b^{2} \sinh\left(x\right)^{12} + 6 \, b^{2} \cosh\left(x\right)^{10} + 64 \, a b \cosh\left(x\right)^{9} + 6 \, {\left(11 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{10} + 15 \, b^{2} \cosh\left(x\right)^{8} + 4 \, {\left(55 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right) + 16 \, a b\right)} \sinh\left(x\right)^{9} + 192 \, a b \cosh\left(x\right)^{7} + 3 \, {\left(165 \, b^{2} \cosh\left(x\right)^{4} + 90 \, b^{2} \cosh\left(x\right)^{2} + 192 \, a b \cosh\left(x\right) + 5 \, b^{2}\right)} \sinh\left(x\right)^{8} + 24 \, {\left(33 \, b^{2} \cosh\left(x\right)^{5} + 30 \, b^{2} \cosh\left(x\right)^{3} + 96 \, a b \cosh\left(x\right)^{2} + 5 \, b^{2} \cosh\left(x\right) + 8 \, a b\right)} \sinh\left(x\right)^{7} + 192 \, a b \cosh\left(x\right)^{5} + 4 \, {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(231 \, b^{2} \cosh\left(x\right)^{6} + 315 \, b^{2} \cosh\left(x\right)^{4} + 1344 \, a b \cosh\left(x\right)^{3} + 105 \, b^{2} \cosh\left(x\right)^{2} + 336 \, a b \cosh\left(x\right) + 128 \, a^{2} + 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 24 \, {\left(33 \, b^{2} \cosh\left(x\right)^{7} + 63 \, b^{2} \cosh\left(x\right)^{5} + 336 \, a b \cosh\left(x\right)^{4} + 35 \, b^{2} \cosh\left(x\right)^{3} + 168 \, a b \cosh\left(x\right)^{2} + 8 \, a b + {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 64 \, a b \cosh\left(x\right)^{3} + 3 \, {\left(165 \, b^{2} \cosh\left(x\right)^{8} + 420 \, b^{2} \cosh\left(x\right)^{6} + 2688 \, a b \cosh\left(x\right)^{5} + 350 \, b^{2} \cosh\left(x\right)^{4} + 2240 \, a b \cosh\left(x\right)^{3} + 320 \, a b \cosh\left(x\right) + 20 \, {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, b^{2}\right)} \sinh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(55 \, b^{2} \cosh\left(x\right)^{9} + 180 \, b^{2} \cosh\left(x\right)^{7} + 1344 \, a b \cosh\left(x\right)^{6} + 210 \, b^{2} \cosh\left(x\right)^{5} + 1680 \, a b \cosh\left(x\right)^{4} + 480 \, a b \cosh\left(x\right)^{2} + 20 \, {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right) + 16 \, a b\right)} \sinh\left(x\right)^{3} + 6 \, {\left(11 \, b^{2} \cosh\left(x\right)^{10} + 45 \, b^{2} \cosh\left(x\right)^{8} + 384 \, a b \cosh\left(x\right)^{7} + 70 \, b^{2} \cosh\left(x\right)^{6} + 672 \, a b \cosh\left(x\right)^{5} + 320 \, a b \cosh\left(x\right)^{3} + 10 \, {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + 32 \, a b \cosh\left(x\right) + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} - 16 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} + 3 \, b \cosh\left(x\right)^{6} + {\left(28 \, b \cosh\left(x\right)^{2} + 3 \, b\right)} \sinh\left(x\right)^{6} + 16 \, a \cosh\left(x\right)^{5} + 2 \, {\left(28 \, b \cosh\left(x\right)^{3} + 9 \, b \cosh\left(x\right) + 8 \, a\right)} \sinh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{4} + {\left(70 \, b \cosh\left(x\right)^{4} + 45 \, b \cosh\left(x\right)^{2} + 80 \, a \cosh\left(x\right) + 3 \, b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, b \cosh\left(x\right)^{5} + 15 \, b \cosh\left(x\right)^{3} + 40 \, a \cosh\left(x\right)^{2} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + b \cosh\left(x\right)^{2} + {\left(28 \, b \cosh\left(x\right)^{6} + 45 \, b \cosh\left(x\right)^{4} + 160 \, a \cosh\left(x\right)^{3} + 18 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(4 \, b \cosh\left(x\right)^{7} + 9 \, b \cosh\left(x\right)^{5} + 40 \, a \cosh\left(x\right)^{4} + 6 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + 3 \, b \cosh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 12 \, {\left(b^{2} \cosh\left(x\right)^{11} + 5 \, b^{2} \cosh\left(x\right)^{9} + 48 \, a b \cosh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{7} + 112 \, a b \cosh\left(x\right)^{6} + 80 \, a b \cosh\left(x\right)^{4} + 2 \, {\left(128 \, a^{2} + 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + 16 \, a b \cosh\left(x\right)^{2} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{12} + 12 \, \cosh\left(x\right) \sinh\left(x\right)^{11} + \sinh\left(x\right)^{12} + 6 \, {\left(11 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{10} + 6 \, \cosh\left(x\right)^{10} + 20 \, {\left(11 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{9} + 15 \, {\left(33 \, \cosh\left(x\right)^{4} + 18 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{8} + 15 \, \cosh\left(x\right)^{8} + 24 \, {\left(33 \, \cosh\left(x\right)^{5} + 30 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 4 \, {\left(231 \, \cosh\left(x\right)^{6} + 315 \, \cosh\left(x\right)^{4} + 105 \, \cosh\left(x\right)^{2} + 5\right)} \sinh\left(x\right)^{6} + 20 \, \cosh\left(x\right)^{6} + 24 \, {\left(33 \, \cosh\left(x\right)^{7} + 63 \, \cosh\left(x\right)^{5} + 35 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 15 \, {\left(33 \, \cosh\left(x\right)^{8} + 84 \, \cosh\left(x\right)^{6} + 70 \, \cosh\left(x\right)^{4} + 20 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{4} + 20 \, {\left(11 \, \cosh\left(x\right)^{9} + 36 \, \cosh\left(x\right)^{7} + 42 \, \cosh\left(x\right)^{5} + 20 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 6 \, {\left(11 \, \cosh\left(x\right)^{10} + 45 \, \cosh\left(x\right)^{8} + 70 \, \cosh\left(x\right)^{6} + 50 \, \cosh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 6 \, \cosh\left(x\right)^{2} + 12 \, {\left(\cosh\left(x\right)^{11} + 5 \, \cosh\left(x\right)^{9} + 10 \, \cosh\left(x\right)^{7} + 10 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + 3 \, b \cosh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}, \frac{\sqrt{-a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \arctan\left(\frac{8 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + 3 \, b \cosh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} + 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{4} + 16 \, a \cosh\left(x\right)^{3} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) + 4 \, a\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} + 6 \, b \cosh\left(x\right)^{2} + 16 \, a \cosh\left(x\right) + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + 8 \, a \cosh\left(x\right)^{2} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + \sqrt{\frac{b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right) \sinh\left(x\right)^{2} + 3 \, b \cosh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{3 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}\right]"," ",0,"[1/6*(sqrt(a)*(cosh(x) + sinh(x))*log(-(b^2*cosh(x)^12 + 12*b^2*cosh(x)*sinh(x)^11 + b^2*sinh(x)^12 + 6*b^2*cosh(x)^10 + 64*a*b*cosh(x)^9 + 6*(11*b^2*cosh(x)^2 + b^2)*sinh(x)^10 + 15*b^2*cosh(x)^8 + 4*(55*b^2*cosh(x)^3 + 15*b^2*cosh(x) + 16*a*b)*sinh(x)^9 + 192*a*b*cosh(x)^7 + 3*(165*b^2*cosh(x)^4 + 90*b^2*cosh(x)^2 + 192*a*b*cosh(x) + 5*b^2)*sinh(x)^8 + 24*(33*b^2*cosh(x)^5 + 30*b^2*cosh(x)^3 + 96*a*b*cosh(x)^2 + 5*b^2*cosh(x) + 8*a*b)*sinh(x)^7 + 192*a*b*cosh(x)^5 + 4*(128*a^2 + 5*b^2)*cosh(x)^6 + 4*(231*b^2*cosh(x)^6 + 315*b^2*cosh(x)^4 + 1344*a*b*cosh(x)^3 + 105*b^2*cosh(x)^2 + 336*a*b*cosh(x) + 128*a^2 + 5*b^2)*sinh(x)^6 + 15*b^2*cosh(x)^4 + 24*(33*b^2*cosh(x)^7 + 63*b^2*cosh(x)^5 + 336*a*b*cosh(x)^4 + 35*b^2*cosh(x)^3 + 168*a*b*cosh(x)^2 + 8*a*b + (128*a^2 + 5*b^2)*cosh(x))*sinh(x)^5 + 64*a*b*cosh(x)^3 + 3*(165*b^2*cosh(x)^8 + 420*b^2*cosh(x)^6 + 2688*a*b*cosh(x)^5 + 350*b^2*cosh(x)^4 + 2240*a*b*cosh(x)^3 + 320*a*b*cosh(x) + 20*(128*a^2 + 5*b^2)*cosh(x)^2 + 5*b^2)*sinh(x)^4 + 6*b^2*cosh(x)^2 + 4*(55*b^2*cosh(x)^9 + 180*b^2*cosh(x)^7 + 1344*a*b*cosh(x)^6 + 210*b^2*cosh(x)^5 + 1680*a*b*cosh(x)^4 + 480*a*b*cosh(x)^2 + 20*(128*a^2 + 5*b^2)*cosh(x)^3 + 15*b^2*cosh(x) + 16*a*b)*sinh(x)^3 + 6*(11*b^2*cosh(x)^10 + 45*b^2*cosh(x)^8 + 384*a*b*cosh(x)^7 + 70*b^2*cosh(x)^6 + 672*a*b*cosh(x)^5 + 320*a*b*cosh(x)^3 + 10*(128*a^2 + 5*b^2)*cosh(x)^4 + 15*b^2*cosh(x)^2 + 32*a*b*cosh(x) + b^2)*sinh(x)^2 + b^2 - 16*(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 + 3*b*cosh(x)^6 + (28*b*cosh(x)^2 + 3*b)*sinh(x)^6 + 16*a*cosh(x)^5 + 2*(28*b*cosh(x)^3 + 9*b*cosh(x) + 8*a)*sinh(x)^5 + 3*b*cosh(x)^4 + (70*b*cosh(x)^4 + 45*b*cosh(x)^2 + 80*a*cosh(x) + 3*b)*sinh(x)^4 + 4*(14*b*cosh(x)^5 + 15*b*cosh(x)^3 + 40*a*cosh(x)^2 + 3*b*cosh(x))*sinh(x)^3 + b*cosh(x)^2 + (28*b*cosh(x)^6 + 45*b*cosh(x)^4 + 160*a*cosh(x)^3 + 18*b*cosh(x)^2 + b)*sinh(x)^2 + 2*(4*b*cosh(x)^7 + 9*b*cosh(x)^5 + 40*a*cosh(x)^4 + 6*b*cosh(x)^3 + b*cosh(x))*sinh(x))*sqrt(a)*sqrt((b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + 3*b*cosh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 12*(b^2*cosh(x)^11 + 5*b^2*cosh(x)^9 + 48*a*b*cosh(x)^8 + 10*b^2*cosh(x)^7 + 112*a*b*cosh(x)^6 + 80*a*b*cosh(x)^4 + 2*(128*a^2 + 5*b^2)*cosh(x)^5 + 5*b^2*cosh(x)^3 + 16*a*b*cosh(x)^2 + b^2*cosh(x))*sinh(x))/(cosh(x)^12 + 12*cosh(x)*sinh(x)^11 + sinh(x)^12 + 6*(11*cosh(x)^2 + 1)*sinh(x)^10 + 6*cosh(x)^10 + 20*(11*cosh(x)^3 + 3*cosh(x))*sinh(x)^9 + 15*(33*cosh(x)^4 + 18*cosh(x)^2 + 1)*sinh(x)^8 + 15*cosh(x)^8 + 24*(33*cosh(x)^5 + 30*cosh(x)^3 + 5*cosh(x))*sinh(x)^7 + 4*(231*cosh(x)^6 + 315*cosh(x)^4 + 105*cosh(x)^2 + 5)*sinh(x)^6 + 20*cosh(x)^6 + 24*(33*cosh(x)^7 + 63*cosh(x)^5 + 35*cosh(x)^3 + 5*cosh(x))*sinh(x)^5 + 15*(33*cosh(x)^8 + 84*cosh(x)^6 + 70*cosh(x)^4 + 20*cosh(x)^2 + 1)*sinh(x)^4 + 15*cosh(x)^4 + 20*(11*cosh(x)^9 + 36*cosh(x)^7 + 42*cosh(x)^5 + 20*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 6*(11*cosh(x)^10 + 45*cosh(x)^8 + 70*cosh(x)^6 + 50*cosh(x)^4 + 15*cosh(x)^2 + 1)*sinh(x)^2 + 6*cosh(x)^2 + 12*(cosh(x)^11 + 5*cosh(x)^9 + 10*cosh(x)^7 + 10*cosh(x)^5 + 5*cosh(x)^3 + cosh(x))*sinh(x) + 1)) + 2*sqrt((b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + 3*b*cosh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x)), 1/3*(sqrt(-a)*(cosh(x) + sinh(x))*arctan(8*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)*sqrt(-a)*sqrt((b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + 3*b*cosh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 + 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 + b)*sinh(x)^4 + 16*a*cosh(x)^3 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x) + 4*a)*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + 16*a*cosh(x) + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + 8*a*cosh(x)^2 + b*cosh(x))*sinh(x) + b)) + sqrt((b*cosh(x)^3 + 3*b*cosh(x)*sinh(x)^2 + 3*b*cosh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x))]","B",0
84,1,113,0,0.480035," ","integrate(tanh(x)/(a+b*cosh(x)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) - 2 \, \sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a} \sqrt{a} + 2 \, a}{\cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + \sinh\left(n \log\left(\cosh\left(x\right)\right)\right)}\right)}{\sqrt{a} n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log((b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) - 2*sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a)*sqrt(a) + 2*a)/(cosh(n*log(cosh(x))) + sinh(n*log(cosh(x)))))/(sqrt(a)*n), 2*sqrt(-a)*arctan(sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a)*sqrt(-a)/a)/(a*n)]","A",0
85,1,156,0,0.473805," ","integrate((a+b*cosh(x)^n)^(1/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) - 2 \, \sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a} \sqrt{a} + 2 \, a}{\cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + \sinh\left(n \log\left(\cosh\left(x\right)\right)\right)}\right) + 2 \, \sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a}}{n}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a} \sqrt{-a}}{a}\right) + \sqrt{b \cosh\left(n \log\left(\cosh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\cosh\left(x\right)\right)\right) + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log((b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) - 2*sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a)*sqrt(a) + 2*a)/(cosh(n*log(cosh(x))) + sinh(n*log(cosh(x))))) + 2*sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a))/n, 2*(sqrt(-a)*arctan(sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a)*sqrt(-a)/a) + sqrt(b*cosh(n*log(cosh(x))) + b*sinh(n*log(cosh(x))) + a))/n]","A",0
