1,1,929,0,0.422333," ","integrate((a+b*csch(d*x+c)^2)^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(105 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(105 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} - 28 \, {\left(75 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4} - 3 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 140 \, {\left({\left(105 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(75 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(45 \, a^{3} b - 75 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(315 \, a^{4} d x + 5 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 1260 \, a^{3} b - 1260 \, a^{2} b^{2} + 672 \, a b^{3} - 144 \, b^{4} - 10 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 28 \, {\left(3 \, {\left(105 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(75 \, a^{3} b - 105 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(45 \, a^{3} b - 75 \, a^{2} b^{2} + 56 \, a b^{3} - 12 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 420 \, {\left(5 \, a^{3} b - 9 \, a^{2} b^{2} + 8 \, a b^{3} - 4 \, b^{4}\right)} \cosh\left(d x + c\right) - 7 \, {\left({\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 525 \, a^{4} d x - 5 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 2100 \, a^{3} b + 2100 \, a^{2} b^{2} - 1120 \, a b^{3} + 240 \, b^{4} + 9 \, {\left(105 \, a^{4} d x + 420 \, a^{3} b - 420 \, a^{2} b^{2} + 224 \, a b^{3} - 48 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{105 \, {\left(d \sinh\left(d x + c\right)^{7} + 7 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{5} + 7 \, {\left(5 \, d \cosh\left(d x + c\right)^{4} - 10 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(d \cosh\left(d x + c\right)^{6} - 5 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/105*(4*(105*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^7 + 28*(105*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 - (105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*sinh(d*x + c)^7 - 28*(75*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^5 + 7*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4 - 3*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 140*((105*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^3 - (75*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(45*a^3*b - 75*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^3 - 7*(315*a^4*d*x + 5*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^4 + 1260*a^3*b - 1260*a^2*b^2 + 672*a*b^3 - 144*b^4 - 10*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 28*(3*(105*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^5 - 10*(75*a^3*b - 105*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c)^3 + 9*(45*a^3*b - 75*a^2*b^2 + 56*a*b^3 - 12*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - 420*(5*a^3*b - 9*a^2*b^2 + 8*a*b^3 - 4*b^4)*cosh(d*x + c) - 7*((105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^6 - 525*a^4*d*x - 5*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^4 - 2100*a^3*b + 2100*a^2*b^2 - 1120*a*b^3 + 240*b^4 + 9*(105*a^4*d*x + 420*a^3*b - 420*a^2*b^2 + 224*a*b^3 - 48*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^7 + 7*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^5 + 7*(5*d*cosh(d*x + c)^4 - 10*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^3 + 7*(d*cosh(d*x + c)^6 - 5*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c))","B",0
2,1,461,0,0.440341," ","integrate((a+b*csch(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{3} d x + 45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(27 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(15 \, a^{3} d x + 45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3} - 2 \, {\left(15 \, a^{3} d x + 45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(27 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(9 \, a^{2} b - 12 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right) - 5 \, {\left(30 \, a^{3} d x + {\left(15 \, a^{3} d x + 45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 90 \, a^{2} b - 60 \, a b^{2} + 16 \, b^{3} - 3 \, {\left(15 \, a^{3} d x + 45 \, a^{2} b - 30 \, a b^{2} + 8 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{15 \, {\left(d \sinh\left(d x + c\right)^{5} + 5 \, {\left(2 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(d \cosh\left(d x + c\right)^{4} - 3 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/15*((45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^5 + 5*(45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^3*d*x + 45*a^2*b - 30*a*b^2 + 8*b^3)*sinh(d*x + c)^5 - 5*(27*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^3 + 5*(15*a^3*d*x + 45*a^2*b - 30*a*b^2 + 8*b^3 - 2*(15*a^3*d*x + 45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^3 - 3*(27*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(9*a^2*b - 12*a*b^2 + 8*b^3)*cosh(d*x + c) - 5*(30*a^3*d*x + (15*a^3*d*x + 45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^4 + 90*a^2*b - 60*a*b^2 + 16*b^3 - 3*(15*a^3*d*x + 45*a^2*b - 30*a*b^2 + 8*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^5 + 5*(2*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 5*(d*cosh(d*x + c)^4 - 3*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c))","B",0
3,1,180,0,0.450058," ","integrate((a+b*csch(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, a^{2} d x + 6 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(3 \, a^{2} d x - {\left(3 \, a^{2} d x + 6 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)}{3 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*(3*a*b - b^2)*cosh(d*x + c)^3 + 6*(3*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*a^2*d*x + 6*a*b - 2*b^2)*sinh(d*x + c)^3 - 6*(a*b - b^2)*cosh(d*x + c) + 3*(3*a^2*d*x - (3*a^2*d*x + 6*a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a*b - 2*b^2)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
4,1,36,0,0.396225," ","integrate(a+b*csch(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b \cosh\left(d x + c\right) - {\left(a d x + b\right)} \sinh\left(d x + c\right)}{d \sinh\left(d x + c\right)}"," ",0,"-(b*cosh(d*x + c) - (a*d*x + b)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
5,1,457,0,0.451115," ","integrate(1/(a+b*csch(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{-\frac{b}{a - b}} \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sqrt{-\frac{b}{a - b}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right)}{2 \, a d}, \frac{d x - \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right)}{a d}\right]"," ",0,"[1/2*(2*d*x + sqrt(-b/(a - b))*log((a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4 - 2*(a^2 - 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 - a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 - 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 - (a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 - a*b)*cosh(d*x + c)^2 + 2*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - a*b)*sinh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sqrt(-b/(a - b)))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/(a*d), (d*x - sqrt(b/(a - b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + 2*b)*sqrt(b/(a - b))/b))/(a*d)]","A",0
6,1,1747,0,0.475634," ","integrate(1/(a+b*csch(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} - a b\right)} d x \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - a b\right)} d x - 4 \, {\left(2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x - a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 8 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b + 4 \, {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sqrt{-\frac{b}{a - b}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - 4 \, a b + 8 \, {\left(2 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x - a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d + 4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} - a b\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - a b\right)} d x - 2 \, {\left(2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x - a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 8 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b + 4 \, {\left({\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 8 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) - 2 \, a b + 4 \, {\left(2 \, {\left(a^{2} - a b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} d x - a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d + 4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a^2 - a*b)*d*x*cosh(d*x + c)^4 + 16*(a^2 - a*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(a^2 - a*b)*d*x*sinh(d*x + c)^4 + 4*(a^2 - a*b)*d*x - 4*(2*(a^2 - 3*a*b + 2*b^2)*d*x - a*b + 2*b^2)*cosh(d*x + c)^2 + 4*(6*(a^2 - a*b)*d*x*cosh(d*x + c)^2 - 2*(a^2 - 3*a*b + 2*b^2)*d*x + a*b - 2*b^2)*sinh(d*x + c)^2 + ((3*a^2 - 2*a*b)*cosh(d*x + c)^4 + 4*(3*a^2 - 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 - 2*a*b)*sinh(d*x + c)^4 - 2*(3*a^2 - 8*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 - 3*a^2 + 8*a*b - 4*b^2)*sinh(d*x + c)^2 + 3*a^2 - 2*a*b + 4*((3*a^2 - 2*a*b)*cosh(d*x + c)^3 - (3*a^2 - 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4 - 2*(a^2 - 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 - a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 - 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 - (a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 - a*b)*cosh(d*x + c)^2 + 2*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - a*b)*sinh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sqrt(-b/(a - b)))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*a*b + 8*(2*(a^2 - a*b)*d*x*cosh(d*x + c)^3 - (2*(a^2 - 3*a*b + 2*b^2)*d*x - a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^3*b)*d*sinh(d*x + c)^4 - 2*(a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 - a^3*b)*d + 4*((a^4 - a^3*b)*d*cosh(d*x + c)^3 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^2 - a*b)*d*x*cosh(d*x + c)^4 + 8*(a^2 - a*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 - a*b)*d*x*sinh(d*x + c)^4 + 2*(a^2 - a*b)*d*x - 2*(2*(a^2 - 3*a*b + 2*b^2)*d*x - a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(6*(a^2 - a*b)*d*x*cosh(d*x + c)^2 - 2*(a^2 - 3*a*b + 2*b^2)*d*x + a*b - 2*b^2)*sinh(d*x + c)^2 - ((3*a^2 - 2*a*b)*cosh(d*x + c)^4 + 4*(3*a^2 - 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 - 2*a*b)*sinh(d*x + c)^4 - 2*(3*a^2 - 8*a*b + 4*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 - 3*a^2 + 8*a*b - 4*b^2)*sinh(d*x + c)^2 + 3*a^2 - 2*a*b + 4*((3*a^2 - 2*a*b)*cosh(d*x + c)^3 - (3*a^2 - 8*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + 2*b)*sqrt(b/(a - b))/b) - 2*a*b + 4*(2*(a^2 - a*b)*d*x*cosh(d*x + c)^3 - (2*(a^2 - 3*a*b + 2*b^2)*d*x - a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^3*b)*d*sinh(d*x + c)^4 - 2*(a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 - a^3*b)*d + 4*((a^4 - a^3*b)*d*cosh(d*x + c)^3 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
7,1,6569,0,0.634691," ","integrate(1/(a+b*csch(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b + 90 \, a^{2} b^{2} - 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x + 15 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 36 \, a^{3} b + 24 \, a^{2} b^{2} + 16 \, {\left(56 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x + 4 \, {\left(27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x - 6 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3} - 7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4} - 30 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{4} + 50 \, a^{3} b - 48 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{a^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 8 \, a b + 8 \, b^{2} + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sqrt{-\frac{b}{a - b}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) + 8 \, {\left(16 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b + 90 \, a^{2} b^{2} - 120 \, a b^{3} + 48 \, b^{4} + 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x + 15 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 18 \, a^{3} b + 12 \, a^{2} b^{2} + 8 \, {\left(56 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x + 2 \, {\left(27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x - 6 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3} - 7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4} - 30 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2} + 8 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{4} + 50 \, a^{3} b - 48 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} - 20 \, a^{3} b + 8 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} - 180 \, a^{3} b + 304 \, a^{2} b^{2} - 224 \, a b^{3} + 64 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{4} - 50 \, a^{3} b + 48 \, a^{2} b^{2} - 16 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 4 \, {\left(16 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(9 \, a^{3} b - 28 \, a^{2} b^{2} + 16 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 90 \, a^{2} b^{2} + 120 \, a b^{3} - 48 \, b^{4} - 8 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b - 68 \, a^{2} b^{2} + 32 \, a b^{3} - 16 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^8 + 128*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^4 - 2*a^3*b + a^2*b^2)*d*x*sinh(d*x + c)^8 + 4*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^6 + 4*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^2 + 9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^3 + 3*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^4 - 27*a^3*b + 90*a^2*b^2 - 120*a*b^3 + 48*b^4 + 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x + 15*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 36*a^3*b + 24*a^2*b^2 + 16*(56*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^4 - 2*a^3*b + a^2*b^2)*d*x + 4*(27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^6 + 15*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x - 6*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 - 20*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^6 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3 - 7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - 3*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4 - 30*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 - 20*a^3*b + 8*a^2*b^2 + 8*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 - 10*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^3 + (45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 - 15*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^4 - 15*a^4 + 50*a^3*b - 48*a^2*b^2 + 16*a*b^3 + 3*(45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 - 3*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^5 + (45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^3 - (15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4 - 2*(a^2 - 2*a*b)*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 - a^2 + 2*a*b)*sinh(d*x + c)^2 + a^2 - 8*a*b + 8*b^2 + 4*(a^2*cosh(d*x + c)^3 - (a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 - a*b)*cosh(d*x + c)^2 + 2*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 - a*b)*sinh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sqrt(-b/(a - b)))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + 8*(16*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 + 3*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 + (27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 - 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 - 30*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 - 10*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 - 15*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 - 2*a^6*b + a^5*b^2)*d + 8*((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^8 + 64*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^4 - 2*a^3*b + a^2*b^2)*d*x*sinh(d*x + c)^8 + 2*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^6 + 2*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^2 + 9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^3 + 3*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^4 - 27*a^3*b + 90*a^2*b^2 - 120*a*b^3 + 48*b^4 + 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x + 15*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 18*a^3*b + 12*a^2*b^2 + 8*(56*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^4 - 2*a^3*b + a^2*b^2)*d*x + 2*(27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^6 + 15*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x - 6*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^8 + 8*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 - 20*a^3*b + 8*a^2*b^2)*sinh(d*x + c)^8 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^6 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3 - 7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^3 - 3*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^4 + 45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4 - 30*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 - 20*a^3*b + 8*a^2*b^2 + 8*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^5 - 10*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^3 + (45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^2 + 4*(7*(15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^6 - 15*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^4 - 15*a^4 + 50*a^3*b - 48*a^2*b^2 + 16*a*b^3 + 3*(45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 - 20*a^3*b + 8*a^2*b^2)*cosh(d*x + c)^7 - 3*(15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c)^5 + (45*a^4 - 180*a^3*b + 304*a^2*b^2 - 224*a*b^3 + 64*b^4)*cosh(d*x + c)^3 - (15*a^4 - 50*a^3*b + 48*a^2*b^2 - 16*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a + 2*b)*sqrt(b/(a - b))/b) + 4*(16*(a^4 - 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 + 3*(9*a^3*b - 28*a^2*b^2 + 16*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 90*a^2*b^2 + 120*a*b^3 - 48*b^4 - 8*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*d*x)*cosh(d*x + c)^3 + (27*a^3*b - 68*a^2*b^2 + 32*a*b^3 - 16*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 - 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 - 30*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 - 10*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 - 15*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 - 2*a^6*b + a^5*b^2)*d + 8*((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
8,-1,0,0,0.000000," ","integrate(1/(a+b*csch(d*x+c)^2)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate((a+b*csch(d*x+c)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,6645,0,0.853193," ","integrate((a+b*csch(d*x+c)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) - {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a - b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a - b\right)} \sqrt{b} \log\left(\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1}\right) + {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{4 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}, \frac{2 \, {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a - b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a - b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) + {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{4 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}, -\frac{2 \, {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + 2 \, {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) + {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a - b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a - b\right)} \sqrt{b} \log\left(\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1}\right) + 2 \, \sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{4 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}, -\frac{{\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a - b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a - b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) + \sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{2 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) - ((3*a - b)*cosh(d*x + c)^4 + 4*(3*a - b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a - b)*sinh(d*x + c)^4 - 2*(3*a - b)*cosh(d*x + c)^2 + 2*(3*(3*a - b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^2 + 4*((3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + 3*a - b)*sqrt(b)*log(((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + 3*b)*sinh(d*x + c)^2 + 2*sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*((a + b)*cosh(d*x + c)^3 - (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)) + (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d), 1/4*(2*((3*a - b)*cosh(d*x + c)^4 + 4*(3*a - b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a - b)*sinh(d*x + c)^4 - 2*(3*a - b)*cosh(d*x + c)^2 + 2*(3*(3*a - b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^2 + 4*((3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + 3*a - b)*sqrt(-b)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d), -1/4*(2*(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + 2*(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + ((3*a - b)*cosh(d*x + c)^4 + 4*(3*a - b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a - b)*sinh(d*x + c)^4 - 2*(3*a - b)*cosh(d*x + c)^2 + 2*(3*(3*a - b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^2 + 4*((3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + 3*a - b)*sqrt(b)*log(((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + 3*b)*sinh(d*x + c)^2 + 2*sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*((a + b)*cosh(d*x + c)^3 - (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)) + 2*sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d), -1/2*((a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - ((3*a - b)*cosh(d*x + c)^4 + 4*(3*a - b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a - b)*sinh(d*x + c)^4 - 2*(3*a - b)*cosh(d*x + c)^2 + 2*(3*(3*a - b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^2 + 4*((3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + 3*a - b)*sqrt(-b)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)]","B",0
11,1,4389,0,0.851295," ","integrate((a+b*csch(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + 2 \, \sqrt{b} \log\left(\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, d}, \frac{4 \, \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) + \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, d}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - \sqrt{b} \log\left(\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}{\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1}\right)}{2 \, d}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - 2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right)}{2 \, d}\right]"," ",0,"[1/4*(sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + 2*sqrt(b)*log(((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + 3*b)*sinh(d*x + c)^2 - 2*sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*((a + b)*cosh(d*x + c)^3 - (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)) + sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, 1/4*(4*sqrt(-b)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) + sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/d, -1/2*(sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - sqrt(b)*log(((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + 3*b)*sinh(d*x + c)^2 - 2*sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*((a + b)*cosh(d*x + c)^3 - (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)))/d, -1/2*(sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 2*sqrt(-b)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)*sqrt(-b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/d]","B",0
12,1,1645,0,0.460717," ","integrate(1/(a+b*csch(d*x+c)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right)}{4 \, a d}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right)}{2 \, a d}\right]"," ",0,"[1/4*(sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/(a*d), -1/2*(sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)))/(a*d)]","B",0
13,1,3009,0,0.828558," ","integrate(1/(a+b*csch(d*x+c)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b + 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b + 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{2} {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d + 4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{{\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b + 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b + 4 \, {\left({\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - 2 \, \sqrt{2} {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{2 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d + 4 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(((a^2 - a*b)*cosh(d*x + c)^4 + 4*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - a*b)*sinh(d*x + c)^4 - 2*(a^2 - 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - a*b)*cosh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sinh(d*x + c)^2 + a^2 - a*b + 4*((a^2 - a*b)*cosh(d*x + c)^3 - (a^2 - 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + ((a^2 - a*b)*cosh(d*x + c)^4 + 4*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - a*b)*sinh(d*x + c)^4 - 2*(a^2 - 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - a*b)*cosh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sinh(d*x + c)^2 + a^2 - a*b + 4*((a^2 - a*b)*cosh(d*x + c)^3 - (a^2 - 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*sqrt(2)*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + a*b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^4 - a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^3*b)*d*sinh(d*x + c)^4 - 2*(a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 - a^3*b)*d + 4*((a^4 - a^3*b)*d*cosh(d*x + c)^3 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(((a^2 - a*b)*cosh(d*x + c)^4 + 4*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - a*b)*sinh(d*x + c)^4 - 2*(a^2 - 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - a*b)*cosh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sinh(d*x + c)^2 + a^2 - a*b + 4*((a^2 - a*b)*cosh(d*x + c)^3 - (a^2 - 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + ((a^2 - a*b)*cosh(d*x + c)^4 + 4*(a^2 - a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - a*b)*sinh(d*x + c)^4 - 2*(a^2 - 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - a*b)*cosh(d*x + c)^2 - a^2 + 3*a*b - 2*b^2)*sinh(d*x + c)^2 + a^2 - a*b + 4*((a^2 - a*b)*cosh(d*x + c)^3 - (a^2 - 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 2*sqrt(2)*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + a*b)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^4 - a^3*b)*d*cosh(d*x + c)^4 + 4*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^3*b)*d*sinh(d*x + c)^4 - 2*(a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 - a^3*b)*d + 4*((a^4 - a^3*b)*d*cosh(d*x + c)^3 - (a^4 - 3*a^3*b + 2*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
14,1,7831,0,1.218032," ","integrate(1/(a+b*csch(d*x+c)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4} - 30 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, a b^{2} \cosh\left(d x + c\right)^{4} + a^{3} - 4 \, a^{2} b + 9 \, a b^{2} + 30 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} + 3 \, a^{2} b + 3 \, {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 18 \, b^{2} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 6 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{3} - 4 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right) + 15 \, \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{2} + 20 \, \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3} + 15 \, \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{4} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6}}\right) + 3 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4} - 30 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + \sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}{\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}\right) + 8 \, \sqrt{2} {\left({\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} - 5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - a^{3} b + 4 \, a^{2} b^{2} - 2 \, a b^{3} - 6 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{12 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{3 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4} - 30 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + a\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(6 \, a b \cosh\left(d x + c\right)^{2} - a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right) + 3 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4} - 30 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 14 \, a^{3} b + 27 \, a^{2} b^{2} - 24 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} - 5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{3} b - 2 \, a^{2} b^{2} + 4 \, {\left(5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - a^{3} b + 4 \, a^{2} b^{2} - 2 \, a b^{3} - 6 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b - 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a \cosh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{2} - a + 2 \, b}{\cosh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2}}}}{6 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d + 8 \, {\left({\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} - 14 \, a^{6} b + 27 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} - 4 \, a^{6} b + 5 \, a^{5} b^{2} - 2 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(3*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4 - 30*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 2*a^3*b + a^2*b^2 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 - 10*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 - 15*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - a^4 + 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 - (a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log((a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + a*b^2 + b^3)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (70*a*b^2*cosh(d*x + c)^4 + a^3 - 4*a^2*b + 9*a*b^2 + 30*(a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(14*a*b^2*cosh(d*x + c)^5 + 10*(a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 2*(a^3 - 3*a^2*b)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 + 3*a^2*b + 3*(a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + sqrt(2)*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 18*b^2*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^2 + a^2 + 2*(3*b^2*cosh(d*x + c)^5 + 6*b^2*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(a*b^2 + b^3)*cosh(d*x + c)^5 + (a^3 - 4*a^2*b + 9*a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c))/(cosh(d*x + c)^6 + 6*cosh(d*x + c)^5*sinh(d*x + c) + 15*cosh(d*x + c)^4*sinh(d*x + c)^2 + 20*cosh(d*x + c)^3*sinh(d*x + c)^3 + 15*cosh(d*x + c)^2*sinh(d*x + c)^4 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6)) + 3*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4 - 30*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 2*a^3*b + a^2*b^2 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 - 10*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 - 15*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - a^4 + 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 - (a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a)*log(-(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 4*(a*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a)/(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*sqrt(2)*((3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^6 + 6*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3*b - 2*a^2*b^2)*sinh(d*x + c)^6 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3 - 5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^3*b - 2*a^2*b^2 + 4*(5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + 3*(5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^4 - a^3*b + 4*a^2*b^2 - 2*a*b^3 - 6*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 6*((3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^5 - 2*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 - 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 - 30*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 - 10*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 - 15*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 - 2*a^6*b + a^5*b^2)*d + 8*((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/6*(3*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4 - 30*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 2*a^3*b + a^2*b^2 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 - 10*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 - 15*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - a^4 + 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 - (a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan(sqrt(2)*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + a)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 - (a^2 - 3*a*b)*cosh(d*x + c)^2 + (6*a*b*cosh(d*x + c)^2 - a^2 + 3*a*b)*sinh(d*x + c)^2 + a^2 + 2*(2*a*b*cosh(d*x + c)^3 - (a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c))) + 3*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4 - 30*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 2*a^3*b + a^2*b^2 + 8*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 - 10*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2 + 4*(7*(a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 - 15*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - a^4 + 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*(3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 - 3*(a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + (3*a^4 - 14*a^3*b + 27*a^2*b^2 - 24*a*b^3 + 8*b^4)*cosh(d*x + c)^3 - (a^4 - 4*a^3*b + 5*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a)*arctan(sqrt(2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-a)*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2))/(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a)) - 4*sqrt(2)*((3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^6 + 6*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3*b - 2*a^2*b^2)*sinh(d*x + c)^6 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3 - 5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^3*b - 2*a^2*b^2 + 4*(5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + 3*(5*(3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^4 - a^3*b + 4*a^2*b^2 - 2*a*b^3 - 6*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 6*((3*a^3*b - 2*a^2*b^2)*cosh(d*x + c)^5 - 2*(a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (a^3*b - 4*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a*cosh(d*x + c)^2 + a*sinh(d*x + c)^2 - a + 2*b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^8 + 8*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 - 2*a^6*b + a^5*b^2)*d*sinh(d*x + c)^8 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^3 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^4 - 30*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d)*sinh(d*x + c)^4 - 4*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^5 - 10*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^3 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^6 - 15*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d)*sinh(d*x + c)^2 + (a^7 - 2*a^6*b + a^5*b^2)*d + 8*((a^7 - 2*a^6*b + a^5*b^2)*d*cosh(d*x + c)^7 - 3*(a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c)^5 + (3*a^7 - 14*a^6*b + 27*a^5*b^2 - 24*a^4*b^3 + 8*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 - 4*a^6*b + 5*a^5*b^2 - 2*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
15,-1,0,0,0.000000," ","integrate(1/(a+b*csch(d*x+c)^2)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,190,0,0.423201," ","integrate((1+csch(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{x \cosh\left(x\right)^{4} + 4 \, x \cosh\left(x\right) \sinh\left(x\right)^{3} + x \sinh\left(x\right)^{4} - 2 \, {\left(x - 1\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, x \cosh\left(x\right)^{2} - x + 1\right)} \sinh\left(x\right)^{2} - {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 4 \, {\left(x \cosh\left(x\right)^{3} - {\left(x - 1\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + x}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}"," ",0,"-(x*cosh(x)^4 + 4*x*cosh(x)*sinh(x)^3 + x*sinh(x)^4 - 2*(x - 1)*cosh(x)^2 + 2*(3*x*cosh(x)^2 - x + 1)*sinh(x)^2 - (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log(2*sinh(x)/(cosh(x) - sinh(x))) + 4*(x*cosh(x)^3 - (x - 1)*cosh(x))*sinh(x) + x)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
17,1,18,0,0.451804," ","integrate((1+csch(x)^2)^(1/2),x, algorithm=""fricas"")","-x + \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-x + log(2*sinh(x)/(cosh(x) - sinh(x)))","A",0
18,1,18,0,0.489177," ","integrate(1/(1+csch(x)^2)^(1/2),x, algorithm=""fricas"")","-x + \log\left(\frac{2 \, \cosh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-x + log(2*cosh(x)/(cosh(x) - sinh(x)))","A",0
19,1,528,0,0.503896," ","integrate((1-csch(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{\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} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 8 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(-\frac{1}{2} \, \cosh\left(x\right)^{2} - \cosh\left(x\right) \sinh\left(x\right) - \frac{1}{2} \, \sinh\left(x\right)^{2} + \frac{1}{2} \, \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}}} + \frac{1}{2}\right) - 2 \, \cosh\left(x\right)^{2} - {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\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} - 2\right)} \sinh\left(x\right)^{2} - \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{\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}}} - 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right) + {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(-\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) - \sinh\left(x\right)^{2} + \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}}} + 1\right) + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"1/2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 8*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*arctan(-1/2*cosh(x)^2 - cosh(x)*sinh(x) - 1/2*sinh(x)^2 + 1/2*sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1/2) - 2*cosh(x)^2 - (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 2)*sinh(x)^2 - sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*cosh(x)^2 + 4*(cosh(x)^3 - 2*cosh(x))*sinh(x) - 1) + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log(-cosh(x)^2 - 2*cosh(x)*sinh(x) - sinh(x)^2 + sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1) + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
20,1,221,0,0.441406," ","integrate((1-csch(x)^2)^(1/2),x, algorithm=""fricas"")","-2 \, \arctan\left(-\frac{1}{2} \, \cosh\left(x\right)^{2} - \cosh\left(x\right) \sinh\left(x\right) - \frac{1}{2} \, \sinh\left(x\right)^{2} + \frac{1}{2} \, \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}}} + \frac{1}{2}\right) - \frac{1}{2} \, \log\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 2\right)} \sinh\left(x\right)^{2} - \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{\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}}} - 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right) + \frac{1}{2} \, \log\left(-\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) - \sinh\left(x\right)^{2} + \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}}} + 1\right)"," ",0,"-2*arctan(-1/2*cosh(x)^2 - cosh(x)*sinh(x) - 1/2*sinh(x)^2 + 1/2*sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1/2) - 1/2*log(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 2)*sinh(x)^2 - sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*cosh(x)^2 + 4*(cosh(x)^3 - 2*cosh(x))*sinh(x) - 1) + 1/2*log(-cosh(x)^2 - 2*cosh(x)*sinh(x) - sinh(x)^2 + sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)","B",0
21,1,163,0,0.416714," ","integrate(1/(1-csch(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 2\right)} \sinh\left(x\right)^{2} - \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{\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}}} - 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right) + \frac{1}{2} \, \log\left(-\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) - \sinh\left(x\right)^{2} + \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}}} + 1\right)"," ",0,"-1/2*log(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 2)*sinh(x)^2 - sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*cosh(x)^2 + 4*(cosh(x)^3 - 2*cosh(x))*sinh(x) - 1) + 1/2*log(-cosh(x)^2 - 2*cosh(x)*sinh(x) - sinh(x)^2 + sqrt(2)*sqrt((cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)","B",0
22,1,666,0,0.451336," ","integrate((-1+csch(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-\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}}} + {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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} + 2\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1}\right) + {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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) - 2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + \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}}} + 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - \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}}} + 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-1/2*(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 2)*sinh(x)^2 + 4*cosh(x)^2 + 4*(cosh(x)^3 + 2*cosh(x))*sinh(x) - 1)) + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(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)) - 2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + sqrt(2)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - sqrt(2)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
23,1,358,0,0.418154," ","integrate((-1+csch(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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} + 2\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1}\right) + \frac{1}{2} \, \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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) - \frac{1}{2} \, \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + \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}}} + 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \frac{1}{2} \, \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - \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}}} + 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)"," ",0,"1/2*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 2)*sinh(x)^2 + 4*cosh(x)^2 + 4*(cosh(x)^3 + 2*cosh(x))*sinh(x) - 1)) + 1/2*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(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)) - 1/2*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + sqrt(2)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1/2*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - sqrt(2)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2))","B",0
24,1,213,0,0.405911," ","integrate(1/(-1+csch(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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} + 2\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + 2 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 1}\right) - \frac{1}{2} \, \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-\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}}}}{\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,"-1/2*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 2)*sinh(x)^2 + 4*cosh(x)^2 + 4*(cosh(x)^3 + 2*cosh(x))*sinh(x) - 1)) - 1/2*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(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
25,1,58,0,0.438216," ","integrate((-1-csch(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{i \, x e^{\left(4 \, x\right)} + {\left(-2 i \, x + 2 i\right)} e^{\left(2 \, x\right)} + {\left(-i \, e^{\left(4 \, x\right)} + 2 i \, e^{\left(2 \, x\right)} - i\right)} \log\left(e^{\left(2 \, x\right)} - 1\right) + i \, x}{e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 1}"," ",0,"(I*x*e^(4*x) + (-2*I*x + 2*I)*e^(2*x) + (-I*e^(4*x) + 2*I*e^(2*x) - I)*log(e^(2*x) - 1) + I*x)/(e^(4*x) - 2*e^(2*x) + 1)","C",0
26,1,13,0,0.453406," ","integrate((-1-csch(x)^2)^(1/2),x, algorithm=""fricas"")","-i \, x + i \, \log\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"-I*x + I*log(e^(2*x) - 1)","C",0
27,1,13,0,0.418021," ","integrate(1/(-1-csch(x)^2)^(1/2),x, algorithm=""fricas"")","i \, x - i \, \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"I*x - I*log(e^(2*x) + 1)","C",0
