1,1,2111,0,0.429827," ","integrate((a+b*coth(d*x+c)^2)^5,x, algorithm=""fricas"")","-\frac{{\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \sinh\left(d x + c\right)^{9} - 9 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x - 4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 890 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 9 \, {\left(6300 \, a^{4} b + 16800 \, a^{3} b^{2} + 19320 \, a^{2} b^{3} + 10560 \, a b^{4} + 2252 \, b^{5} + 14 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 1260 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x - 21 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(14 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 890 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 84 \, {\left(525 \, a^{4} b + 950 \, a^{3} b^{2} + 980 \, a^{2} b^{3} + 490 \, a b^{4} + 63 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(28 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 44100 \, a^{4} b - 117600 \, a^{3} b^{2} - 135240 \, a^{2} b^{3} - 73920 \, a b^{4} - 15764 \, b^{5} - 105 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 8820 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x + 120 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} - 21 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 890 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - 28 \, {\left(525 \, a^{4} b + 950 \, a^{3} b^{2} + 980 \, a^{2} b^{3} + 490 \, a b^{4} + 63 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, {\left(175 \, a^{4} b + 300 \, a^{3} b^{2} + 330 \, a^{2} b^{3} + 140 \, a b^{4} + 63 \, b^{5}\right)} \cosh\left(d x + c\right) - 9 \, {\left({\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 7 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 22050 \, a^{4} b + 58800 \, a^{3} b^{2} + 67620 \, a^{2} b^{3} + 36960 \, a b^{4} + 7882 \, b^{5} + 20 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4410 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x - 28 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{315 \, {\left(d \sinh\left(d x + c\right)^{9} + 9 \, {\left(4 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{7} + 9 \, {\left(14 \, d \cosh\left(d x + c\right)^{4} - 21 \, d \cosh\left(d x + c\right)^{2} + 4 \, d\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(28 \, d \cosh\left(d x + c\right)^{6} - 105 \, d \cosh\left(d x + c\right)^{4} + 120 \, d \cosh\left(d x + c\right)^{2} - 28 \, d\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(d \cosh\left(d x + c\right)^{8} - 7 \, d \cosh\left(d x + c\right)^{6} + 20 \, d \cosh\left(d x + c\right)^{4} - 28 \, d \cosh\left(d x + c\right)^{2} + 14 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/315*((1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^9 + 9*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)*sinh(d*x + c)^8 - (1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*sinh(d*x + c)^9 - 9*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^7 + 9*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x - 4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^3 - 3*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 890*a*b^4 + 213*b^5)*cosh(d*x + c)^5 - 9*(6300*a^4*b + 16800*a^3*b^2 + 19320*a^2*b^3 + 10560*a*b^4 + 2252*b^5 + 14*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^4 + 1260*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x - 21*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(14*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^5 - 35*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^3 + 20*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 890*a*b^4 + 213*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 - 84*(525*a^4*b + 950*a^3*b^2 + 980*a^2*b^3 + 490*a*b^4 + 63*b^5)*cosh(d*x + c)^3 - 3*(28*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^6 - 44100*a^4*b - 117600*a^3*b^2 - 135240*a^2*b^3 - 73920*a*b^4 - 15764*b^5 - 105*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^4 - 8820*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x + 120*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^7 - 21*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^5 + 40*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 890*a*b^4 + 213*b^5)*cosh(d*x + c)^3 - 28*(525*a^4*b + 950*a^3*b^2 + 980*a^2*b^3 + 490*a*b^4 + 63*b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + 126*(175*a^4*b + 300*a^3*b^2 + 330*a^2*b^3 + 140*a*b^4 + 63*b^5)*cosh(d*x + c) - 9*((1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^8 - 7*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^6 + 22050*a^4*b + 58800*a^3*b^2 + 67620*a^2*b^3 + 36960*a*b^4 + 7882*b^5 + 20*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^4 + 4410*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x - 28*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^9 + 9*(4*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^7 + 9*(14*d*cosh(d*x + c)^4 - 21*d*cosh(d*x + c)^2 + 4*d)*sinh(d*x + c)^5 + 3*(28*d*cosh(d*x + c)^6 - 105*d*cosh(d*x + c)^4 + 120*d*cosh(d*x + c)^2 - 28*d)*sinh(d*x + c)^3 + 9*(d*cosh(d*x + c)^8 - 7*d*cosh(d*x + c)^6 + 20*d*cosh(d*x + c)^4 - 28*d*cosh(d*x + c)^2 + 14*d)*sinh(d*x + c))","B",0
2,1,1164,0,0.460578," ","integrate((a+b*coth(d*x+c)^2)^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{7} - 28 \, {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x - 3 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 140 \, {\left({\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(45 \, a^{3} b + 60 \, a^{2} b^{2} + 41 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(5 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 1260 \, a^{3} b + 2520 \, a^{2} b^{2} + 1932 \, a b^{3} + 528 \, b^{4} + 315 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x - 10 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 28 \, {\left(3 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(45 \, a^{3} b + 60 \, a^{2} b^{2} + 41 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 420 \, {\left(5 \, a^{3} b + 6 \, a^{2} b^{2} + 5 \, a b^{3}\right)} \cosh\left(d x + c\right) - 7 \, {\left({\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2100 \, a^{3} b - 4200 \, a^{2} b^{2} - 3220 \, a b^{3} - 880 \, b^{4} - 525 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x + 9 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{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 + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^7 + 28*(105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 - (420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*sinh(d*x + c)^7 - 28*(75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4)*cosh(d*x + c)^5 + 7*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x - 3*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 140*((105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^3 - (75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(45*a^3*b + 60*a^2*b^2 + 41*a*b^3 + 14*b^4)*cosh(d*x + c)^3 - 7*(5*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^4 + 1260*a^3*b + 2520*a^2*b^2 + 1932*a*b^3 + 528*b^4 + 315*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x - 10*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 28*(3*(105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^5 - 10*(75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4)*cosh(d*x + c)^3 + 9*(45*a^3*b + 60*a^2*b^2 + 41*a*b^3 + 14*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - 420*(5*a^3*b + 6*a^2*b^2 + 5*a*b^3)*cosh(d*x + c) - 7*((420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^6 - 5*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^4 - 2100*a^3*b - 4200*a^2*b^2 - 3220*a*b^3 - 880*b^4 - 525*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x + 9*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(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
3,1,557,0,0.452778," ","integrate((a+b*coth(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(27 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 2 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(27 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 90 \, a^{2} b + 120 \, a b^{2} + 46 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 3 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\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 + 60*a*b^2 + 23*b^3)*cosh(d*x + c)^5 + 5*(45*a^2*b + 60*a*b^2 + 23*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 - (45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^5 - 5*(27*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 5*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 2*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(45*a^2*b + 60*a*b^2 + 23*b^3)*cosh(d*x + c)^3 - 3*(27*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(9*a^2*b + 6*a*b^2 + 5*b^3)*cosh(d*x + c) - 5*((45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 90*a^2*b + 120*a*b^2 + 46*b^3 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 3*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*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
4,1,197,0,0.502610," ","integrate((a+b*coth(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} - 6 \, a b \cosh\left(d x + c\right) + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a b + 4 \, 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 + 2*b^2)*cosh(d*x + c)^3 + 6*(3*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*(a^2 + 2*a*b + b^2)*d*x + 6*a*b + 4*b^2)*sinh(d*x + c)^3 - 6*a*b*cosh(d*x + c) + 3*(3*(a^2 + 2*a*b + b^2)*d*x - (3*(a^2 + 2*a*b + b^2)*d*x + 6*a*b + 4*b^2)*cosh(d*x + c)^2 + 6*a*b + 4*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
5,1,488,0,0.428703," ","integrate(1/(a+b*coth(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{-\frac{b}{a}} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - b^{2}\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} + a b\right)} \sqrt{-\frac{b}{a}}}{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}\right)}{2 \, {\left(a + b\right)} d}, \frac{d x - \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a + b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right)}{{\left(a + b\right)} d}\right]"," ",0,"[1/2*(2*d*x + sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 - b^2)*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 + a*b)*sqrt(-b/a))/((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)))/((a + b)*d), (d*x - sqrt(b/a)*arctan(1/2*((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(b/a)/b))/((a + b)*d)]","B",0
6,1,1952,0,0.476482," ","integrate(1/(a+b*coth(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} - a b\right)} d x - a b + 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} - a b\right)} d x + a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + b^{2} + 4 \, {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - b^{2}\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} + a b\right)} \sqrt{-\frac{b}{a}}}{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}\right) - 4 \, a b - 4 \, b^{2} + 8 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} + a b\right)} 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} - a b\right)} d x - a b + 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} - a b\right)} d x + a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + b^{2} + 4 \, {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a + b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 2 \, a b - 2 \, b^{2} + 4 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a^2 + a*b)*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 - a*b)*d*x - a*b + b^2)*cosh(d*x + c)^2 + 4*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 - 2*(a^2 - a*b)*d*x + a*b - b^2)*sinh(d*x + c)^2 + ((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^4 - 2*(3*a^2 - 2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 - 3*a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + b^2 + 4*((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 - (3*a^2 - 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 - b^2)*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 + a*b)*sqrt(-b/a))/((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)) - 4*a*b - 4*b^2 + 8*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 - (2*(a^2 - a*b)*d*x - a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 - 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*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 - a*b)*d*x - a*b + b^2)*cosh(d*x + c)^2 + 2*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 - 2*(a^2 - a*b)*d*x + a*b - b^2)*sinh(d*x + c)^2 - ((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^4 - 2*(3*a^2 - 2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 - 3*a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + b^2 + 4*((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 - (3*a^2 - 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*((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(b/a)/b) - 2*a*b - 2*b^2 + 4*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 - (2*(a^2 - a*b)*d*x - a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 - 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
7,1,7508,0,0.668558," ","integrate(1/(a+b*coth(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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\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 + 9 \, a^{2} b^{2} - 21 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x + 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 36 \, a^{3} b - 84 \, a^{2} b^{2} - 60 \, a b^{3} - 12 \, b^{4} + 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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\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 + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x - 6 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} - 7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4} - 30 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{4} - 10 \, a^{3} b + 12 \, a^{2} b^{2} + 10 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - b^{2}\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} + a b\right)} \sqrt{-\frac{b}{a}}}{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b}\right) + 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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\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 + 9 \, a^{2} b^{2} - 21 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x + 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 18 \, a^{3} b - 42 \, a^{2} b^{2} - 30 \, a b^{3} - 6 \, b^{4} + 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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\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 + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x - 6 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} - 7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4} - 30 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{4} - 10 \, a^{3} b + 12 \, a^{2} b^{2} + 10 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} - a + b\right)} \sqrt{\frac{b}{a}}}{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 - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*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 + 9*a^2*b^2 - 21*a*b^3 - 9*b^4 + 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x + 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 36*a^3*b - 84*a^2*b^2 - 60*a*b^3 - 12*b^4 + 16*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*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 + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^4 + 27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x - 6*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*sinh(d*x + c)^8 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^6 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 - 7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^3 - 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4 - 30*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^5 - 10*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^6 - 15*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^4 - 15*a^4 - 10*a^3*b + 12*a^2*b^2 + 10*a*b^3 + 3*b^4 + 3*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^7 - 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^3 - (15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 - 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 - b^2)*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 + a*b)*sqrt(-b/a))/((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 - 2*(a - b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)) + 8*(16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 + 3*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 - 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 - 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 - 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 - 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 - 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*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 + 9*a^2*b^2 - 21*a*b^3 - 9*b^4 + 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x + 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 18*a^3*b - 42*a^2*b^2 - 30*a*b^3 - 6*b^4 + 8*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 + 5*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*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 + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^4 + 27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x - 6*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*sinh(d*x + c)^8 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^6 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 - 7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^3 - 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4 - 30*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^5 - 10*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^6 - 15*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^4 - 15*a^4 - 10*a^3*b + 12*a^2*b^2 + 10*a*b^3 + 3*b^4 + 3*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^7 - 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^3 - (15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*((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(b/a)/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 - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 - 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 - 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 - 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 - 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 - 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 - (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
8,-1,0,0,0.000000," ","integrate(1/(a+b*coth(d*x+c)^2)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,70,0,0.634488," ","integrate(1/(1-2*coth(x)^2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} - 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} + 3}\right) - x"," ",0,"1/2*sqrt(2)*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 + 2*sqrt(2) - 3)/(cosh(x)^2 + sinh(x)^2 + 3)) - x","B",0
10,1,1,0,0.483635," ","integrate((1-coth(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
11,1,17,0,0.444051," ","integrate((-1+coth(x)^2)^(1/2),x, algorithm=""fricas"")","-\log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \log\left(\cosh\left(x\right) + \sinh\left(x\right) - 1\right)"," ",0,"-log(cosh(x) + sinh(x) + 1) + log(cosh(x) + sinh(x) - 1)","A",0
12,1,1,0,0.430551," ","integrate((1-coth(x)^2)^(3/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
13,1,211,0,0.415134," ","integrate((-1+coth(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \cosh\left(x\right)^{3} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + 2 \, \sinh\left(x\right)^{3} - {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \log\left(\cosh\left(x\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) + \sinh\left(x\right) - 1\right) + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\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)}}"," ",0,"-1/2*(2*cosh(x)^3 + 6*cosh(x)*sinh(x)^2 + 2*sinh(x)^3 - (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*log(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) + sinh(x) - 1) + 2*(3*cosh(x)^2 + 1)*sinh(x) + 2*cosh(x))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
14,1,1,0,0.406875," ","integrate(1/(1-coth(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
15,1,2,0,0.396465," ","integrate(1/(-1+coth(x)^2)^(1/2),x, algorithm=""fricas"")","\cosh\left(x\right)"," ",0,"cosh(x)","A",0
16,1,2367,0,0.568839," ","integrate(coth(x)^3*(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 4 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 4 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 4 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 4 \, b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)}}, -\frac{3 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 4 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 4 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 4 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 4 \, b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)}}\right]"," ",0,"[1/12*(3*(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + 4*b)*cosh(x)^4 + 4*(a + 4*b)*cosh(x)*sinh(x)^3 + (a + 4*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 4*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 4*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 4*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b), -1/6*(3*(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + 4*b)*cosh(x)^4 + 4*(a + 4*b)*cosh(x)*sinh(x)^3 + (a + 4*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 4*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 4*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 4*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)]","B",0
17,1,4877,0,0.656012," ","integrate(coth(x)^2*(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, \frac{2 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{{\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}\right]"," ",0,"[1/4*((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b), 1/4*(2*((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b), -1/4*(2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b), -1/2*((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a - 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 - (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)]","B",0
18,1,1551,0,0.482566," ","integrate(coth(x)*(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, -\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}\right]"," ",0,"[1/4*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), -1/2*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)]","B",0
19,1,3455,0,0.593125," ","integrate((a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{2} \, \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{2} \, \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)\right]"," ",0,"[1/4*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/2*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 1/4*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 1/4*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 1/2*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b))]","B",0
20,1,3479,0,0.811260," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{2} \, \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{2} \, \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right), \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)\right]"," ",0,"[1/4*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/2*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + 1/4*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 1/4*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 1/2*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)), sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b))]","B",0
21,1,1539,0,0.473476," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""fricas"")","\left[\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, -\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}\right]"," ",0,"[1/4*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), -1/2*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)]","B",0
22,1,4940,0,0.804332," ","integrate(coth(x)^3*(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 20 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 20 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 26 \, a b + 23 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{60 \, {\left(b \cosh\left(x\right)^{10} + 10 \, b \cosh\left(x\right) \sinh\left(x\right)^{9} + b \sinh\left(x\right)^{10} - 5 \, b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, b \cosh\left(x\right)^{6} + 10 \, {\left(21 \, b \cosh\left(x\right)^{4} - 14 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b \cosh\left(x\right)^{5} - 70 \, b \cosh\left(x\right)^{3} + 15 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, b \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b \cosh\left(x\right)^{6} - 35 \, b \cosh\left(x\right)^{4} + 15 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b \cosh\left(x\right)^{7} - 7 \, b \cosh\left(x\right)^{5} + 5 \, b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, b \cosh\left(x\right)^{2} + 5 \, {\left(9 \, b \cosh\left(x\right)^{8} - 28 \, b \cosh\left(x\right)^{6} + 30 \, b \cosh\left(x\right)^{4} - 12 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b \cosh\left(x\right)^{9} - 4 \, b \cosh\left(x\right)^{7} + 6 \, b \cosh\left(x\right)^{5} - 4 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)}}, -\frac{15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} - 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 20 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{2} - 3 \, a^{2} - 20 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 26 \, a b + 23 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{30 \, {\left(b \cosh\left(x\right)^{10} + 10 \, b \cosh\left(x\right) \sinh\left(x\right)^{9} + b \sinh\left(x\right)^{10} - 5 \, b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, b \cosh\left(x\right)^{6} + 10 \, {\left(21 \, b \cosh\left(x\right)^{4} - 14 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b \cosh\left(x\right)^{5} - 70 \, b \cosh\left(x\right)^{3} + 15 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 10 \, b \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b \cosh\left(x\right)^{6} - 35 \, b \cosh\left(x\right)^{4} + 15 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b \cosh\left(x\right)^{7} - 7 \, b \cosh\left(x\right)^{5} + 5 \, b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, b \cosh\left(x\right)^{2} + 5 \, {\left(9 \, b \cosh\left(x\right)^{8} - 28 \, b \cosh\left(x\right)^{6} + 30 \, b \cosh\left(x\right)^{4} - 12 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b \cosh\left(x\right)^{9} - 4 \, b \cosh\left(x\right)^{7} + 6 \, b \cosh\left(x\right)^{5} - 4 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b\right)}}\right]"," ",0,"[1/60*(15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 - 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 - 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 - 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 - 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 - 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 - 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 - 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 - 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a*b - b^2 + 10*((a*b + b^2)*cosh(x)^9 - 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 - 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 - 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 - 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 - 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 - 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 - 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 - 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 - 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 - 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a*b - b^2 + 10*((a*b + b^2)*cosh(x)^9 - 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 - 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^8 + 8*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 26*a*b + 23*b^2)*sinh(x)^8 - 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^2 - 3*a^2 - 20*a*b - 12*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^3 - 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^4 - 30*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 9*a^2 + 54*a*b + 49*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^5 - 10*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^3 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^6 - 15*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^4 + 3*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^2 - 3*a^2 - 20*a*b - 12*b^2)*sinh(x)^2 + 3*a^2 + 26*a*b + 23*b^2 + 8*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^7 - 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^5 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x)^3 - (3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^10 + 10*b*cosh(x)*sinh(x)^9 + b*sinh(x)^10 - 5*b*cosh(x)^8 + 5*(9*b*cosh(x)^2 - b)*sinh(x)^8 + 40*(3*b*cosh(x)^3 - b*cosh(x))*sinh(x)^7 + 10*b*cosh(x)^6 + 10*(21*b*cosh(x)^4 - 14*b*cosh(x)^2 + b)*sinh(x)^6 + 4*(63*b*cosh(x)^5 - 70*b*cosh(x)^3 + 15*b*cosh(x))*sinh(x)^5 - 10*b*cosh(x)^4 + 10*(21*b*cosh(x)^6 - 35*b*cosh(x)^4 + 15*b*cosh(x)^2 - b)*sinh(x)^4 + 40*(3*b*cosh(x)^7 - 7*b*cosh(x)^5 + 5*b*cosh(x)^3 - b*cosh(x))*sinh(x)^3 + 5*b*cosh(x)^2 + 5*(9*b*cosh(x)^8 - 28*b*cosh(x)^6 + 30*b*cosh(x)^4 - 12*b*cosh(x)^2 + b)*sinh(x)^2 + 10*(b*cosh(x)^9 - 4*b*cosh(x)^7 + 6*b*cosh(x)^5 - 4*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b), -1/30*(15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 - 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 - 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 - 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 - 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 - 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 - 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 - 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 - 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a*b - b^2 + 10*((a*b + b^2)*cosh(x)^9 - 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 - 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 - 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 - 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 - 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 - 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 - 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 - 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 - (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 - 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 - 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a*b - b^2 + 10*((a*b + b^2)*cosh(x)^9 - 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 - 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^8 + 8*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 26*a*b + 23*b^2)*sinh(x)^8 - 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^2 - 3*a^2 - 20*a*b - 12*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^3 - 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^4 - 30*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 9*a^2 + 54*a*b + 49*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^5 - 10*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^3 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x))*sinh(x)^3 - 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^6 - 15*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^4 + 3*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^2 - 3*a^2 - 20*a*b - 12*b^2)*sinh(x)^2 + 3*a^2 + 26*a*b + 23*b^2 + 8*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^7 - 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^5 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x)^3 - (3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^10 + 10*b*cosh(x)*sinh(x)^9 + b*sinh(x)^10 - 5*b*cosh(x)^8 + 5*(9*b*cosh(x)^2 - b)*sinh(x)^8 + 40*(3*b*cosh(x)^3 - b*cosh(x))*sinh(x)^7 + 10*b*cosh(x)^6 + 10*(21*b*cosh(x)^4 - 14*b*cosh(x)^2 + b)*sinh(x)^6 + 4*(63*b*cosh(x)^5 - 70*b*cosh(x)^3 + 15*b*cosh(x))*sinh(x)^5 - 10*b*cosh(x)^4 + 10*(21*b*cosh(x)^6 - 35*b*cosh(x)^4 + 15*b*cosh(x)^2 - b)*sinh(x)^4 + 40*(3*b*cosh(x)^7 - 7*b*cosh(x)^5 + 5*b*cosh(x)^3 - b*cosh(x))*sinh(x)^3 + 5*b*cosh(x)^2 + 5*(9*b*cosh(x)^8 - 28*b*cosh(x)^6 + 30*b*cosh(x)^4 - 12*b*cosh(x)^2 + b)*sinh(x)^2 + 10*(b*cosh(x)^9 - 4*b*cosh(x)^7 + 6*b*cosh(x)^5 - 4*b*cosh(x)^3 + b*cosh(x))*sinh(x) - b)]","B",0
23,-1,0,0,0.000000," ","integrate(coth(x)^2*(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,1,2362,0,0.581468," ","integrate(coth(x)*(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - a - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - a - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{4} - 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \cosh\left(x\right)^{4} - 6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 3 \, \cosh\left(x\right)^{2} + 6 \, {\left(\cosh\left(x\right)^{5} - 2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right)}}, -\frac{3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 8 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{4} - 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \cosh\left(x\right)^{4} - 6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 3 \, \cosh\left(x\right)^{2} + 6 \, {\left(\cosh\left(x\right)^{5} - 2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) - 1\right)}}\right]"," ",0,"[1/12*(3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 - 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 - a - b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 - 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 - 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 - 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) - a - b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 - 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 - a - b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 - 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 - 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 - 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) - a - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - (2*a + b)*cosh(x)^2 + (6*(a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 2*(2*(a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + 3*(5*cosh(x)^2 - 1)*sinh(x)^4 - 3*cosh(x)^4 + 4*(5*cosh(x)^3 - 3*cosh(x))*sinh(x)^3 + 3*(5*cosh(x)^4 - 6*cosh(x)^2 + 1)*sinh(x)^2 + 3*cosh(x)^2 + 6*(cosh(x)^5 - 2*cosh(x)^3 + cosh(x))*sinh(x) - 1), -1/6*(3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 - 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 - a - b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 - 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 - 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 - 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) - a - b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 - 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 - a - b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 - 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 - 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 - 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) - a - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 8*sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - (2*a + b)*cosh(x)^2 + (6*(a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 2*(2*(a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + 3*(5*cosh(x)^2 - 1)*sinh(x)^4 - 3*cosh(x)^4 + 4*(5*cosh(x)^3 - 3*cosh(x))*sinh(x)^3 + 3*(5*cosh(x)^4 - 6*cosh(x)^2 + 1)*sinh(x)^2 + 3*cosh(x)^2 + 6*(cosh(x)^5 - 2*cosh(x)^3 + cosh(x))*sinh(x) - 1)]","B",0
25,1,5037,0,0.735202," ","integrate((a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, \frac{2 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, -\frac{2 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} - 3 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 - 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 - 3*a - 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 - (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), 1/4*(2*((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 - 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 - 3*a - 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 - (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), -1/4*(2*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 2*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 - 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 - 3*a - 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 - (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 - 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 - 3*a - 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 - (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)]","B",0
26,1,3949,0,0.678141," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, \frac{4 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, \frac{2 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - 2 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), 1/4*(4*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), 1/2*(2*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - 2*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)]","B",0
27,1,4025,0,0.659699," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, \frac{4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), 1/4*(4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - 2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)]","B",0
28,1,683,0,0.437510," ","integrate((1+coth(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 4\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{4} + 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} + 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} + 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\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} + 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\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} - 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\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,"1/4*sqrt(2)*log(2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 3)*sinh(x)^6 + 3*cosh(x)^6 + 2*(28*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 + 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 45*cosh(x)^4 + 30*cosh(x)^2 + 4)*sinh(x)^2 + 4*cosh(x)^2 + 2*(4*cosh(x)^7 + 9*cosh(x)^5 + 10*cosh(x)^3 + 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^4 + 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 + 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 + 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) + 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(2)*log(-2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 - 1)*sinh(x)^2 - cosh(x)^2 + 2*(2*cosh(x)^3 - cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(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 + 2*sqrt((cosh(x)^2 + sinh(x)^2)/(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 - 2*sqrt((cosh(x)^2 + sinh(x)^2)/(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
29,1,228,0,0.456655," ","integrate((-1-coth(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-2} \log\left(-{\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{4} \, \sqrt{-2} \log\left({\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{4} \, \sqrt{-2} \log\left(-2 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} + \sqrt{-2} e^{\left(4 \, x\right)} + \sqrt{-2} e^{\left(2 \, x\right)} + 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) - \frac{1}{4} \, \sqrt{-2} \log\left(-2 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} - \sqrt{-2} e^{\left(4 \, x\right)} - \sqrt{-2} e^{\left(2 \, x\right)} - 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) - \frac{1}{2} i \, \log\left({\left(4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} - 4\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{2} i \, \log\left({\left(-4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} - 4\right)} e^{\left(-2 \, x\right)}\right)"," ",0,"-1/4*sqrt(-2)*log(-(sqrt(-2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) - 2)*e^(-2*x)) + 1/4*sqrt(-2)*log((sqrt(-2)*sqrt(-2*e^(4*x) - 2) - 2*e^(2*x) + 2)*e^(-2*x)) + 1/4*sqrt(-2)*log(-2*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) + sqrt(-2)*e^(4*x) + sqrt(-2)*e^(2*x) + 2*sqrt(-2))*e^(-4*x)) - 1/4*sqrt(-2)*log(-2*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) - sqrt(-2)*e^(4*x) - sqrt(-2)*e^(2*x) - 2*sqrt(-2))*e^(-4*x)) - 1/2*I*log((4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) - 4)*e^(-2*x)) + 1/2*I*log((-4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) - 4)*e^(-2*x))","C",0
30,1,1043,0,0.447993," ","integrate((1+coth(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 4\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{4} + 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} + 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} + 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 5 \, {\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} + 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\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) + 5 \, {\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} - 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\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) - 4 \, {\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}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"1/4*(2*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 3)*sinh(x)^6 + 3*cosh(x)^6 + 2*(28*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 + 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 45*cosh(x)^4 + 30*cosh(x)^2 + 4)*sinh(x)^2 + 4*cosh(x)^2 + 2*(4*cosh(x)^7 + 9*cosh(x)^5 + 10*cosh(x)^3 + 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^4 + 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 + 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 + 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) + 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 - 1)*sinh(x)^2 - cosh(x)^2 + 2*(2*cosh(x)^3 - cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 5*(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 + 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 5*(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 - 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt((cosh(x)^2 + sinh(x)^2)/(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
31,1,361,0,0.443381," ","integrate((-1-coth(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} - 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(2 \, {\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) - 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} - 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(-2 \, {\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) + {\left(5 i \, e^{\left(4 \, x\right)} - 10 i \, e^{\left(2 \, x\right)} + 5 i\right)} \log\left({\left(4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} - 4\right)} e^{\left(-2 \, x\right)}\right) + {\left(-5 i \, e^{\left(4 \, x\right)} + 10 i \, e^{\left(2 \, x\right)} - 5 i\right)} \log\left({\left(-4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} - 4\right)} e^{\left(-2 \, x\right)}\right) - 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} - 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(4 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} + \sqrt{-2} e^{\left(4 \, x\right)} + \sqrt{-2} e^{\left(2 \, x\right)} + 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) + 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} - 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(4 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} - \sqrt{-2} e^{\left(4 \, x\right)} - \sqrt{-2} e^{\left(2 \, x\right)} - 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) + 2 \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 1\right)}}{4 \, {\left(e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"1/4*(2*(sqrt(-2)*e^(4*x) - 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(2*(sqrt(-2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) - 2)*e^(-2*x)) - 2*(sqrt(-2)*e^(4*x) - 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(-2*(sqrt(-2)*sqrt(-2*e^(4*x) - 2) - 2*e^(2*x) + 2)*e^(-2*x)) + (5*I*e^(4*x) - 10*I*e^(2*x) + 5*I)*log((4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) - 4)*e^(-2*x)) + (-5*I*e^(4*x) + 10*I*e^(2*x) - 5*I)*log((-4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) - 4)*e^(-2*x)) - 2*(sqrt(-2)*e^(4*x) - 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(4*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) + sqrt(-2)*e^(4*x) + sqrt(-2)*e^(2*x) + 2*sqrt(-2))*e^(-4*x)) + 2*(sqrt(-2)*e^(4*x) - 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(4*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) - sqrt(-2)*e^(4*x) - sqrt(-2)*e^(2*x) - 2*sqrt(-2))*e^(-4*x)) + 2*sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 1))/(e^(4*x) - 2*e^(2*x) + 1)","C",0
32,1,1576,0,0.534117," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)}}, -\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)}}\right]"," ",0,"[1/4*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2), -1/2*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)]","B",0
33,1,3513,0,0.651249," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} b \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \sqrt{a + b} b \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a b + b^{2}\right)}}, \frac{4 \, {\left(a + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{a + b} b \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} b \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a b + b^{2}\right)}}, -\frac{\sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(a + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right)}{2 \, {\left(a b + b^{2}\right)}}, -\frac{\sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, {\left(a + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)}{2 \, {\left(a b + b^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*b*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)) + sqrt(a + b)*b*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b + b^2), 1/4*(4*(a + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(a + b)*b*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*b*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b + b^2), -1/2*(sqrt(-a - b)*b*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*b*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - (a + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 - 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)))/(a*b + b^2), -1/2*(sqrt(-a - b)*b*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*b*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - 2*(a + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)))/(a*b + b^2)]","B",0
34,1,1298,0,0.477813," ","integrate(coth(x)/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a + b\right)}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a + b), -1/2*(sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)))/(a + b)]","B",0
35,1,1357,0,0.497492," ","integrate(1/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a + b\right)}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a + b), -1/2*(sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)))/(a + b)]","B",0
36,1,3397,0,0.644348," ","integrate(tanh(x)/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} a \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + \sqrt{a + b} a \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, \frac{4 \, \sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{a + b} a \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} a \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, -\frac{a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - {\left(a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right)}{2 \, {\left(a^{2} + a b\right)}}, \frac{2 \, \sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right)}{2 \, {\left(a^{2} + a b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*a*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + sqrt(a + b)*a*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), 1/4*(4*sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(a + b)*a*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*a*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), -1/2*(a*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + a*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - (a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)))/(a^2 + a*b), 1/2*(2*sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - a*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - a*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)))/(a^2 + a*b)]","B",0
37,1,1621,0,0.531644," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)}}, -\frac{{\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)}}\right]"," ",0,"[1/4*((a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b), -1/2*((a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)]","B",0
38,1,2541,0,0.586512," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} - 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4} - 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} - 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4} - 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 - a*b + b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 - (a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 - a*b + b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 - (a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 - a^2 - a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)*sinh(x)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sinh(x)^4 + a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 - 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x)^2 - 2*(a^3*b + a^2*b^2 - a*b^3 - b^4 - 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^3 - (a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x))*sinh(x)), -1/2*(((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 - a*b + b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 - (a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 - a*b + b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 - (a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 - a^2 - a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)*sinh(x)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sinh(x)^4 + a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 - 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x)^2 - 2*(a^3*b + a^2*b^2 - a*b^3 - b^4 - 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^3 - (a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x))*sinh(x))]","B",0
39,1,2279,0,0.606351," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x)), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))]","B",0
40,1,2299,0,0.589449," ","integrate(coth(x)/(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x)), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))]","B",0
41,1,6991,0,0.894389," ","integrate(tanh(x)/(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} - a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), 1/4*(4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a + b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 - (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), 1/2*(2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - a*b^2 - b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 - (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 - a^2*b)*cosh(x)^2 - 2*(a^3 - a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 - 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x))]","B",0
42,1,3931,0,0.822401," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} - {\left(a^{3} - 3 \, a^{2} b - 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b - 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} - {\left(a^{3} - 3 \, a^{2} b - 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b - 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} - {\left(a^{3} - 3 \, a^{2} b - 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b - 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} - {\left(a^{3} - 3 \, a^{2} b - 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b - 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 - (a^3 - 3*a^2*b)*cosh(x)^4 - (a^3 - 3*a^2*b - 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 + a^3 + a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b - 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 - 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 - (a^3 - 3*a^2*b)*cosh(x)^4 - (a^3 - 3*a^2*b - 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 + a^3 + a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b - 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 - 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 - 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3 - 3*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^3 - (a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 + 6*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^5 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^6 + a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^4 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 - 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 - (a^3 - 3*a^2*b)*cosh(x)^4 - (a^3 - 3*a^2*b - 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 + a^3 + a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b - 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 - 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 - (a^3 - 3*a^2*b)*cosh(x)^4 - (a^3 - 3*a^2*b - 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 + a^3 + a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b - 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 - 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 - 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x)^2 - 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3 - 3*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^3 - (a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 + 6*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^5 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^6 + a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^4 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 - 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x))]","B",0
43,1,6560,0,1.001540," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{2} b - b^{3} - 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} - a^{2} b + b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{2} b - b^{3} - 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} - a^{2} b + b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} - 5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} + a^{2} b + 5 \, a b^{2} + 3 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b - a b^{2} + b^{3} - 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} - 7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6} + 35 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{6} - a^{5} b - 3 \, a^{4} b^{2} - 2 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + 3 \, a b^{5} + b^{6} - 15 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{2} b - b^{3} - 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} - a^{2} b + b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{2} b - b^{3} - 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} - 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} - a^{2} b + b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - 2 \, \sqrt{2} {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} - 5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} + a^{2} b + 5 \, a b^{2} + 3 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b - a b^{2} + b^{3} - 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} - 7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6} + 35 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{6} - a^{5} b - 3 \, a^{4} b^{2} - 2 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + 3 \, a b^{5} + b^{6} - 15 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 - 4*(a^2*b - b^3)*cosh(x)^6 - 4*(a^2*b - b^3 - 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 - 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 - 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 - 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 - 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 - 15*(a^2*b - b^3)*cosh(x)^4 - a^2*b + b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 - 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 - (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 - 4*(a^2*b - b^3)*cosh(x)^6 - 4*(a^2*b - b^3 - 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 - 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 - 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 - 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 - 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 - 15*(a^2*b - b^3)*cosh(x)^4 - a^2*b + b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 - 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 - (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^6 + 6*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)*sinh(x)^5 + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*sinh(x)^6 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 - 3*(a^3 - a^2*b - a*b^2 + b^3 - 5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 - a^3 + a^2*b + 5*a*b^2 + 3*b^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^4 + a^3 - a^2*b - a*b^2 + b^3 - 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^5 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^8 + 8*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)*sinh(x)^7 + (a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*sinh(x)^8 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^6 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 - 7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^2)*sinh(x)^6 + a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^3 - 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^4 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6 + 35*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^4 - 30*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^5 - 10*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^3 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x))*sinh(x)^3 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2 + 4*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^6 - a^5*b - 3*a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + 3*a*b^5 + b^6 - 15*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^4 + 3*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^7 - 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^5 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^3 - (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)), -1/6*(3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 - 4*(a^2*b - b^3)*cosh(x)^6 - 4*(a^2*b - b^3 - 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 - 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 - 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 - 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 - 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 - 15*(a^2*b - b^3)*cosh(x)^4 - a^2*b + b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 - 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 - (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 - 4*(a^2*b - b^3)*cosh(x)^6 - 4*(a^2*b - b^3 - 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 - 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 - 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 - 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 - 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 - 15*(a^2*b - b^3)*cosh(x)^4 - a^2*b + b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 - 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 - (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - 2*sqrt(2)*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^6 + 6*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)*sinh(x)^5 + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*sinh(x)^6 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 - 3*(a^3 - a^2*b - a*b^2 + b^3 - 5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 - a^3 + a^2*b + 5*a*b^2 + 3*b^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^4 + a^3 - a^2*b - a*b^2 + b^3 - 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^5 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^8 + 8*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)*sinh(x)^7 + (a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*sinh(x)^8 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^6 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 - 7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^2)*sinh(x)^6 + a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^3 - 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^4 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6 + 35*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^4 - 30*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^5 - 10*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^3 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x))*sinh(x)^3 - 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2 + 4*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^6 - a^5*b - 3*a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + 3*a*b^5 + b^6 - 15*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^4 + 3*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^7 - 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^5 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^3 - (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x))]","B",0
44,1,6591,0,1.018211," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} - a b^{2} - 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} - 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} + a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} - a b^{2} - 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} - 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} + a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} - 5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + a^{2} b + a b^{2} - b^{3} - 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} - 7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5} + 35 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{6} - a^{6} - 3 \, a^{5} b - 2 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 3 \, a^{2} b^{4} + a b^{5} - 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} - a b^{2} - 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} - 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} + a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{3} - a b^{2} - 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} - 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} - 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} - a^{3} + a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} - 5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + a^{2} b + a b^{2} - b^{3} - 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} - 7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5} + 35 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{6} - a^{6} - 3 \, a^{5} b - 2 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 3 \, a^{2} b^{4} + a b^{5} - 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 - 4*(a^3 - a*b^2)*cosh(x)^6 - 4*(a^3 - a*b^2 - 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 - 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 - 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 - 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 - 15*(a^3 - a*b^2)*cosh(x)^4 - a^3 + a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 - 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 - 4*(a^3 - a*b^2)*cosh(x)^6 - 4*(a^3 - a*b^2 - 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 - 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 - 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 - 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 - 15*(a^3 - a*b^2)*cosh(x)^4 - a^3 + a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 - 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)*sinh(x)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(x)^6 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 - 3*(a^3 - a^2*b - a*b^2 + b^3 - 5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + 3*a^3 + 5*a^2*b + a*b^2 - b^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^4 - a^3 + a^2*b + a*b^2 - b^3 - 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^5 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^8 + 8*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)*sinh(x)^7 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*sinh(x)^8 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^6 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 - 7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^2)*sinh(x)^6 + a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^3 - 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^4 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5 + 35*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^4 - 30*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^5 - 10*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^3 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x))*sinh(x)^3 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2 + 4*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^6 - a^6 - 3*a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + 3*a^2*b^4 + a*b^5 - 15*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^4 + 3*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^7 - 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^5 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^3 - (a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 - 4*(a^3 - a*b^2)*cosh(x)^6 - 4*(a^3 - a*b^2 - 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 - 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 - 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 - 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 - 15*(a^3 - a*b^2)*cosh(x)^4 - a^3 + a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 - 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 - 4*(a^3 - a*b^2)*cosh(x)^6 - 4*(a^3 - a*b^2 - 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 - 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 - 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 - 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 - 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 - 15*(a^3 - a*b^2)*cosh(x)^4 - a^3 + a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 - 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 - (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)*sinh(x)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(x)^6 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 - 3*(a^3 - a^2*b - a*b^2 + b^3 - 5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + 3*a^3 + 5*a^2*b + a*b^2 - b^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^4 - a^3 + a^2*b + a*b^2 - b^3 - 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^5 - 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^8 + 8*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)*sinh(x)^7 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*sinh(x)^8 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^6 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 - 7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^2)*sinh(x)^6 + a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^3 - 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^4 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5 + 35*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^4 - 30*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^5 - 10*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^3 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x))*sinh(x)^3 - 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2 + 4*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^6 - a^6 - 3*a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + 3*a^2*b^4 + a*b^5 - 15*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^4 + 3*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^7 - 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^5 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^3 - (a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x))]","B",0
45,1,5736,0,0.994553," ","integrate(coth(x)/(a+b*coth(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} - 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 2 \, {\left(2 \, a^{3} + a^{2} b - 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} - 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - 2 \, a^{3} - 3 \, a^{2} b + b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} - 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} - 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} - 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} - 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} - a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 8 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} - 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} - a^{5} - 3 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 - 2*(2*a^3 + a^2*b)*cosh(x)^6 - 2*(2*a^3 + a^2*b - 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 - 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 - 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 - 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 - 15*(2*a^3 + a^2*b)*cosh(x)^4 - 2*a^3 - 3*a^2*b + b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 - 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 - a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 - 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*a^2*cosh(x)^5 - 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 - 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 - (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 - 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - a*b)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 3*(a^2 + a*b)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 - 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 - 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 - 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 - 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 - 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 - a^5 - 3*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4 + b^5 - 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 - 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 - (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 - (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 8*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 - 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 - a*b)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 3*(a^2 + a*b)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 - 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 - 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 - 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 - 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 - 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 - 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 - a^5 - 3*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4 + b^5 - 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 - 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 - (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x))]","B",0
46,-1,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,1,10729,0,1.904974," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} - 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} - 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a b^{2} + 2 \, b^{3} + 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a b^{2} + 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} + 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} + 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} - 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} - 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} - 7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5} + 6 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 21 \, a^{4} b + 9 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 54 \, a b^{4} + 24 \, b^{5} + 35 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 9 \, a^{4} b - 6 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 22 \, a b^{4} + 8 \, b^{5} - 15 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5} - 45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 7 \, a^{7} b + 2 \, a^{6} b^{2} + 18 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 5 \, a^{3} b^{5} - 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} - 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} - 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} - 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 2 \, a^{4} b + a^{3} b^{2} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} - 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} - 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} - 7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5} + 6 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 21 \, a^{4} b + 9 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 54 \, a b^{4} + 24 \, b^{5} + 35 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} - 9 \, a^{4} b - 6 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 22 \, a b^{4} + 8 \, b^{5} - 15 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} - a + b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{10} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5} - 45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} - 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 7 \, a^{7} b + 2 \, a^{6} b^{2} + 18 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 5 \, a^{3} b^{5} - 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{9} - 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 - (3*a^5 - 2*a^4*b - 5*a^3*b^2 - 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 + a^5 + 2*a^4*b + a^3*b^2 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + a^5 - 2*a^4*b + 5*a^3*b^2 - 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 - 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 + (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 - 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 + 2*(a*b^2 + 2*b^3)*cosh(x)^6 + 2*(a*b^2 + 2*b^3 + 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 + 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 + 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 + 15*(a*b^2 + 2*b^3)*cosh(x)^4 - a^3 + 3*a*b^2 + 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 + 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*b^2*cosh(x)^5 + 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 + 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 - (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 - (3*a^5 - 2*a^4*b - 5*a^3*b^2 - 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 + a^5 + 2*a^4*b + a^3*b^2 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + a^5 - 2*a^4*b + 5*a^3*b^2 - 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 - 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 + (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 - 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^8 + 8*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)*sinh(x)^7 + (3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*sinh(x)^8 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^6 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 - 7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^3 - 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x)^5 + 3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5 + 6*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(9*a^5 + 21*a^4*b + 9*a^3*b^2 + 27*a^2*b^3 + 54*a*b^4 + 24*b^5 + 35*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^4 - 30*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^5 - 10*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2 + 4*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^6 - 3*a^5 - 9*a^4*b - 6*a^3*b^2 + 14*a^2*b^3 + 22*a*b^4 + 8*b^5 - 15*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^4 + 9*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^7 - 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^5 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sinh(x)^10 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^8 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5 - 45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^8 + a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)^7 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^6 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 - 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 - 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^5 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 - 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^4 + 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^7 - 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 + (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^8 - 3*a^8 - 7*a^7*b + 2*a^6*b^2 + 18*a^5*b^3 + 17*a^4*b^4 + 5*a^3*b^5 - 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 + 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^9 - 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^5 + 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 - (3*a^5 - 2*a^4*b - 5*a^3*b^2 - 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 + a^5 + 2*a^4*b + a^3*b^2 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + a^5 - 2*a^4*b + 5*a^3*b^2 - 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 - 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 + (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 - 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 - (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 - a^2 + a*b + 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 - (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 - (3*a^5 - 2*a^4*b - 5*a^3*b^2 - 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 - 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 + a^5 + 2*a^4*b + a^3*b^2 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 + a^5 - 2*a^4*b + 5*a^3*b^2 - 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 - 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 + (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 - 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^8 + 8*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)*sinh(x)^7 + (3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*sinh(x)^8 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^6 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 - 7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^3 - 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x)^5 + 3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5 + 6*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(9*a^5 + 21*a^4*b + 9*a^3*b^2 + 27*a^2*b^3 + 54*a*b^4 + 24*b^5 + 35*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^4 - 30*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^5 - 10*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 - 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2 + 4*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^6 - 3*a^5 - 9*a^4*b - 6*a^3*b^2 + 14*a^2*b^3 + 22*a*b^4 + 8*b^5 - 15*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^4 + 9*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^7 - 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^5 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^3 - (3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 - a + b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sinh(x)^10 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^8 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5 - 45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^8 + a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)^7 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^6 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 - 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 - 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^5 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 - 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^4 + 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^7 - 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 + (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^8 - 3*a^8 - 7*a^7*b + 2*a^6*b^2 + 18*a^5*b^3 + 17*a^4*b^4 + 5*a^3*b^5 - 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 + 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^9 - 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^5 + 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x))]","B",0
48,1,547,0,0.451572," ","integrate(1/(1+coth(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{6} + 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 4\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{4} + 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} + 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} + 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} + 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} - \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)"," ",0,"1/8*sqrt(2)*log(2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 3)*sinh(x)^6 + 3*cosh(x)^6 + 2*(28*cosh(x)^3 + 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 + 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 45*cosh(x)^4 + 30*cosh(x)^2 + 4)*sinh(x)^2 + 4*cosh(x)^2 + 2*(4*cosh(x)^7 + 9*cosh(x)^5 + 10*cosh(x)^3 + 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^4 + 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 + 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 + 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 + 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) + 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/8*sqrt(2)*log(-2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 - 1)*sinh(x)^2 - cosh(x)^2 + 2*(2*cosh(x)^3 - cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 - sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(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
49,1,175,0,0.452402," ","integrate(1/(-1-coth(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} i \, \sqrt{2} \log\left(\frac{1}{2} \, {\left(i \, \sqrt{2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) - \frac{1}{8} i \, \sqrt{2} \log\left(\frac{1}{2} \, {\left(-i \, \sqrt{2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) - \frac{1}{8} i \, \sqrt{2} \log\left({\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} + i \, \sqrt{2} e^{\left(4 \, x\right)} + i \, \sqrt{2} e^{\left(2 \, x\right)} + 2 i \, \sqrt{2}\right)} e^{\left(-4 \, x\right)}\right) + \frac{1}{8} i \, \sqrt{2} \log\left({\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} + 2\right)} - i \, \sqrt{2} e^{\left(4 \, x\right)} - i \, \sqrt{2} e^{\left(2 \, x\right)} - 2 i \, \sqrt{2}\right)} e^{\left(-4 \, x\right)}\right)"," ",0,"1/8*I*sqrt(2)*log(1/2*(I*sqrt(2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) - 2)*e^(-2*x)) - 1/8*I*sqrt(2)*log(1/2*(-I*sqrt(2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) - 2)*e^(-2*x)) - 1/8*I*sqrt(2)*log((sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) + I*sqrt(2)*e^(4*x) + I*sqrt(2)*e^(2*x) + 2*I*sqrt(2))*e^(-4*x)) + 1/8*I*sqrt(2)*log((sqrt(-2*e^(4*x) - 2)*(e^(2*x) + 2) - I*sqrt(2)*e^(4*x) - I*sqrt(2)*e^(2*x) - 2*I*sqrt(2))*e^(-4*x))","C",0
50,1,95,0,0.449522," ","integrate(1/(1+coth(x)^3),x, algorithm=""fricas"")","\frac{18 \, x \cosh\left(x\right)^{2} + 36 \, x \cosh\left(x\right) \sinh\left(x\right) + 18 \, x \sinh\left(x\right)^{2} + 8 \, {\left(\sqrt{3} \cosh\left(x\right)^{2} + 2 \, \sqrt{3} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{3} \sinh\left(x\right)^{2}\right)} \arctan\left(-\frac{\sqrt{3} \cosh\left(x\right) + \sqrt{3} \sinh\left(x\right)}{3 \, {\left(\cosh\left(x\right) - \sinh\left(x\right)\right)}}\right) + 3}{36 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"1/36*(18*x*cosh(x)^2 + 36*x*cosh(x)*sinh(x) + 18*x*sinh(x)^2 + 8*(sqrt(3)*cosh(x)^2 + 2*sqrt(3)*cosh(x)*sinh(x) + sqrt(3)*sinh(x)^2)*arctan(-1/3*(sqrt(3)*cosh(x) + sqrt(3)*sinh(x))/(cosh(x) - sinh(x))) + 3)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
51,1,5172,0,0.679378," ","integrate(coth(x)*(a+b*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\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)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 6 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{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)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + {\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)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, -\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\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)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 6 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} - a + 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{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)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{6} - 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, \frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + {\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)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, -\frac{{\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\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)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}\right]"," ",0,"[1/4*((cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(b)*log(-((a + 2*b)*cosh(x)^8 + 8*(a + 2*b)*cosh(x)*sinh(x)^7 + (a + 2*b)*sinh(x)^8 - 4*(a - 2*b)*cosh(x)^6 + 4*(7*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^6 + 8*(7*(a + 2*b)*cosh(x)^3 - 3*(a - 2*b)*cosh(x))*sinh(x)^5 + 6*(a + 2*b)*cosh(x)^4 + 2*(35*(a + 2*b)*cosh(x)^4 - 30*(a - 2*b)*cosh(x)^2 + 3*a + 6*b)*sinh(x)^4 + 8*(7*(a + 2*b)*cosh(x)^5 - 10*(a - 2*b)*cosh(x)^3 + 3*(a + 2*b)*cosh(x))*sinh(x)^3 - 4*(a - 2*b)*cosh(x)^2 + 4*(7*(a + 2*b)*cosh(x)^6 - 15*(a - 2*b)*cosh(x)^4 + 9*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(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)*sqrt(b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*((a + 2*b)*cosh(x)^7 - 3*(a - 2*b)*cosh(x)^5 + 3*(a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), -1/4*(2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(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)*sqrt(b)*log(-((a + 2*b)*cosh(x)^8 + 8*(a + 2*b)*cosh(x)*sinh(x)^7 + (a + 2*b)*sinh(x)^8 - 4*(a - 2*b)*cosh(x)^6 + 4*(7*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^6 + 8*(7*(a + 2*b)*cosh(x)^3 - 3*(a - 2*b)*cosh(x))*sinh(x)^5 + 6*(a + 2*b)*cosh(x)^4 + 2*(35*(a + 2*b)*cosh(x)^4 - 30*(a - 2*b)*cosh(x)^2 + 3*a + 6*b)*sinh(x)^4 + 8*(7*(a + 2*b)*cosh(x)^5 - 10*(a - 2*b)*cosh(x)^3 + 3*(a + 2*b)*cosh(x))*sinh(x)^3 - 4*(a - 2*b)*cosh(x)^2 + 4*(7*(a + 2*b)*cosh(x)^6 - 15*(a - 2*b)*cosh(x)^4 + 9*(a + 2*b)*cosh(x)^2 - a + 2*b)*sinh(x)^2 - 2*sqrt(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)*sqrt(b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*((a + 2*b)*cosh(x)^7 - 3*(a - 2*b)*cosh(x)^5 + 3*(a + 2*b)*cosh(x)^3 - (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 1)*sinh(x)^6 - 4*cosh(x)^6 + 8*(7*cosh(x)^3 - 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 - 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 15*cosh(x)^4 + 9*cosh(x)^2 - 1)*sinh(x)^2 - 4*cosh(x)^2 + 8*(cosh(x)^7 - 3*cosh(x)^5 + 3*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), 1/4*(2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(-b)*arctan(sqrt(2)*sqrt(-b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)) + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1), -1/2*((cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(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)*sqrt(-b)*arctan(sqrt(2)*sqrt(-b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)) + sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(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
52,1,1290,0,0.682766," ","integrate(coth(x)/(a+b*coth(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, \sqrt{a + b}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/sqrt(a + b), -1/2*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x)))/(a + b)]","B",0
53,1,3938,0,0.825575," ","integrate(coth(x)/(a+b*coth(x)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - a^{2} + a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 8 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - 7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} + 9 \, a^{3} b + 9 \, a^{2} b^{2} + 3 \, a b^{3} - 30 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} - a^{4} - a^{3} b + a^{2} b^{2} + a b^{3} + 9 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - a^{2} + a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} - a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 8 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - 2 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{6} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - 7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} + 9 \, a^{3} b + 9 \, a^{2} b^{2} + 3 \, a b^{3} - 30 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} - a^{4} - a^{3} b + a^{2} b^{2} + a b^{3} + 9 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^2 + a*b)*cosh(x)^8 + 8*(a^2 + a*b)*cosh(x)*sinh(x)^7 + (a^2 + a*b)*sinh(x)^8 - 4*(a^2 - a*b)*cosh(x)^6 + 4*(7*(a^2 + a*b)*cosh(x)^2 - a^2 + a*b)*sinh(x)^6 + 8*(7*(a^2 + a*b)*cosh(x)^3 - 3*(a^2 - a*b)*cosh(x))*sinh(x)^5 + 6*(a^2 + a*b)*cosh(x)^4 + 2*(35*(a^2 + a*b)*cosh(x)^4 - 30*(a^2 - a*b)*cosh(x)^2 + 3*a^2 + 3*a*b)*sinh(x)^4 + 8*(7*(a^2 + a*b)*cosh(x)^5 - 10*(a^2 - a*b)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*b)*cosh(x)^2 + 4*(7*(a^2 + a*b)*cosh(x)^6 - 15*(a^2 - a*b)*cosh(x)^4 + 9*(a^2 + a*b)*cosh(x)^2 - a^2 + a*b)*sinh(x)^2 + a^2 + a*b + 8*((a^2 + a*b)*cosh(x)^7 - 3*(a^2 - a*b)*cosh(x)^5 + 3*(a^2 + a*b)*cosh(x)^3 - (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^8 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^6 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3 - 7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^5 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 3*a^4 + 9*a^3*b + 9*a^2*b^2 + 3*a*b^3 - 30*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 - 10*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 - 15*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^4 - a^4 - a^3*b + a^2*b^2 + a*b^3 + 9*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^7 - 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^5 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)), -1/2*(((a^2 + a*b)*cosh(x)^8 + 8*(a^2 + a*b)*cosh(x)*sinh(x)^7 + (a^2 + a*b)*sinh(x)^8 - 4*(a^2 - a*b)*cosh(x)^6 + 4*(7*(a^2 + a*b)*cosh(x)^2 - a^2 + a*b)*sinh(x)^6 + 8*(7*(a^2 + a*b)*cosh(x)^3 - 3*(a^2 - a*b)*cosh(x))*sinh(x)^5 + 6*(a^2 + a*b)*cosh(x)^4 + 2*(35*(a^2 + a*b)*cosh(x)^4 - 30*(a^2 - a*b)*cosh(x)^2 + 3*a^2 + 3*a*b)*sinh(x)^4 + 8*(7*(a^2 + a*b)*cosh(x)^5 - 10*(a^2 - a*b)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 - 4*(a^2 - a*b)*cosh(x)^2 + 4*(7*(a^2 + a*b)*cosh(x)^6 - 15*(a^2 - a*b)*cosh(x)^4 + 9*(a^2 + a*b)*cosh(x)^2 - a^2 + a*b)*sinh(x)^2 + a^2 + a*b + 8*((a^2 + a*b)*cosh(x)^7 - 3*(a^2 - a*b)*cosh(x)^5 + 3*(a^2 + a*b)*cosh(x)^3 - (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 - (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 - 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 - 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 - 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 - 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a^2 + b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 - 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 - (a^2 - b^2)*cosh(x))*sinh(x))) + sqrt(2)*((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 - 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 - a^2 - 2*a*b - b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 - (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 - 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - 2*a + 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^8 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^6 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3 - 7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^5 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 3*a^4 + 9*a^3*b + 9*a^2*b^2 + 3*a*b^3 - 30*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 - 10*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 - 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 - 15*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^4 - a^4 - a^3*b + a^2*b^2 + a*b^3 + 9*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^7 - 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^5 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 - (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x))]","B",0
