1,1,145,0,0.201694," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{24 \, {\left(a + 5 \, b\right)} d x - {\left(18 \, a e^{\left(4 \, d x + 4 \, c\right)} + 90 \, b e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a e^{\left(2 \, d x + 2 \, c\right)} - 16 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a e^{\left(4 \, d x + 20 \, c\right)} + b e^{\left(4 \, d x + 20 \, c\right)} - 8 \, a e^{\left(2 \, d x + 18 \, c\right)} - 16 \, b e^{\left(2 \, d x + 18 \, c\right)}\right)} e^{\left(-16 \, c\right)} + \frac{128 \, b}{e^{\left(2 \, d x + 2 \, c\right)} + 1}}{64 \, d}"," ",0,"1/64*(24*(a + 5*b)*d*x - (18*a*e^(4*d*x + 4*c) + 90*b*e^(4*d*x + 4*c) - 8*a*e^(2*d*x + 2*c) - 16*b*e^(2*d*x + 2*c) + a + b)*e^(-4*d*x - 4*c) + (a*e^(4*d*x + 20*c) + b*e^(4*d*x + 20*c) - 8*a*e^(2*d*x + 18*c) - 16*b*e^(2*d*x + 18*c))*e^(-16*c) + 128*b/(e^(2*d*x + 2*c) + 1))/d","B",0
2,1,120,0,0.167988," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} + 21 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-3 \, d x - 3 \, c\right)} - {\left(a e^{\left(3 \, d x + 24 \, c\right)} + b e^{\left(3 \, d x + 24 \, c\right)} - 9 \, a e^{\left(d x + 22 \, c\right)} - 21 \, b e^{\left(d x + 22 \, c\right)}\right)} e^{\left(-21 \, c\right)} + \frac{48 \, b e^{\left(d x + c\right)}}{e^{\left(2 \, d x + 2 \, c\right)} + 1}}{24 \, d}"," ",0,"-1/24*((9*a*e^(2*d*x + 2*c) + 21*b*e^(2*d*x + 2*c) - a - b)*e^(-3*d*x - 3*c) - (a*e^(3*d*x + 24*c) + b*e^(3*d*x + 24*c) - 9*a*e^(d*x + 22*c) - 21*b*e^(d*x + 22*c))*e^(-21*c) + 48*b*e^(d*x + c)/(e^(2*d*x + 2*c) + 1))/d","B",0
3,1,109,0,0.175875," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{4 \, {\left(a + 3 \, b\right)} d x - {\left(a e^{\left(2 \, d x + 8 \, c\right)} + b e^{\left(2 \, d x + 8 \, c\right)}\right)} e^{\left(-6 \, c\right)} - \frac{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 14 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-2 \, c\right)}}{e^{\left(2 \, d x\right)} + e^{\left(4 \, d x + 2 \, c\right)}}}{8 \, d}"," ",0,"-1/8*(4*(a + 3*b)*d*x - (a*e^(2*d*x + 8*c) + b*e^(2*d*x + 8*c))*e^(-6*c) - (a*e^(4*d*x + 4*c) + 3*b*e^(4*d*x + 4*c) - 14*b*e^(2*d*x + 2*c) - a - b)*e^(-2*c)/(e^(2*d*x) + e^(4*d*x + 2*c)))/d","B",0
4,1,79,0,0.149950," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(a e^{\left(d x + 6 \, c\right)} + b e^{\left(d x + 6 \, c\right)}\right)} e^{\left(-5 \, c\right)} + \frac{{\left(a e^{\left(2 \, d x + 2 \, c\right)} + 5 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-c\right)}}{e^{\left(3 \, d x + 2 \, c\right)} + e^{\left(d x\right)}}}{2 \, d}"," ",0,"1/2*((a*e^(d*x + 6*c) + b*e^(d*x + 6*c))*e^(-5*c) + (a*e^(2*d*x + 2*c) + 5*b*e^(2*d*x + 2*c) + a + b)*e^(-c)/(e^(3*d*x + 2*c) + e^(d*x)))/d","B",0
5,1,52,0,0.155340," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{a \log\left(e^{\left(d x + c\right)} + 1\right) - a \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) + \frac{2 \, b e^{\left(d x + c\right)}}{e^{\left(2 \, d x + 2 \, c\right)} + 1}}{d}"," ",0,"-(a*log(e^(d*x + c) + 1) - a*log(abs(e^(d*x + c) - 1)) + 2*b*e^(d*x + c)/(e^(2*d*x + 2*c) + 1))/d","A",0
6,1,45,0,0.161878," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b\right)}}{d {\left(e^{\left(4 \, d x + 4 \, c\right)} - 1\right)}}"," ",0,"-2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/(d*(e^(4*d*x + 4*c) - 1))","A",0
7,1,113,0,0.148001," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(a e^{c} - 2 \, b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - {\left(a e^{c} - 2 \, b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) + \frac{4 \, b e^{\left(d x + c\right)}}{e^{\left(2 \, d x + 2 \, c\right)} + 1} - \frac{2 \, {\left(a e^{\left(3 \, d x + 3 \, c\right)} + a e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a*e^c - 2*b*e^c)*e^(-c)*log(e^(d*x + c) + 1) - (a*e^c - 2*b*e^c)*e^(-c)*log(abs(e^(d*x + c) - 1)) + 4*b*e^(d*x + c)/(e^(2*d*x + 2*c) + 1) - 2*(a*e^(3*d*x + 3*c) + a*e^(d*x + c))/(e^(2*d*x + 2*c) - 1)^2)/d","B",0
8,1,80,0,0.150751," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, b}{e^{\left(2 \, d x + 2 \, c\right)} + 1} - \frac{3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b e^{\left(2 \, d x + 2 \, c\right)} - 2 \, a + 3 \, b}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*b/(e^(2*d*x + 2*c) + 1) - (3*b*e^(4*d*x + 4*c) + 6*a*e^(2*d*x + 2*c) - 6*b*e^(2*d*x + 2*c) - 2*a + 3*b)/(e^(2*d*x + 2*c) - 1)^3)/d","A",0
9,1,295,0,0.458133," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{24 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} d x - 3 \, {\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 180 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 210 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 32 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 24 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(a^{2} e^{\left(4 \, d x + 28 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 28 \, c\right)} + b^{2} e^{\left(4 \, d x + 28 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 26 \, c\right)} - 32 \, a b e^{\left(2 \, d x + 26 \, c\right)} - 24 \, b^{2} e^{\left(2 \, d x + 26 \, c\right)}\right)} e^{\left(-24 \, c\right)} + \frac{256 \, {\left(3 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 9 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a b + 5 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{192 \, d}"," ",0,"1/192*(24*(3*a^2 + 30*a*b + 35*b^2)*d*x - 3*(18*a^2*e^(4*d*x + 4*c) + 180*a*b*e^(4*d*x + 4*c) + 210*b^2*e^(4*d*x + 4*c) - 8*a^2*e^(2*d*x + 2*c) - 32*a*b*e^(2*d*x + 2*c) - 24*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) + 3*(a^2*e^(4*d*x + 28*c) + 2*a*b*e^(4*d*x + 28*c) + b^2*e^(4*d*x + 28*c) - 8*a^2*e^(2*d*x + 26*c) - 32*a*b*e^(2*d*x + 26*c) - 24*b^2*e^(2*d*x + 26*c))*e^(-24*c) + 256*(3*a*b*e^(4*d*x + 4*c) + 6*b^2*e^(4*d*x + 4*c) + 6*a*b*e^(2*d*x + 2*c) + 9*b^2*e^(2*d*x + 2*c) + 3*a*b + 5*b^2)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
10,1,290,0,0.420143," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{{\left(a^{2} e^{\left(3 \, d x + 36 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 36 \, c\right)} + b^{2} e^{\left(3 \, d x + 36 \, c\right)} - 9 \, a^{2} e^{\left(d x + 34 \, c\right)} - 42 \, a b e^{\left(d x + 34 \, c\right)} - 33 \, b^{2} e^{\left(d x + 34 \, c\right)}\right)} e^{\left(-33 \, c\right)} - \frac{{\left(9 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 138 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 177 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 26 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} + 316 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 322 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 24 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 216 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 240 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 36 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 30 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2} - 2 \, a b - b^{2}\right)} e^{\left(-3 \, c\right)}}{{\left(e^{\left(3 \, d x + 2 \, c\right)} + e^{\left(d x\right)}\right)}^{3}}}{24 \, d}"," ",0,"1/24*((a^2*e^(3*d*x + 36*c) + 2*a*b*e^(3*d*x + 36*c) + b^2*e^(3*d*x + 36*c) - 9*a^2*e^(d*x + 34*c) - 42*a*b*e^(d*x + 34*c) - 33*b^2*e^(d*x + 34*c))*e^(-33*c) - (9*a^2*e^(8*d*x + 8*c) + 138*a*b*e^(8*d*x + 8*c) + 177*b^2*e^(8*d*x + 8*c) + 26*a^2*e^(6*d*x + 6*c) + 316*a*b*e^(6*d*x + 6*c) + 322*b^2*e^(6*d*x + 6*c) + 24*a^2*e^(4*d*x + 4*c) + 216*a*b*e^(4*d*x + 4*c) + 240*b^2*e^(4*d*x + 4*c) + 6*a^2*e^(2*d*x + 2*c) + 36*a*b*e^(2*d*x + 2*c) + 30*b^2*e^(2*d*x + 2*c) - a^2 - 2*a*b - b^2)*e^(-3*c)/(e^(3*d*x + 2*c) + e^(d*x))^3)/d","B",0
11,1,215,0,0.326159," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{12 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} d x - 3 \, {\left(2 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 10 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2} - 2 \, a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, {\left(a^{2} e^{\left(2 \, d x + 12 \, c\right)} + 2 \, a b e^{\left(2 \, d x + 12 \, c\right)} + b^{2} e^{\left(2 \, d x + 12 \, c\right)}\right)} e^{\left(-10 \, c\right)} + \frac{16 \, {\left(6 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 12 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, a b + 7 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{24 \, d}"," ",0,"-1/24*(12*(a^2 + 6*a*b + 5*b^2)*d*x - 3*(2*a^2*e^(2*d*x + 2*c) + 12*a*b*e^(2*d*x + 2*c) + 10*b^2*e^(2*d*x + 2*c) - a^2 - 2*a*b - b^2)*e^(-2*d*x - 2*c) - 3*(a^2*e^(2*d*x + 12*c) + 2*a*b*e^(2*d*x + 12*c) + b^2*e^(2*d*x + 12*c))*e^(-10*c) + 16*(6*a*b*e^(4*d*x + 4*c) + 9*b^2*e^(4*d*x + 4*c) + 12*a*b*e^(2*d*x + 2*c) + 12*b^2*e^(2*d*x + 2*c) + 6*a*b + 7*b^2)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
12,1,162,0,0.215546," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-d x - c\right)} + 3 \, {\left(a^{2} e^{\left(d x + 10 \, c\right)} + 2 \, a b e^{\left(d x + 10 \, c\right)} + b^{2} e^{\left(d x + 10 \, c\right)}\right)} e^{\left(-9 \, c\right)} + \frac{8 \, {\left(3 \, a b e^{\left(5 \, d x + 5 \, c\right)} + 3 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 6 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 4 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 3 \, a b e^{\left(d x + c\right)} + 3 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(a^2 + 2*a*b + b^2)*e^(-d*x - c) + 3*(a^2*e^(d*x + 10*c) + 2*a*b*e^(d*x + 10*c) + b^2*e^(d*x + 10*c))*e^(-9*c) + 8*(3*a*b*e^(5*d*x + 5*c) + 3*b^2*e^(5*d*x + 5*c) + 6*a*b*e^(3*d*x + 3*c) + 4*b^2*e^(3*d*x + 3*c) + 3*a*b*e^(d*x + c) + 3*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
13,1,126,0,0.231791," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \log\left(e^{\left(d x + c\right)} + 1\right) - 3 \, a^{2} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) + \frac{2 \, {\left(6 \, a b e^{\left(5 \, d x + 5 \, c\right)} + 3 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 12 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 2 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 6 \, a b e^{\left(d x + c\right)} + 3 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*a^2*log(e^(d*x + c) + 1) - 3*a^2*log(abs(e^(d*x + c) - 1)) + 2*(6*a*b*e^(5*d*x + 5*c) + 3*b^2*e^(5*d*x + 5*c) + 12*a*b*e^(3*d*x + 3*c) + 2*b^2*e^(3*d*x + 3*c) + 6*a*b*e^(d*x + c) + 3*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
14,1,86,0,0.264791," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, a^{2}}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{6 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 6 \, a b + b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"-2/3*(3*a^2/(e^(2*d*x + 2*c) - 1) + (6*a*b*e^(4*d*x + 4*c) + 3*b^2*e^(4*d*x + 4*c) + 12*a*b*e^(2*d*x + 2*c) + 6*a*b + b^2)/(e^(2*d*x + 2*c) + 1)^3)/d","A",0
15,1,168,0,0.265789," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} e^{c} - 4 \, a b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - 3 \, {\left(a^{2} e^{c} - 4 \, a b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{6 \, {\left(a^{2} e^{\left(3 \, d x + 3 \, c\right)} + a^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}} + \frac{8 \, {\left(3 \, a b e^{\left(5 \, d x + 5 \, c\right)} + 6 \, a b e^{\left(3 \, d x + 3 \, c\right)} - 2 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 3 \, a b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(a^2*e^c - 4*a*b*e^c)*e^(-c)*log(e^(d*x + c) + 1) - 3*(a^2*e^c - 4*a*b*e^c)*e^(-c)*log(abs(e^(d*x + c) - 1)) - 6*(a^2*e^(3*d*x + 3*c) + a^2*e^(d*x + c))/(e^(2*d*x + 2*c) - 1)^2 + 8*(3*a*b*e^(5*d*x + 5*c) + 6*a*b*e^(3*d*x + 3*c) - 2*b^2*e^(3*d*x + 3*c) + 3*a*b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
16,1,143,0,0.258890," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(3 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 6 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 3 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 8 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} - 8 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 12 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - a^{2} + 6 \, a b - b^{2}\right)}}{3 \, d {\left(e^{\left(4 \, d x + 4 \, c\right)} - 1\right)}^{3}}"," ",0,"-4/3*(3*a^2*e^(8*d*x + 8*c) + 6*a*b*e^(8*d*x + 8*c) + 3*b^2*e^(8*d*x + 8*c) + 8*a^2*e^(6*d*x + 6*c) - 8*b^2*e^(6*d*x + 6*c) + 6*a^2*e^(4*d*x + 4*c) - 12*a*b*e^(4*d*x + 4*c) + 6*b^2*e^(4*d*x + 4*c) - a^2 + 6*a*b - b^2)/(d*(e^(4*d*x + 4*c) - 1)^3)","B",0
17,1,507,0,0.793110," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{120 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x - 5 \, {\left(18 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 270 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 630 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 378 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 48 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 72 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 32 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 5 \, {\left(a^{3} e^{\left(4 \, d x + 36 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, d x + 36 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, d x + 36 \, c\right)} + b^{3} e^{\left(4 \, d x + 36 \, c\right)} - 8 \, a^{3} e^{\left(2 \, d x + 34 \, c\right)} - 48 \, a^{2} b e^{\left(2 \, d x + 34 \, c\right)} - 72 \, a b^{2} e^{\left(2 \, d x + 34 \, c\right)} - 32 \, b^{3} e^{\left(2 \, d x + 34 \, c\right)}\right)} e^{\left(-32 \, c\right)} + \frac{128 \, {\left(15 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 50 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 210 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 150 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 90 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 290 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 210 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 60 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 190 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 130 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 15 \, a^{2} b + 50 \, a b^{2} + 36 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{320 \, d}"," ",0,"1/320*(120*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x - 5*(18*a^3*e^(4*d*x + 4*c) + 270*a^2*b*e^(4*d*x + 4*c) + 630*a*b^2*e^(4*d*x + 4*c) + 378*b^3*e^(4*d*x + 4*c) - 8*a^3*e^(2*d*x + 2*c) - 48*a^2*b*e^(2*d*x + 2*c) - 72*a*b^2*e^(2*d*x + 2*c) - 32*b^3*e^(2*d*x + 2*c) + a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-4*d*x - 4*c) + 5*(a^3*e^(4*d*x + 36*c) + 3*a^2*b*e^(4*d*x + 36*c) + 3*a*b^2*e^(4*d*x + 36*c) + b^3*e^(4*d*x + 36*c) - 8*a^3*e^(2*d*x + 34*c) - 48*a^2*b*e^(2*d*x + 34*c) - 72*a*b^2*e^(2*d*x + 34*c) - 32*b^3*e^(2*d*x + 34*c))*e^(-32*c) + 128*(15*a^2*b*e^(8*d*x + 8*c) + 60*a*b^2*e^(8*d*x + 8*c) + 50*b^3*e^(8*d*x + 8*c) + 60*a^2*b*e^(6*d*x + 6*c) + 210*a*b^2*e^(6*d*x + 6*c) + 150*b^3*e^(6*d*x + 6*c) + 90*a^2*b*e^(4*d*x + 4*c) + 290*a*b^2*e^(4*d*x + 4*c) + 210*b^3*e^(4*d*x + 4*c) + 60*a^2*b*e^(2*d*x + 2*c) + 190*a*b^2*e^(2*d*x + 2*c) + 130*b^3*e^(2*d*x + 2*c) + 15*a^2*b + 50*a*b^2 + 36*b^3)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
18,1,442,0,0.660034," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(9 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 63 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 99 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 45 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} e^{\left(-3 \, d x - 3 \, c\right)} - 5 \, {\left(a^{3} e^{\left(3 \, d x + 48 \, c\right)} + 3 \, a^{2} b e^{\left(3 \, d x + 48 \, c\right)} + 3 \, a b^{2} e^{\left(3 \, d x + 48 \, c\right)} + b^{3} e^{\left(3 \, d x + 48 \, c\right)} - 9 \, a^{3} e^{\left(d x + 46 \, c\right)} - 63 \, a^{2} b e^{\left(d x + 46 \, c\right)} - 99 \, a b^{2} e^{\left(d x + 46 \, c\right)} - 45 \, b^{3} e^{\left(d x + 46 \, c\right)}\right)} e^{\left(-45 \, c\right)} + \frac{16 \, {\left(45 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 135 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 90 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} + 180 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 480 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 280 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 270 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 690 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 428 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 180 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 480 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 280 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 45 \, a^{2} b e^{\left(d x + c\right)} + 135 \, a b^{2} e^{\left(d x + c\right)} + 90 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(5*(9*a^3*e^(2*d*x + 2*c) + 63*a^2*b*e^(2*d*x + 2*c) + 99*a*b^2*e^(2*d*x + 2*c) + 45*b^3*e^(2*d*x + 2*c) - a^3 - 3*a^2*b - 3*a*b^2 - b^3)*e^(-3*d*x - 3*c) - 5*(a^3*e^(3*d*x + 48*c) + 3*a^2*b*e^(3*d*x + 48*c) + 3*a*b^2*e^(3*d*x + 48*c) + b^3*e^(3*d*x + 48*c) - 9*a^3*e^(d*x + 46*c) - 63*a^2*b*e^(d*x + 46*c) - 99*a*b^2*e^(d*x + 46*c) - 45*b^3*e^(d*x + 46*c))*e^(-45*c) + 16*(45*a^2*b*e^(9*d*x + 9*c) + 135*a*b^2*e^(9*d*x + 9*c) + 90*b^3*e^(9*d*x + 9*c) + 180*a^2*b*e^(7*d*x + 7*c) + 480*a*b^2*e^(7*d*x + 7*c) + 280*b^3*e^(7*d*x + 7*c) + 270*a^2*b*e^(5*d*x + 5*c) + 690*a*b^2*e^(5*d*x + 5*c) + 428*b^3*e^(5*d*x + 5*c) + 180*a^2*b*e^(3*d*x + 3*c) + 480*a*b^2*e^(3*d*x + 3*c) + 280*b^3*e^(3*d*x + 3*c) + 45*a^2*b*e^(d*x + c) + 135*a*b^2*e^(d*x + c) + 90*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
19,1,395,0,0.642657," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{60 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x - 15 \, {\left(2 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 30 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 14 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, {\left(a^{3} e^{\left(2 \, d x + 16 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, d x + 16 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, d x + 16 \, c\right)} + b^{3} e^{\left(2 \, d x + 16 \, c\right)}\right)} e^{\left(-14 \, c\right)} + \frac{16 \, {\left(45 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 135 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 90 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 180 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 450 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 240 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 270 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 600 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 340 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 180 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 390 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 200 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 45 \, a^{2} b + 105 \, a b^{2} + 58 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(60*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x - 15*(2*a^3*e^(2*d*x + 2*c) + 18*a^2*b*e^(2*d*x + 2*c) + 30*a*b^2*e^(2*d*x + 2*c) + 14*b^3*e^(2*d*x + 2*c) - a^3 - 3*a^2*b - 3*a*b^2 - b^3)*e^(-2*d*x - 2*c) - 15*(a^3*e^(2*d*x + 16*c) + 3*a^2*b*e^(2*d*x + 16*c) + 3*a*b^2*e^(2*d*x + 16*c) + b^3*e^(2*d*x + 16*c))*e^(-14*c) + 16*(45*a^2*b*e^(8*d*x + 8*c) + 135*a*b^2*e^(8*d*x + 8*c) + 90*b^3*e^(8*d*x + 8*c) + 180*a^2*b*e^(6*d*x + 6*c) + 450*a*b^2*e^(6*d*x + 6*c) + 240*b^3*e^(6*d*x + 6*c) + 270*a^2*b*e^(4*d*x + 4*c) + 600*a*b^2*e^(4*d*x + 4*c) + 340*b^3*e^(4*d*x + 4*c) + 180*a^2*b*e^(2*d*x + 2*c) + 390*a*b^2*e^(2*d*x + 2*c) + 200*b^3*e^(2*d*x + 2*c) + 45*a^2*b + 105*a*b^2 + 58*b^3)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
20,1,322,0,0.391002," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-d x - c\right)} + 5 \, {\left(a^{3} e^{\left(d x + 14 \, c\right)} + 3 \, a^{2} b e^{\left(d x + 14 \, c\right)} + 3 \, a b^{2} e^{\left(d x + 14 \, c\right)} + b^{3} e^{\left(d x + 14 \, c\right)}\right)} e^{\left(-13 \, c\right)} + \frac{4 \, {\left(15 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 30 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 15 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} + 60 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 100 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 40 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 90 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 140 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 66 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 60 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 100 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 40 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 15 \, a^{2} b e^{\left(d x + c\right)} + 30 \, a b^{2} e^{\left(d x + c\right)} + 15 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{10 \, d}"," ",0,"1/10*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-d*x - c) + 5*(a^3*e^(d*x + 14*c) + 3*a^2*b*e^(d*x + 14*c) + 3*a*b^2*e^(d*x + 14*c) + b^3*e^(d*x + 14*c))*e^(-13*c) + 4*(15*a^2*b*e^(9*d*x + 9*c) + 30*a*b^2*e^(9*d*x + 9*c) + 15*b^3*e^(9*d*x + 9*c) + 60*a^2*b*e^(7*d*x + 7*c) + 100*a*b^2*e^(7*d*x + 7*c) + 40*b^3*e^(7*d*x + 7*c) + 90*a^2*b*e^(5*d*x + 5*c) + 140*a*b^2*e^(5*d*x + 5*c) + 66*b^3*e^(5*d*x + 5*c) + 60*a^2*b*e^(3*d*x + 3*c) + 100*a*b^2*e^(3*d*x + 3*c) + 40*b^3*e^(3*d*x + 3*c) + 15*a^2*b*e^(d*x + c) + 30*a*b^2*e^(d*x + c) + 15*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
21,1,262,0,0.365296," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{15 \, a^{3} \log\left(e^{\left(d x + c\right)} + 1\right) - 15 \, a^{3} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) + \frac{2 \, {\left(45 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 45 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 15 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} + 180 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 120 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 20 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 270 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 150 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 58 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 180 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 120 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 20 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 45 \, a^{2} b e^{\left(d x + c\right)} + 45 \, a b^{2} e^{\left(d x + c\right)} + 15 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"-1/15*(15*a^3*log(e^(d*x + c) + 1) - 15*a^3*log(abs(e^(d*x + c) - 1)) + 2*(45*a^2*b*e^(9*d*x + 9*c) + 45*a*b^2*e^(9*d*x + 9*c) + 15*b^3*e^(9*d*x + 9*c) + 180*a^2*b*e^(7*d*x + 7*c) + 120*a*b^2*e^(7*d*x + 7*c) + 20*b^3*e^(7*d*x + 7*c) + 270*a^2*b*e^(5*d*x + 5*c) + 150*a*b^2*e^(5*d*x + 5*c) + 58*b^3*e^(5*d*x + 5*c) + 180*a^2*b*e^(3*d*x + 3*c) + 120*a*b^2*e^(3*d*x + 3*c) + 20*b^3*e^(3*d*x + 3*c) + 45*a^2*b*e^(d*x + c) + 45*a*b^2*e^(d*x + c) + 15*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
22,1,202,0,0.443450," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, a^{3}}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{15 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 15 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 5 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 30 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 90 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 20 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 10 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 60 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 10 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 15 \, a^{2} b + 5 \, a b^{2} + b^{3}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}\right)}}{5 \, d}"," ",0,"-2/5*(5*a^3/(e^(2*d*x + 2*c) - 1) + (15*a^2*b*e^(8*d*x + 8*c) + 15*a*b^2*e^(8*d*x + 8*c) + 5*b^3*e^(8*d*x + 8*c) + 60*a^2*b*e^(6*d*x + 6*c) + 30*a*b^2*e^(6*d*x + 6*c) + 90*a^2*b*e^(4*d*x + 4*c) + 20*a*b^2*e^(4*d*x + 4*c) + 10*b^3*e^(4*d*x + 4*c) + 60*a^2*b*e^(2*d*x + 2*c) + 10*a*b^2*e^(2*d*x + 2*c) + 15*a^2*b + 5*a*b^2 + b^3)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
23,1,281,0,0.495099," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{15 \, {\left(a^{3} e^{c} - 6 \, a^{2} b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - 15 \, {\left(a^{3} e^{c} - 6 \, a^{2} b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{30 \, {\left(a^{3} e^{\left(3 \, d x + 3 \, c\right)} + a^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}} + \frac{4 \, {\left(45 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 180 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} - 60 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 20 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 270 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 120 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 8 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 180 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} - 60 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 20 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 45 \, a^{2} b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(15*(a^3*e^c - 6*a^2*b*e^c)*e^(-c)*log(e^(d*x + c) + 1) - 15*(a^3*e^c - 6*a^2*b*e^c)*e^(-c)*log(abs(e^(d*x + c) - 1)) - 30*(a^3*e^(3*d*x + 3*c) + a^3*e^(d*x + c))/(e^(2*d*x + 2*c) - 1)^2 + 4*(45*a^2*b*e^(9*d*x + 9*c) + 180*a^2*b*e^(7*d*x + 7*c) - 60*a*b^2*e^(7*d*x + 7*c) - 20*b^3*e^(7*d*x + 7*c) + 270*a^2*b*e^(5*d*x + 5*c) - 120*a*b^2*e^(5*d*x + 5*c) + 8*b^3*e^(5*d*x + 5*c) + 180*a^2*b*e^(3*d*x + 3*c) - 60*a*b^2*e^(3*d*x + 3*c) - 20*b^3*e^(3*d*x + 3*c) + 45*a^2*b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
24,1,257,0,0.461677," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, {\left(9 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 18 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 2 \, a^{3} + 9 \, a^{2} b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}} - \frac{45 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 180 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 90 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 30 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 270 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 210 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 10 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 180 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 150 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 10 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 45 \, a^{2} b - 30 \, a b^{2} - 2 \, b^{3}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}\right)}}{15 \, d}"," ",0,"-2/15*(5*(9*a^2*b*e^(4*d*x + 4*c) + 6*a^3*e^(2*d*x + 2*c) - 18*a^2*b*e^(2*d*x + 2*c) - 2*a^3 + 9*a^2*b)/(e^(2*d*x + 2*c) - 1)^3 - (45*a^2*b*e^(8*d*x + 8*c) + 180*a^2*b*e^(6*d*x + 6*c) - 90*a*b^2*e^(6*d*x + 6*c) - 30*b^3*e^(6*d*x + 6*c) + 270*a^2*b*e^(4*d*x + 4*c) - 210*a*b^2*e^(4*d*x + 4*c) + 10*b^3*e^(4*d*x + 4*c) + 180*a^2*b*e^(2*d*x + 2*c) - 150*a*b^2*e^(2*d*x + 2*c) - 10*b^3*e^(2*d*x + 2*c) + 45*a^2*b - 30*a*b^2 - 2*b^3)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
25,1,301,0,1.092796," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{64 \, a^{2} b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} + \frac{8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{{\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 8 \, a b e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x\right)}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}} + \frac{a e^{\left(4 \, d x + 20 \, c\right)} + b e^{\left(4 \, d x + 20 \, c\right)} - 8 \, a e^{\left(2 \, d x + 18 \, c\right)}}{a^{2} e^{\left(16 \, c\right)} + 2 \, a b e^{\left(16 \, c\right)} + b^{2} e^{\left(16 \, c\right)}}}{64 \, d}"," ",0,"1/64*(64*a^2*b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) + 8*(3*a^2 - 6*a*b - b^2)*d*x/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (18*a^2*e^(4*d*x + 4*c) - 36*a*b*e^(4*d*x + 4*c) - 6*b^2*e^(4*d*x + 4*c) - 8*a^2*e^(2*d*x + 2*c) - 8*a*b*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-4*d*x)/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c)) + (a*e^(4*d*x + 20*c) + b*e^(4*d*x + 20*c) - 8*a*e^(2*d*x + 18*c))/(a^2*e^(16*c) + 2*a*b*e^(16*c) + b^2*e^(16*c)))/d","B",0
26,1,810,0,0.494733," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{24 \, \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(a b - \sqrt{-a b} a\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 2 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{-a b}} + \frac{24 \, {\left(3 \, a^{2} b - a b^{2} + {\left(a^{2} - 3 \, a b\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}}} + \frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} - 3 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-3 \, d x\right)}}{a^{2} e^{\left(3 \, c\right)} + 2 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}} - \frac{a^{2} e^{\left(3 \, d x + 24 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 24 \, c\right)} + b^{2} e^{\left(3 \, d x + 24 \, c\right)} - 9 \, a^{2} e^{\left(d x + 22 \, c\right)} - 6 \, a b e^{\left(d x + 22 \, c\right)} + 3 \, b^{2} e^{\left(d x + 22 \, c\right)}}{a^{3} e^{\left(21 \, c\right)} + 3 \, a^{2} b e^{\left(21 \, c\right)} + 3 \, a b^{2} e^{\left(21 \, c\right)} + b^{3} e^{\left(21 \, c\right)}}}{24 \, d}"," ",0,"-1/24*(24*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*(a*b - sqrt(-a*b)*a)*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) + sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 2*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt(-a*b)) + 24*(3*a^2*b - a*b^2 + (a^2 - 3*a*b)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) - sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/((a^4 + 2*a^3*b - 2*a*b^3 - b^4 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))) + (9*a*e^(2*d*x + 2*c) - 3*b*e^(2*d*x + 2*c) - a - b)*e^(-3*d*x)/(a^2*e^(3*c) + 2*a*b*e^(3*c) + b^2*e^(3*c)) - (a^2*e^(3*d*x + 24*c) + 2*a*b*e^(3*d*x + 24*c) + b^2*e^(3*d*x + 24*c) - 9*a^2*e^(d*x + 22*c) - 6*a*b*e^(d*x + 22*c) + 3*b^2*e^(d*x + 22*c))/(a^3*e^(21*c) + 3*a^2*b*e^(21*c) + 3*a*b^2*e^(21*c) + b^3*e^(21*c)))/d","B",0
27,1,176,0,0.589834," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(a - b\right)} d x}{a^{2} + 2 \, a b + b^{2}} + \frac{8 \, a b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{{\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-2 \, d x\right)}}{a^{2} e^{\left(2 \, c\right)} + 2 \, a b e^{\left(2 \, c\right)} + b^{2} e^{\left(2 \, c\right)}} - \frac{e^{\left(2 \, d x + 8 \, c\right)}}{a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}}}{8 \, d}"," ",0,"-1/8*(4*(a - b)*d*x/(a^2 + 2*a*b + b^2) + 8*a*b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) - (2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) - a - b)*e^(-2*d*x)/(a^2*e^(2*c) + 2*a*b*e^(2*c) + b^2*e^(2*c)) - e^(2*d*x + 8*c)/(a*e^(6*c) + b*e^(6*c)))/d","B",0
28,1,1065,0,0.250393," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, {\left(2 \, a b^{2} - {\left(a b - b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4} + 2 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(2 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{7} + 5 \, a^{6} b + 9 \, a^{5} b^{2} + 5 \, a^{4} b^{3} - 5 \, a^{3} b^{4} - 9 \, a^{2} b^{5} - 5 \, a b^{6} - b^{7} + 2 \, {\left(a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right)} \sqrt{-a b}\right)} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|}} + \frac{2 \, {\left(2 \, {\left(4 \, a^{2} b^{2} - 4 \, a b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(a^{4} b - 4 \, a^{3} b^{2} - 10 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5} - 4 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(4 \, a^{5} b - 8 \, a^{3} b^{3} + 4 \, a b^{5} + {\left(a^{5} - 5 \, a^{4} b - 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} - 5 \, a^{2} b^{4} - 4 \, a b^{5} - b^{6} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|}} - \frac{e^{\left(d x + 6 \, c\right)}}{a e^{\left(5 \, c\right)} + b e^{\left(5 \, c\right)}} - \frac{e^{\left(-d x\right)}}{a e^{c} + b e^{c}}}{2 \, d}"," ",0,"-1/2*(2*(2*(2*a*b^2 - (a*b - b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*(a*e^(2*c) + b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (a^3*b + a^2*b^2 - a*b^3 - b^4 + 2*(a^2*b + 2*a*b^2 + b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(-a*e^(2*c) - b*e^(2*c))*e^(2*c) + (2*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 - (a^4 - 2*a^2*b^2 + b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - b^2*e^(2*c) - sqrt((a^2*e^(2*c) - b^2*e^(2*c))^2 - (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*(a^2 + 2*a*b + b^2)))/(a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))))*e^(-4*c)/((a^7 + 5*a^6*b + 9*a^5*b^2 + 5*a^4*b^3 - 5*a^3*b^4 - 9*a^2*b^5 - 5*a*b^6 - b^7 + 2*(a^6 + 6*a^5*b + 15*a^4*b^2 + 20*a^3*b^3 + 15*a^2*b^4 + 6*a*b^5 + b^6)*sqrt(-a*b))*abs(-a*e^(2*c) - b*e^(2*c))) + 2*(2*(4*a^2*b^2 - 4*a*b^3 + (a^2*b - 6*a*b^2 + b^3)*sqrt(-a*b))*(a*e^(2*c) + b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (a^4*b - 4*a^3*b^2 - 10*a^2*b^3 - 4*a*b^4 + b^5 - 4*(a^3*b + a^2*b^2 - a*b^3 - b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*abs(-a*e^(2*c) - b*e^(2*c))*e^(2*c) + (4*a^5*b - 8*a^3*b^3 + 4*a*b^5 + (a^5 - 5*a^4*b - 6*a^3*b^2 + 6*a^2*b^3 + 5*a*b^4 - b^5)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - b^2*e^(2*c) + sqrt((a^2*e^(2*c) - b^2*e^(2*c))^2 - (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*(a^2 + 2*a*b + b^2)))/(a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))))*e^(-4*c)/((a^6 + 4*a^5*b + 5*a^4*b^2 - 5*a^2*b^4 - 4*a*b^5 - b^6 - 2*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a*e^(2*c) - b*e^(2*c))) - e^(d*x + 6*c)/(a*e^(5*c) + b*e^(5*c)) - e^(-d*x)/(a*e^c + b*e^c))/d","B",0
29,1,958,0,0.214951," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(4 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{4} b - 5 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4} + 4 \, {\left(a^{3} b - a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} + {\left(4 \, a^{5} b - 8 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - {\left(a^{5} - 7 \, a^{4} b + 7 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} {\left(a^{2} + a b\right)}}}{a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} - 2 \, a^{7} b - 17 \, a^{6} b^{2} - 28 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6} + 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)} \sqrt{-a b}\right)} {\left| a \right|}} + \frac{{\left(2 \, {\left(4 \, a^{2} b^{2} - 4 \, a b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{4} b - 5 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4} - 4 \, {\left(a^{3} b - a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} + {\left(4 \, a^{5} b - 8 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + {\left(a^{5} - 7 \, a^{4} b + 7 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} {\left(a^{2} + a b\right)}}}{a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} - 2 \, a^{7} b - 17 \, a^{6} b^{2} - 28 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6} - 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)} \sqrt{-a b}\right)} {\left| a \right|}} + \frac{\log\left(e^{\left(d x + c\right)} + 1\right)}{a} - \frac{\log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a}}{d}"," ",0,"-((2*(4*a^2*b^2 - 4*a*b^3 - (a^2*b - 6*a*b^2 + b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^4*b - 5*a^3*b^2 - 5*a^2*b^3 + a*b^4 + 4*(a^3*b - a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) + (4*a^5*b - 8*a^4*b^2 + 4*a^3*b^3 - (a^5 - 7*a^4*b + 7*a^3*b^2 - a^2*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - a*b*e^(2*c) + sqrt((a^2*e^(2*c) - a*b*e^(2*c))^2 - (a^2*e^(4*c) + a*b*e^(4*c))*(a^2 + a*b)))/(a^2*e^(4*c) + a*b*e^(4*c))))*e^(-2*c)/((a^8 - 2*a^7*b - 17*a^6*b^2 - 28*a^5*b^3 - 17*a^4*b^4 - 2*a^3*b^5 + a^2*b^6 + 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)*sqrt(-a*b))*abs(a)) + (2*(4*a^2*b^2 - 4*a*b^3 + (a^2*b - 6*a*b^2 + b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^4*b - 5*a^3*b^2 - 5*a^2*b^3 + a*b^4 - 4*(a^3*b - a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) + (4*a^5*b - 8*a^4*b^2 + 4*a^3*b^3 + (a^5 - 7*a^4*b + 7*a^3*b^2 - a^2*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - a*b*e^(2*c) - sqrt((a^2*e^(2*c) - a*b*e^(2*c))^2 - (a^2*e^(4*c) + a*b*e^(4*c))*(a^2 + a*b)))/(a^2*e^(4*c) + a*b*e^(4*c))))*e^(-2*c)/((a^8 - 2*a^7*b - 17*a^6*b^2 - 28*a^5*b^3 - 17*a^4*b^4 - 2*a^3*b^5 + a^2*b^6 - 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)*sqrt(-a*b))*abs(a)) + log(e^(d*x + c) + 1)/a - log(abs(e^(d*x + c) - 1))/a)/d","B",0
30,1,69,0,0.347722," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{2}{a {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}}}{d}"," ",0,"-(b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a) + 2/(a*(e^(2*d*x + 2*c) - 1)))/d","A",0
31,1,475,0,0.376835," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, a b - b^{2} - \sqrt{-a b} {\left(a - 3 \, b\right)}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} {\left(a^{3} + a^{2} b\right)}}}{a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} - a^{2} b + 2 \, \sqrt{-a b} a^{2}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}}} + \frac{2 \, {\left(3 \, a b - b^{2} + \sqrt{-a b} {\left(a - 3 \, b\right)}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} {\left(a^{3} + a^{2} b\right)}}}{a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} - a^{2} b - 2 \, \sqrt{-a b} a^{2}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}}} + \frac{{\left(a e^{c} + 2 \, b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right)}{a^{2}} - \frac{{\left(a e^{c} + 2 \, b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}\right)}}{a {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(3*a*b - b^2 - sqrt(-a*b)*(a - 3*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a^2*b*e^(2*c) + sqrt((a^3*e^(2*c) - a^2*b*e^(2*c))^2 - (a^3*e^(4*c) + a^2*b*e^(4*c))*(a^3 + a^2*b)))/(a^3*e^(4*c) + a^2*b*e^(4*c))))*e^(-2*c)/((a^3 - a^2*b + 2*sqrt(-a*b)*a^2)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))) + 2*(3*a*b - b^2 + sqrt(-a*b)*(a - 3*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a^2*b*e^(2*c) - sqrt((a^3*e^(2*c) - a^2*b*e^(2*c))^2 - (a^3*e^(4*c) + a^2*b*e^(4*c))*(a^3 + a^2*b)))/(a^3*e^(4*c) + a^2*b*e^(4*c))))*e^(-2*c)/((a^3 - a^2*b - 2*sqrt(-a*b)*a^2)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))) + (a*e^c + 2*b*e^c)*e^(-c)*log(e^(d*x + c) + 1)/a^2 - (a*e^c + 2*b*e^c)*e^(-c)*log(abs(e^(d*x + c) - 1))/a^2 - 2*(e^(3*d*x + 3*c) + e^(d*x + c))/(a*(e^(2*d*x + 2*c) - 1)^2))/d","B",0
32,1,132,0,0.359866," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a b e^{\left(2 \, c\right)} + b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a^{2}} + \frac{2 \, {\left(3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a + 3 \, b\right)}}{a^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a*b*e^(2*c) + b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a^2) + 2*(3*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) - 6*b*e^(2*d*x + 2*c) + 2*a + 3*b)/(a^2*(e^(2*d*x + 2*c) - 1)^3))/d","B",0
33,1,525,0,1.905729," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{2} - 6 \, a b + b^{2}\right)} d x}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{96 \, {\left(a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{{\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 108 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 18 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 8 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x\right)}}{a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}} + \frac{a^{2} e^{\left(4 \, d x + 28 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 28 \, c\right)} + b^{2} e^{\left(4 \, d x + 28 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 26 \, c\right)} + 8 \, b^{2} e^{\left(2 \, d x + 26 \, c\right)}}{a^{4} e^{\left(24 \, c\right)} + 4 \, a^{3} b e^{\left(24 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(24 \, c\right)} + 4 \, a b^{3} e^{\left(24 \, c\right)} + b^{4} e^{\left(24 \, c\right)}} - \frac{64 \, {\left(a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} b + a b^{2}\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{64 \, d}"," ",0,"1/64*(24*(a^2 - 6*a*b + b^2)*d*x/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 96*(a^2*b*e^(2*c) - a*b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt(a*b)) - (18*a^2*e^(4*d*x + 4*c) - 108*a*b*e^(4*d*x + 4*c) + 18*b^2*e^(4*d*x + 4*c) - 8*a^2*e^(2*d*x + 2*c) + 8*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-4*d*x)/(a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c)) + (a^2*e^(4*d*x + 28*c) + 2*a*b*e^(4*d*x + 28*c) + b^2*e^(4*d*x + 28*c) - 8*a^2*e^(2*d*x + 26*c) + 8*b^2*e^(2*d*x + 26*c))/(a^4*e^(24*c) + 4*a^3*b*e^(24*c) + 6*a^2*b^2*e^(24*c) + 4*a*b^3*e^(24*c) + b^4*e^(24*c)) - 64*(a^2*b*e^(2*d*x + 2*c) - a*b^2*e^(2*d*x + 2*c) + a^2*b + a*b^2)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
34,1,1929,0,0.943108," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} - 15 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-3 \, d x\right)}}{a^{3} e^{\left(3 \, c\right)} + 3 \, a^{2} b e^{\left(3 \, c\right)} + 3 \, a b^{2} e^{\left(3 \, c\right)} + b^{3} e^{\left(3 \, c\right)}} - \frac{12 \, {\left(2 \, {\left(6 \, a^{2} b^{2} - 4 \, a b^{3} + {\left(3 \, a^{2} b - 5 \, a b^{2} + 2 \, b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{6} b + 7 \, a^{5} b^{2} - 10 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 3 \, a b^{6} + 2 \, b^{7} - 2 \, {\left(3 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 5 \, a b^{5} - 2 \, b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(6 \, a^{9} b + 26 \, a^{8} b^{2} + 34 \, a^{7} b^{3} - 6 \, a^{6} b^{4} - 50 \, a^{5} b^{5} - 34 \, a^{4} b^{6} + 6 \, a^{3} b^{7} + 14 \, a^{2} b^{8} + 4 \, a b^{9} + {\left(3 \, a^{9} + 10 \, a^{8} b + 4 \, a^{7} b^{2} - 20 \, a^{6} b^{3} - 22 \, a^{5} b^{4} + 8 \, a^{4} b^{5} + 20 \, a^{3} b^{6} + 4 \, a^{2} b^{7} - 5 \, a b^{8} - 2 \, b^{9}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|}} - \frac{12 \, {\left(2 \, {\left(6 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(3 \, a^{2} b - 5 \, a b^{2} + 2 \, b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{6} b + 7 \, a^{5} b^{2} - 10 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 3 \, a b^{6} + 2 \, b^{7} + 2 \, {\left(3 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 5 \, a b^{5} - 2 \, b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(6 \, a^{9} b + 26 \, a^{8} b^{2} + 34 \, a^{7} b^{3} - 6 \, a^{6} b^{4} - 50 \, a^{5} b^{5} - 34 \, a^{4} b^{6} + 6 \, a^{3} b^{7} + 14 \, a^{2} b^{8} + 4 \, a b^{9} - {\left(3 \, a^{9} + 10 \, a^{8} b + 4 \, a^{7} b^{2} - 20 \, a^{6} b^{3} - 22 \, a^{5} b^{4} + 8 \, a^{4} b^{5} + 20 \, a^{3} b^{6} + 4 \, a^{2} b^{7} - 5 \, a b^{8} - 2 \, b^{9}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|}} - \frac{a^{4} e^{\left(3 \, d x + 36 \, c\right)} + 4 \, a^{3} b e^{\left(3 \, d x + 36 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(3 \, d x + 36 \, c\right)} + 4 \, a b^{3} e^{\left(3 \, d x + 36 \, c\right)} + b^{4} e^{\left(3 \, d x + 36 \, c\right)} - 9 \, a^{4} e^{\left(d x + 34 \, c\right)} - 12 \, a^{3} b e^{\left(d x + 34 \, c\right)} + 18 \, a^{2} b^{2} e^{\left(d x + 34 \, c\right)} + 36 \, a b^{3} e^{\left(d x + 34 \, c\right)} + 15 \, b^{4} e^{\left(d x + 34 \, c\right)}}{a^{6} e^{\left(33 \, c\right)} + 6 \, a^{5} b e^{\left(33 \, c\right)} + 15 \, a^{4} b^{2} e^{\left(33 \, c\right)} + 20 \, a^{3} b^{3} e^{\left(33 \, c\right)} + 15 \, a^{2} b^{4} e^{\left(33 \, c\right)} + 6 \, a b^{5} e^{\left(33 \, c\right)} + b^{6} e^{\left(33 \, c\right)}} - \frac{24 \, {\left(a b e^{\left(3 \, d x + 3 \, c\right)} + a b e^{\left(d x + c\right)}\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{24 \, d}"," ",0,"-1/24*((9*a*e^(2*d*x + 2*c) - 15*b*e^(2*d*x + 2*c) - a - b)*e^(-3*d*x)/(a^3*e^(3*c) + 3*a^2*b*e^(3*c) + 3*a*b^2*e^(3*c) + b^3*e^(3*c)) - 12*(2*(6*a^2*b^2 - 4*a*b^3 + (3*a^2*b - 5*a*b^2 + 2*b^3)*sqrt(-a*b))*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^6*b + 7*a^5*b^2 - 10*a^3*b^4 - 5*a^2*b^5 + 3*a*b^6 + 2*b^7 - 2*(3*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 5*a*b^5 - 2*b^6)*sqrt(-a*b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (6*a^9*b + 26*a^8*b^2 + 34*a^7*b^3 - 6*a^6*b^4 - 50*a^5*b^5 - 34*a^4*b^6 + 6*a^3*b^7 + 14*a^2*b^8 + 4*a*b^9 + (3*a^9 + 10*a^8*b + 4*a^7*b^2 - 20*a^6*b^3 - 22*a^5*b^4 + 8*a^4*b^5 + 20*a^3*b^6 + 4*a^2*b^7 - 5*a*b^8 - 2*b^9)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c) + sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))^2 - (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)))/(a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))))*e^(-4*c)/((a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))) - 12*(2*(6*a^2*b^2 - 4*a*b^3 - (3*a^2*b - 5*a*b^2 + 2*b^3)*sqrt(-a*b))*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^6*b + 7*a^5*b^2 - 10*a^3*b^4 - 5*a^2*b^5 + 3*a*b^6 + 2*b^7 + 2*(3*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 - 5*a*b^5 - 2*b^6)*sqrt(-a*b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (6*a^9*b + 26*a^8*b^2 + 34*a^7*b^3 - 6*a^6*b^4 - 50*a^5*b^5 - 34*a^4*b^6 + 6*a^3*b^7 + 14*a^2*b^8 + 4*a*b^9 - (3*a^9 + 10*a^8*b + 4*a^7*b^2 - 20*a^6*b^3 - 22*a^5*b^4 + 8*a^4*b^5 + 20*a^3*b^6 + 4*a^2*b^7 - 5*a*b^8 - 2*b^9)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c) - sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))^2 - (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)))/(a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))))*e^(-4*c)/((a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))) - (a^4*e^(3*d*x + 36*c) + 4*a^3*b*e^(3*d*x + 36*c) + 6*a^2*b^2*e^(3*d*x + 36*c) + 4*a*b^3*e^(3*d*x + 36*c) + b^4*e^(3*d*x + 36*c) - 9*a^4*e^(d*x + 34*c) - 12*a^3*b*e^(d*x + 34*c) + 18*a^2*b^2*e^(d*x + 34*c) + 36*a*b^3*e^(d*x + 34*c) + 15*b^4*e^(d*x + 34*c))/(a^6*e^(33*c) + 6*a^5*b*e^(33*c) + 15*a^4*b^2*e^(33*c) + 20*a^3*b^3*e^(33*c) + 15*a^2*b^4*e^(33*c) + 6*a*b^5*e^(33*c) + b^6*e^(33*c)) - 24*(a*b*e^(3*d*x + 3*c) + a*b*e^(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
35,1,400,0,1.131757," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a - 3 \, b\right)} d x}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{12 \, {\left(3 \, a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{3 \, e^{\left(2 \, d x + 12 \, c\right)}}{a^{2} e^{\left(10 \, c\right)} + 2 \, a b e^{\left(10 \, c\right)} + b^{2} e^{\left(10 \, c\right)}} - \frac{2 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} - 4 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 6 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 15 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 20 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 24 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 3 \, a^{2} - 6 \, a b - 3 \, b^{2}}{{\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)} {\left(a e^{\left(2 \, d x\right)} + b e^{\left(2 \, d x\right)} + a e^{\left(6 \, d x + 4 \, c\right)} + b e^{\left(6 \, d x + 4 \, c\right)} + 2 \, a e^{\left(4 \, d x + 2 \, c\right)} - 2 \, b e^{\left(4 \, d x + 2 \, c\right)}\right)}}}{24 \, d}"," ",0,"-1/24*(12*(a - 3*b)*d*x/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 12*(3*a*b*e^(2*c) - b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) - 3*e^(2*d*x + 12*c)/(a^2*e^(10*c) + 2*a*b*e^(10*c) + b^2*e^(10*c)) - (2*a^2*e^(6*d*x + 6*c) - 4*a*b*e^(6*d*x + 6*c) - 6*b^2*e^(6*d*x + 6*c) + a^2*e^(4*d*x + 4*c) + 2*a*b*e^(4*d*x + 4*c) - 15*b^2*e^(4*d*x + 4*c) - 4*a^2*e^(2*d*x + 2*c) + 20*a*b*e^(2*d*x + 2*c) + 24*b^2*e^(2*d*x + 2*c) - 3*a^2 - 6*a*b - 3*b^2)/((a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))*(a*e^(2*d*x) + b*e^(2*d*x) + a*e^(6*d*x + 4*c) + b*e^(6*d*x + 4*c) + 2*a*e^(4*d*x + 2*c) - 2*b*e^(4*d*x + 2*c))))/d","B",0
36,1,924,0,0.407628," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(5 \, a^{2} b - 10 \, a b^{2} + b^{3} - {\left(a^{2} - 10 \, a b + 5 \, b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{7} - 11 \, a^{6} b - 39 \, a^{5} b^{2} - 27 \, a^{4} b^{3} + 27 \, a^{3} b^{4} + 39 \, a^{2} b^{5} + 11 \, a b^{6} - b^{7} + 2 \, {\left(3 \, a^{6} + 2 \, a^{5} b - 19 \, a^{4} b^{2} - 36 \, a^{3} b^{3} - 19 \, a^{2} b^{4} + 2 \, a b^{5} + 3 \, b^{6}\right)} \sqrt{-a b}} + \frac{3 \, {\left(5 \, a^{2} b - 10 \, a b^{2} + b^{3} + {\left(a^{2} - 10 \, a b + 5 \, b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{7} - 11 \, a^{6} b - 39 \, a^{5} b^{2} - 27 \, a^{4} b^{3} + 27 \, a^{3} b^{4} + 39 \, a^{2} b^{5} + 11 \, a b^{6} - b^{7} - 2 \, {\left(3 \, a^{6} + 2 \, a^{5} b - 19 \, a^{4} b^{2} - 36 \, a^{3} b^{3} - 19 \, a^{2} b^{4} + 2 \, a b^{5} + 3 \, b^{6}\right)} \sqrt{-a b}} + \frac{e^{\left(d x + 10 \, c\right)}}{a^{2} e^{\left(9 \, c\right)} + 2 \, a b e^{\left(9 \, c\right)} + b^{2} e^{\left(9 \, c\right)}} + \frac{a e^{\left(4 \, d x + 4 \, c\right)} - b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b}{{\left(a^{2} e^{c} + 2 \, a b e^{c} + b^{2} e^{c}\right)} {\left(a e^{\left(5 \, d x + 4 \, c\right)} + b e^{\left(5 \, d x + 4 \, c\right)} + 2 \, a e^{\left(3 \, d x + 2 \, c\right)} - 2 \, b e^{\left(3 \, d x + 2 \, c\right)} + a e^{\left(d x\right)} + b e^{\left(d x\right)}\right)}}}{2 \, d}"," ",0,"1/2*(3*(5*a^2*b - 10*a*b^2 + b^3 - (a^2 - 10*a*b + 5*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) + sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^7 - 11*a^6*b - 39*a^5*b^2 - 27*a^4*b^3 + 27*a^3*b^4 + 39*a^2*b^5 + 11*a*b^6 - b^7 + 2*(3*a^6 + 2*a^5*b - 19*a^4*b^2 - 36*a^3*b^3 - 19*a^2*b^4 + 2*a*b^5 + 3*b^6)*sqrt(-a*b)) + 3*(5*a^2*b - 10*a*b^2 + b^3 + (a^2 - 10*a*b + 5*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) - sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^7 - 11*a^6*b - 39*a^5*b^2 - 27*a^4*b^3 + 27*a^3*b^4 + 39*a^2*b^5 + 11*a*b^6 - b^7 - 2*(3*a^6 + 2*a^5*b - 19*a^4*b^2 - 36*a^3*b^3 - 19*a^2*b^4 + 2*a*b^5 + 3*b^6)*sqrt(-a*b)) + e^(d*x + 10*c)/(a^2*e^(9*c) + 2*a*b*e^(9*c) + b^2*e^(9*c)) + (a*e^(4*d*x + 4*c) - b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 4*b*e^(2*d*x + 2*c) + a + b)/((a^2*e^c + 2*a*b*e^c + b^2*e^c)*(a*e^(5*d*x + 4*c) + b*e^(5*d*x + 4*c) + 2*a*e^(3*d*x + 2*c) - 2*b*e^(3*d*x + 2*c) + a*e^(d*x) + b*e^(d*x))))/d","B",0
37,1,1405,0,0.373383," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(6 \, a^{2} b^{2} + 4 \, a b^{3} - {\left(3 \, a^{2} b - a b^{2} - 2 \, b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)}\right)}^{2} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{6} b + 5 \, a^{5} b^{2} - a^{4} b^{3} - 5 \, a^{3} b^{4} - 2 \, a^{2} b^{5} + 2 \, {\left(3 \, a^{5} b + 8 \, a^{4} b^{2} + 7 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(6 \, a^{9} b + 10 \, a^{8} b^{2} - 2 \, a^{7} b^{3} - 10 \, a^{6} b^{4} - 4 \, a^{5} b^{5} - {\left(3 \, a^{9} + 2 \, a^{8} b - 6 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + 3 \, a^{5} b^{4} + 2 \, a^{4} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{11} + 5 \, a^{10} b + 9 \, a^{9} b^{2} + 5 \, a^{8} b^{3} - 5 \, a^{7} b^{4} - 9 \, a^{6} b^{5} - 5 \, a^{5} b^{6} - a^{4} b^{7} + 2 \, {\left(a^{10} + 6 \, a^{9} b + 15 \, a^{8} b^{2} + 20 \, a^{7} b^{3} + 15 \, a^{6} b^{4} + 6 \, a^{5} b^{5} + a^{4} b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(12 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 8 \, a b^{4} + {\left(3 \, a^{3} b - 16 \, a^{2} b^{2} - 9 \, a b^{3} + 2 \, b^{4}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{7} b - 10 \, a^{6} b^{2} - 38 \, a^{5} b^{3} - 32 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + 2 \, a^{2} b^{6} - 4 \, {\left(3 \, a^{6} b + 5 \, a^{5} b^{2} - a^{4} b^{3} - 5 \, a^{3} b^{4} - 2 \, a^{2} b^{5}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(12 \, a^{10} b + 8 \, a^{9} b^{2} - 24 \, a^{8} b^{3} - 16 \, a^{7} b^{4} + 12 \, a^{6} b^{5} + 8 \, a^{5} b^{6} + {\left(3 \, a^{10} - 13 \, a^{9} b - 28 \, a^{8} b^{2} + 6 \, a^{7} b^{3} + 27 \, a^{6} b^{4} + 7 \, a^{5} b^{5} - 2 \, a^{4} b^{6}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{10} + 4 \, a^{9} b + 5 \, a^{8} b^{2} - 5 \, a^{6} b^{4} - 4 \, a^{5} b^{5} - a^{4} b^{6} - 2 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|}} + \frac{2 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(d x + c\right)}\right)}}{{\left(a^{2} + a b\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}} - \frac{2 \, \log\left(e^{\left(d x + c\right)} + 1\right)}{a^{2}} + \frac{2 \, \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*((2*(6*a^2*b^2 + 4*a*b^3 - (3*a^2*b - a*b^2 - 2*b^3)*sqrt(-a*b))*(a^3*e^(2*c) + a^2*b*e^(2*c))^2*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^6*b + 5*a^5*b^2 - a^4*b^3 - 5*a^3*b^4 - 2*a^2*b^5 + 2*(3*a^5*b + 8*a^4*b^2 + 7*a^3*b^3 + 2*a^2*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (6*a^9*b + 10*a^8*b^2 - 2*a^7*b^3 - 10*a^6*b^4 - 4*a^5*b^5 - (3*a^9 + 2*a^8*b - 6*a^7*b^2 - 4*a^6*b^3 + 3*a^5*b^4 + 2*a^4*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c) - sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c))^2 - (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*(a^4 + 2*a^3*b + a^2*b^2)))/(a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))))*e^(-4*c)/((a^11 + 5*a^10*b + 9*a^9*b^2 + 5*a^8*b^3 - 5*a^7*b^4 - 9*a^6*b^5 - 5*a^5*b^6 - a^4*b^7 + 2*(a^10 + 6*a^9*b + 15*a^8*b^2 + 20*a^7*b^3 + 15*a^6*b^4 + 6*a^5*b^5 + a^4*b^6)*sqrt(-a*b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))) + (2*(12*a^3*b^2 - 4*a^2*b^3 - 8*a*b^4 + (3*a^3*b - 16*a^2*b^2 - 9*a*b^3 + 2*b^4)*sqrt(-a*b))*(a^3*e^(2*c) + a^2*b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^7*b - 10*a^6*b^2 - 38*a^5*b^3 - 32*a^4*b^4 - 5*a^3*b^5 + 2*a^2*b^6 - 4*(3*a^6*b + 5*a^5*b^2 - a^4*b^3 - 5*a^3*b^4 - 2*a^2*b^5)*sqrt(-a*b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (12*a^10*b + 8*a^9*b^2 - 24*a^8*b^3 - 16*a^7*b^4 + 12*a^6*b^5 + 8*a^5*b^6 + (3*a^10 - 13*a^9*b - 28*a^8*b^2 + 6*a^7*b^3 + 27*a^6*b^4 + 7*a^5*b^5 - 2*a^4*b^6)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c) + sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c))^2 - (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*(a^4 + 2*a^3*b + a^2*b^2)))/(a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))))*e^(-4*c)/((a^10 + 4*a^9*b + 5*a^8*b^2 - 5*a^6*b^4 - 4*a^5*b^5 - a^4*b^6 - 2*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))) + 2*(b*e^(3*d*x + 3*c) + b*e^(d*x + c))/((a^2 + a*b)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)) - 2*log(e^(d*x + c) + 1)/a^2 + 2*log(abs(e^(d*x + c) - 1))/a^2)/d","B",0
38,1,227,0,0.620816," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{3 \, b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{2 \, {\left(2 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{2} + 5 \, a b + 3 \, b^{2}\right)}}{{\left(a^{3} + a^{2} b\right)} {\left(a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)}}}{2 \, d}"," ",0,"-1/2*(3*b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2) + 2*(2*a^2*e^(4*d*x + 4*c) + 3*a*b*e^(4*d*x + 4*c) + 3*b^2*e^(4*d*x + 4*c) + 4*a^2*e^(2*d*x + 2*c) - 6*b^2*e^(2*d*x + 2*c) + 2*a^2 + 5*a*b + 3*b^2)/((a^3 + a^2*b)*(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) - a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) - a - b)))/d","B",0
39,1,1074,0,0.713368," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(12 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 16 \, a b^{4} + {\left(3 \, a^{3} b - 14 \, a^{2} b^{2} - 21 \, a b^{3} + 4 \, b^{4}\right)} \sqrt{-a b}\right)} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{5} b - 11 \, a^{4} b^{2} - 35 \, a^{3} b^{3} - 17 \, a^{2} b^{4} + 4 \, a b^{5} - 4 \, {\left(3 \, a^{4} b + 4 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} + {\left(12 \, a^{6} b - 8 \, a^{5} b^{2} - 20 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + {\left(3 \, a^{6} - 17 \, a^{5} b - 7 \, a^{4} b^{2} + 25 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{3} b e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{3} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + a^{3} b e^{\left(4 \, c\right)}\right)} {\left(a^{4} + a^{3} b\right)}}}{a^{4} e^{\left(4 \, c\right)} + a^{3} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} + 2 \, a^{7} b - 2 \, a^{5} b^{3} - a^{4} b^{4} - 2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a \right|}} + \frac{{\left(2 \, {\left(12 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 16 \, a b^{4} - {\left(3 \, a^{3} b - 14 \, a^{2} b^{2} - 21 \, a b^{3} + 4 \, b^{4}\right)} \sqrt{-a b}\right)} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(3 \, a^{5} b - 11 \, a^{4} b^{2} - 35 \, a^{3} b^{3} - 17 \, a^{2} b^{4} + 4 \, a b^{5} + 4 \, {\left(3 \, a^{4} b + 4 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 4 \, a b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} + {\left(12 \, a^{6} b - 8 \, a^{5} b^{2} - 20 \, a^{4} b^{3} + 16 \, a^{3} b^{4} - {\left(3 \, a^{6} - 17 \, a^{5} b - 7 \, a^{4} b^{2} + 25 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{3} b e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{3} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + a^{3} b e^{\left(4 \, c\right)}\right)} {\left(a^{4} + a^{3} b\right)}}}{a^{4} e^{\left(4 \, c\right)} + a^{3} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} + 2 \, a^{7} b - 2 \, a^{5} b^{3} - a^{4} b^{4} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a \right|}} - \frac{{\left(a e^{c} + 4 \, b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right)}{a^{3}} + \frac{{\left(a e^{c} + 4 \, b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a^{3}} + \frac{2 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a^{2}} + \frac{2 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}\right)}}{a^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((2*(12*a^3*b^2 + 4*a^2*b^3 - 16*a*b^4 + (3*a^3*b - 14*a^2*b^2 - 21*a*b^3 + 4*b^4)*sqrt(-a*b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^5*b - 11*a^4*b^2 - 35*a^3*b^3 - 17*a^2*b^4 + 4*a*b^5 - 4*(3*a^4*b + 4*a^3*b^2 - 3*a^2*b^3 - 4*a*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) + (12*a^6*b - 8*a^5*b^2 - 20*a^4*b^3 + 16*a^3*b^4 + (3*a^6 - 17*a^5*b - 7*a^4*b^2 + 25*a^3*b^3 - 4*a^2*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^3*b*e^(2*c) + sqrt((a^4*e^(2*c) - a^3*b*e^(2*c))^2 - (a^4*e^(4*c) + a^3*b*e^(4*c))*(a^4 + a^3*b)))/(a^4*e^(4*c) + a^3*b*e^(4*c))))*e^(-2*c)/((a^8 + 2*a^7*b - 2*a^5*b^3 - a^4*b^4 - 2*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a)) + (2*(12*a^3*b^2 + 4*a^2*b^3 - 16*a*b^4 - (3*a^3*b - 14*a^2*b^2 - 21*a*b^3 + 4*b^4)*sqrt(-a*b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) + (3*a^5*b - 11*a^4*b^2 - 35*a^3*b^3 - 17*a^2*b^4 + 4*a*b^5 + 4*(3*a^4*b + 4*a^3*b^2 - 3*a^2*b^3 - 4*a*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) + (12*a^6*b - 8*a^5*b^2 - 20*a^4*b^3 + 16*a^3*b^4 - (3*a^6 - 17*a^5*b - 7*a^4*b^2 + 25*a^3*b^3 - 4*a^2*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^3*b*e^(2*c) - sqrt((a^4*e^(2*c) - a^3*b*e^(2*c))^2 - (a^4*e^(4*c) + a^3*b*e^(4*c))*(a^4 + a^3*b)))/(a^4*e^(4*c) + a^3*b*e^(4*c))))*e^(-2*c)/((a^8 + 2*a^7*b - 2*a^5*b^3 - a^4*b^4 + 2*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a)) - (a*e^c + 4*b*e^c)*e^(-c)*log(e^(d*x + c) + 1)/a^3 + (a*e^c + 4*b*e^c)*e^(-c)*log(abs(e^(d*x + c) - 1))/a^3 + 2*(b*e^(3*d*x + 3*c) + b*e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a^2) + 2*(e^(3*d*x + 3*c) + e^(d*x + c))/(a^2*(e^(2*d*x + 2*c) - 1)^2))/d","B",0
40,1,221,0,0.562570," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a b e^{\left(2 \, c\right)} + 5 \, b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a^{3}} - \frac{6 \, {\left(a b e^{\left(2 \, d x + 2 \, c\right)} - b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a b + b^{2}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a^{3}} + \frac{8 \, {\left(3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 3 \, a e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + 3 \, b\right)}}{a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(3*a*b*e^(2*c) + 5*b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a^3) - 6*(a*b*e^(2*d*x + 2*c) - b^2*e^(2*d*x + 2*c) + a*b + b^2)/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a^3) + 8*(3*b*e^(4*d*x + 4*c) - 3*a*e^(2*d*x + 2*c) - 6*b*e^(2*d*x + 2*c) + a + 3*b)/(a^3*(e^(2*d*x + 2*c) - 1)^3))/d","B",0
41,1,923,0,3.003715," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{2} - 10 \, a b + 5 \, b^{2}\right)} d x}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} + \frac{24 \, {\left(5 \, a^{2} b e^{\left(2 \, c\right)} - 10 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sqrt{a b}} + \frac{a^{3} e^{\left(4 \, d x + 36 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, d x + 36 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, d x + 36 \, c\right)} + b^{3} e^{\left(4 \, d x + 36 \, c\right)} - 8 \, a^{3} e^{\left(2 \, d x + 34 \, c\right)} + 24 \, a b^{2} e^{\left(2 \, d x + 34 \, c\right)} + 16 \, b^{3} e^{\left(2 \, d x + 34 \, c\right)}}{a^{6} e^{\left(32 \, c\right)} + 6 \, a^{5} b e^{\left(32 \, c\right)} + 15 \, a^{4} b^{2} e^{\left(32 \, c\right)} + 20 \, a^{3} b^{3} e^{\left(32 \, c\right)} + 15 \, a^{2} b^{4} e^{\left(32 \, c\right)} + 6 \, a b^{5} e^{\left(32 \, c\right)} + b^{6} e^{\left(32 \, c\right)}} - \frac{6 \, a^{4} e^{\left(12 \, d x + 12 \, c\right)} - 48 \, a^{3} b e^{\left(12 \, d x + 12 \, c\right)} - 84 \, a^{2} b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 30 \, b^{4} e^{\left(12 \, d x + 12 \, c\right)} + 16 \, a^{4} e^{\left(10 \, d x + 10 \, c\right)} - 104 \, a^{3} b e^{\left(10 \, d x + 10 \, c\right)} - 24 \, a^{2} b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 72 \, a b^{3} e^{\left(10 \, d x + 10 \, c\right)} - 24 \, b^{4} e^{\left(10 \, d x + 10 \, c\right)} + 5 \, a^{4} e^{\left(8 \, d x + 8 \, c\right)} + 84 \, a^{3} b e^{\left(8 \, d x + 8 \, c\right)} + 30 \, a^{2} b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 84 \, a b^{3} e^{\left(8 \, d x + 8 \, c\right)} - 123 \, b^{4} e^{\left(8 \, d x + 8 \, c\right)} - 20 \, a^{4} e^{\left(6 \, d x + 6 \, c\right)} + 280 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} - 64 \, a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 152 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 212 \, b^{4} e^{\left(6 \, d x + 6 \, c\right)} - 20 \, a^{4} e^{\left(4 \, d x + 4 \, c\right)} + 136 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} + 224 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 40 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} - 108 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a^{4} e^{\left(2 \, d x + 2 \, c\right)} + 24 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 32 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}}{{\left(a^{5} e^{\left(4 \, c\right)} + 5 \, a^{4} b e^{\left(4 \, c\right)} + 10 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 10 \, a^{2} b^{3} e^{\left(4 \, c\right)} + 5 \, a b^{4} e^{\left(4 \, c\right)} + b^{5} e^{\left(4 \, c\right)}\right)} {\left(a e^{\left(2 \, d x\right)} + b e^{\left(2 \, d x\right)} + a e^{\left(6 \, d x + 4 \, c\right)} + b e^{\left(6 \, d x + 4 \, c\right)} + 2 \, a e^{\left(4 \, d x + 2 \, c\right)} - 2 \, b e^{\left(4 \, d x + 2 \, c\right)}\right)}^{2}}}{64 \, d}"," ",0,"1/64*(24*(a^2 - 10*a*b + 5*b^2)*d*x/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) + 24*(5*a^2*b*e^(2*c) - 10*a*b^2*e^(2*c) + b^3*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sqrt(a*b)) + (a^3*e^(4*d*x + 36*c) + 3*a^2*b*e^(4*d*x + 36*c) + 3*a*b^2*e^(4*d*x + 36*c) + b^3*e^(4*d*x + 36*c) - 8*a^3*e^(2*d*x + 34*c) + 24*a*b^2*e^(2*d*x + 34*c) + 16*b^3*e^(2*d*x + 34*c))/(a^6*e^(32*c) + 6*a^5*b*e^(32*c) + 15*a^4*b^2*e^(32*c) + 20*a^3*b^3*e^(32*c) + 15*a^2*b^4*e^(32*c) + 6*a*b^5*e^(32*c) + b^6*e^(32*c)) - (6*a^4*e^(12*d*x + 12*c) - 48*a^3*b*e^(12*d*x + 12*c) - 84*a^2*b^2*e^(12*d*x + 12*c) + 30*b^4*e^(12*d*x + 12*c) + 16*a^4*e^(10*d*x + 10*c) - 104*a^3*b*e^(10*d*x + 10*c) - 24*a^2*b^2*e^(10*d*x + 10*c) + 72*a*b^3*e^(10*d*x + 10*c) - 24*b^4*e^(10*d*x + 10*c) + 5*a^4*e^(8*d*x + 8*c) + 84*a^3*b*e^(8*d*x + 8*c) + 30*a^2*b^2*e^(8*d*x + 8*c) + 84*a*b^3*e^(8*d*x + 8*c) - 123*b^4*e^(8*d*x + 8*c) - 20*a^4*e^(6*d*x + 6*c) + 280*a^3*b*e^(6*d*x + 6*c) - 64*a^2*b^2*e^(6*d*x + 6*c) - 152*a*b^3*e^(6*d*x + 6*c) + 212*b^4*e^(6*d*x + 6*c) - 20*a^4*e^(4*d*x + 4*c) + 136*a^3*b*e^(4*d*x + 4*c) + 224*a^2*b^2*e^(4*d*x + 4*c) - 40*a*b^3*e^(4*d*x + 4*c) - 108*b^4*e^(4*d*x + 4*c) - 4*a^4*e^(2*d*x + 2*c) + 24*a^2*b^2*e^(2*d*x + 2*c) + 32*a*b^3*e^(2*d*x + 2*c) + 12*b^4*e^(2*d*x + 2*c) + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)/((a^5*e^(4*c) + 5*a^4*b*e^(4*c) + 10*a^3*b^2*e^(4*c) + 10*a^2*b^3*e^(4*c) + 5*a*b^4*e^(4*c) + b^5*e^(4*c))*(a*e^(2*d*x) + b*e^(2*d*x) + a*e^(6*d*x + 4*c) + b*e^(6*d*x + 4*c) + 2*a*e^(4*d*x + 2*c) - 2*b*e^(4*d*x + 2*c))^2))/d","B",0
42,1,1748,0,1.638661," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(15 \, a^{3} b - 50 \, a^{2} b^{2} + 43 \, a b^{3} - 4 \, b^{4} - {\left(3 \, a^{3} - 34 \, a^{2} b + 55 \, a b^{2} - 20 \, b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 2 \, a^{3} b^{2} e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - 3 \, a b^{4} e^{\left(2 \, c\right)} - b^{5} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 2 \, a^{3} b^{2} e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - 3 \, a b^{4} e^{\left(2 \, c\right)} - b^{5} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 5 \, a^{4} b e^{\left(4 \, c\right)} + 10 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 10 \, a^{2} b^{3} e^{\left(4 \, c\right)} + 5 \, a b^{4} e^{\left(4 \, c\right)} + b^{5} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 5 \, a^{4} b e^{\left(4 \, c\right)} + 10 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 10 \, a^{2} b^{3} e^{\left(4 \, c\right)} + 5 \, a b^{4} e^{\left(4 \, c\right)} + b^{5} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{9} - 9 \, a^{8} b - 60 \, a^{7} b^{2} - 116 \, a^{6} b^{3} - 66 \, a^{5} b^{4} + 66 \, a^{4} b^{5} + 116 \, a^{3} b^{6} + 60 \, a^{2} b^{7} + 9 \, a b^{8} - b^{9} + 2 \, {\left(3 \, a^{8} + 8 \, a^{7} b - 12 \, a^{6} b^{2} - 72 \, a^{5} b^{3} - 110 \, a^{4} b^{4} - 72 \, a^{3} b^{5} - 12 \, a^{2} b^{6} + 8 \, a b^{7} + 3 \, b^{8}\right)} \sqrt{-a b}} + \frac{15 \, {\left(15 \, a^{3} b - 50 \, a^{2} b^{2} + 43 \, a b^{3} - 4 \, b^{4} + {\left(3 \, a^{3} - 34 \, a^{2} b + 55 \, a b^{2} - 20 \, b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 2 \, a^{3} b^{2} e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - 3 \, a b^{4} e^{\left(2 \, c\right)} - b^{5} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 2 \, a^{3} b^{2} e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - 3 \, a b^{4} e^{\left(2 \, c\right)} - b^{5} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 5 \, a^{4} b e^{\left(4 \, c\right)} + 10 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 10 \, a^{2} b^{3} e^{\left(4 \, c\right)} + 5 \, a b^{4} e^{\left(4 \, c\right)} + b^{5} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 5 \, a^{4} b e^{\left(4 \, c\right)} + 10 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 10 \, a^{2} b^{3} e^{\left(4 \, c\right)} + 5 \, a b^{4} e^{\left(4 \, c\right)} + b^{5} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{9} - 9 \, a^{8} b - 60 \, a^{7} b^{2} - 116 \, a^{6} b^{3} - 66 \, a^{5} b^{4} + 66 \, a^{4} b^{5} + 116 \, a^{3} b^{6} + 60 \, a^{2} b^{7} + 9 \, a b^{8} - b^{9} - 2 \, {\left(3 \, a^{8} + 8 \, a^{7} b - 12 \, a^{6} b^{2} - 72 \, a^{5} b^{3} - 110 \, a^{4} b^{4} - 72 \, a^{3} b^{5} - 12 \, a^{2} b^{6} + 8 \, a b^{7} + 3 \, b^{8}\right)} \sqrt{-a b}} + \frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} - 27 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-3 \, d x\right)}}{a^{4} e^{\left(3 \, c\right)} + 4 \, a^{3} b e^{\left(3 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(3 \, c\right)} + 4 \, a b^{3} e^{\left(3 \, c\right)} + b^{4} e^{\left(3 \, c\right)}} - \frac{a^{6} e^{\left(3 \, d x + 48 \, c\right)} + 6 \, a^{5} b e^{\left(3 \, d x + 48 \, c\right)} + 15 \, a^{4} b^{2} e^{\left(3 \, d x + 48 \, c\right)} + 20 \, a^{3} b^{3} e^{\left(3 \, d x + 48 \, c\right)} + 15 \, a^{2} b^{4} e^{\left(3 \, d x + 48 \, c\right)} + 6 \, a b^{5} e^{\left(3 \, d x + 48 \, c\right)} + b^{6} e^{\left(3 \, d x + 48 \, c\right)} - 9 \, a^{6} e^{\left(d x + 46 \, c\right)} - 18 \, a^{5} b e^{\left(d x + 46 \, c\right)} + 45 \, a^{4} b^{2} e^{\left(d x + 46 \, c\right)} + 180 \, a^{3} b^{3} e^{\left(d x + 46 \, c\right)} + 225 \, a^{2} b^{4} e^{\left(d x + 46 \, c\right)} + 126 \, a b^{5} e^{\left(d x + 46 \, c\right)} + 27 \, b^{6} e^{\left(d x + 46 \, c\right)}}{a^{9} e^{\left(45 \, c\right)} + 9 \, a^{8} b e^{\left(45 \, c\right)} + 36 \, a^{7} b^{2} e^{\left(45 \, c\right)} + 84 \, a^{6} b^{3} e^{\left(45 \, c\right)} + 126 \, a^{5} b^{4} e^{\left(45 \, c\right)} + 126 \, a^{4} b^{5} e^{\left(45 \, c\right)} + 84 \, a^{3} b^{6} e^{\left(45 \, c\right)} + 36 \, a^{2} b^{7} e^{\left(45 \, c\right)} + 9 \, a b^{8} e^{\left(45 \, c\right)} + b^{9} e^{\left(45 \, c\right)}} - \frac{6 \, {\left(9 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 5 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 4 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 27 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 13 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 4 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 27 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} - 13 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 4 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 9 \, a^{2} b e^{\left(d x + c\right)} + 5 \, a b^{2} e^{\left(d x + c\right)} - 4 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{24 \, d}"," ",0,"-1/24*(15*(15*a^3*b - 50*a^2*b^2 + 43*a*b^3 - 4*b^4 - (3*a^3 - 34*a^2*b + 55*a*b^2 - 20*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 2*a^3*b^2*e^(2*c) - 2*a^2*b^3*e^(2*c) - 3*a*b^4*e^(2*c) - b^5*e^(2*c) + sqrt((a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 2*a^3*b^2*e^(2*c) - 2*a^2*b^3*e^(2*c) - 3*a*b^4*e^(2*c) - b^5*e^(2*c))^2 - (a^5*e^(4*c) + 5*a^4*b*e^(4*c) + 10*a^3*b^2*e^(4*c) + 10*a^2*b^3*e^(4*c) + 5*a*b^4*e^(4*c) + b^5*e^(4*c))*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)))/(a^5*e^(4*c) + 5*a^4*b*e^(4*c) + 10*a^3*b^2*e^(4*c) + 10*a^2*b^3*e^(4*c) + 5*a*b^4*e^(4*c) + b^5*e^(4*c))))*e^(-2*c)/(a^9 - 9*a^8*b - 60*a^7*b^2 - 116*a^6*b^3 - 66*a^5*b^4 + 66*a^4*b^5 + 116*a^3*b^6 + 60*a^2*b^7 + 9*a*b^8 - b^9 + 2*(3*a^8 + 8*a^7*b - 12*a^6*b^2 - 72*a^5*b^3 - 110*a^4*b^4 - 72*a^3*b^5 - 12*a^2*b^6 + 8*a*b^7 + 3*b^8)*sqrt(-a*b)) + 15*(15*a^3*b - 50*a^2*b^2 + 43*a*b^3 - 4*b^4 + (3*a^3 - 34*a^2*b + 55*a*b^2 - 20*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 2*a^3*b^2*e^(2*c) - 2*a^2*b^3*e^(2*c) - 3*a*b^4*e^(2*c) - b^5*e^(2*c) - sqrt((a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 2*a^3*b^2*e^(2*c) - 2*a^2*b^3*e^(2*c) - 3*a*b^4*e^(2*c) - b^5*e^(2*c))^2 - (a^5*e^(4*c) + 5*a^4*b*e^(4*c) + 10*a^3*b^2*e^(4*c) + 10*a^2*b^3*e^(4*c) + 5*a*b^4*e^(4*c) + b^5*e^(4*c))*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)))/(a^5*e^(4*c) + 5*a^4*b*e^(4*c) + 10*a^3*b^2*e^(4*c) + 10*a^2*b^3*e^(4*c) + 5*a*b^4*e^(4*c) + b^5*e^(4*c))))*e^(-2*c)/(a^9 - 9*a^8*b - 60*a^7*b^2 - 116*a^6*b^3 - 66*a^5*b^4 + 66*a^4*b^5 + 116*a^3*b^6 + 60*a^2*b^7 + 9*a*b^8 - b^9 - 2*(3*a^8 + 8*a^7*b - 12*a^6*b^2 - 72*a^5*b^3 - 110*a^4*b^4 - 72*a^3*b^5 - 12*a^2*b^6 + 8*a*b^7 + 3*b^8)*sqrt(-a*b)) + (9*a*e^(2*d*x + 2*c) - 27*b*e^(2*d*x + 2*c) - a - b)*e^(-3*d*x)/(a^4*e^(3*c) + 4*a^3*b*e^(3*c) + 6*a^2*b^2*e^(3*c) + 4*a*b^3*e^(3*c) + b^4*e^(3*c)) - (a^6*e^(3*d*x + 48*c) + 6*a^5*b*e^(3*d*x + 48*c) + 15*a^4*b^2*e^(3*d*x + 48*c) + 20*a^3*b^3*e^(3*d*x + 48*c) + 15*a^2*b^4*e^(3*d*x + 48*c) + 6*a*b^5*e^(3*d*x + 48*c) + b^6*e^(3*d*x + 48*c) - 9*a^6*e^(d*x + 46*c) - 18*a^5*b*e^(d*x + 46*c) + 45*a^4*b^2*e^(d*x + 46*c) + 180*a^3*b^3*e^(d*x + 46*c) + 225*a^2*b^4*e^(d*x + 46*c) + 126*a*b^5*e^(d*x + 46*c) + 27*b^6*e^(d*x + 46*c))/(a^9*e^(45*c) + 9*a^8*b*e^(45*c) + 36*a^7*b^2*e^(45*c) + 84*a^6*b^3*e^(45*c) + 126*a^5*b^4*e^(45*c) + 126*a^4*b^5*e^(45*c) + 84*a^3*b^6*e^(45*c) + 36*a^2*b^7*e^(45*c) + 9*a*b^8*e^(45*c) + b^9*e^(45*c)) - 6*(9*a^2*b*e^(7*d*x + 7*c) + 5*a*b^2*e^(7*d*x + 7*c) - 4*b^3*e^(7*d*x + 7*c) + 27*a^2*b*e^(5*d*x + 5*c) - 13*a*b^2*e^(5*d*x + 5*c) + 4*b^3*e^(5*d*x + 5*c) + 27*a^2*b*e^(3*d*x + 3*c) - 13*a*b^2*e^(3*d*x + 3*c) + 4*b^3*e^(3*d*x + 3*c) + 9*a^2*b*e^(d*x + c) + 5*a*b^2*e^(d*x + c) - 4*b^3*e^(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
43,1,584,0,1.940010," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(a - 5 \, b\right)} d x}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{{\left(15 \, a^{2} b e^{\left(2 \, c\right)} - 10 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b}} - \frac{{\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 10 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} e^{\left(-2 \, d x\right)}}{a^{4} e^{\left(2 \, c\right)} + 4 \, a^{3} b e^{\left(2 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 4 \, a b^{3} e^{\left(2 \, c\right)} + b^{4} e^{\left(2 \, c\right)}} - \frac{e^{\left(2 \, d x + 16 \, c\right)}}{a^{3} e^{\left(14 \, c\right)} + 3 \, a^{2} b e^{\left(14 \, c\right)} + 3 \, a b^{2} e^{\left(14 \, c\right)} + b^{3} e^{\left(14 \, c\right)}} - \frac{2 \, {\left(9 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} - 5 \, a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 13 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} + b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 27 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} - 21 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 29 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} + a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 23 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a^{3} b + 17 \, a^{2} b^{2} + 7 \, a b^{3} - b^{4}\right)}}{{\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(4*(a - 5*b)*d*x/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (15*a^2*b*e^(2*c) - 10*a*b^2*e^(2*c) - b^3*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sqrt(a*b)) - (2*a*e^(2*d*x + 2*c) - 10*b*e^(2*d*x + 2*c) - a - b)*e^(-2*d*x)/(a^4*e^(2*c) + 4*a^3*b*e^(2*c) + 6*a^2*b^2*e^(2*c) + 4*a*b^3*e^(2*c) + b^4*e^(2*c)) - e^(2*d*x + 16*c)/(a^3*e^(14*c) + 3*a^2*b*e^(14*c) + 3*a*b^2*e^(14*c) + b^3*e^(14*c)) - 2*(9*a^3*b*e^(6*d*x + 6*c) - 5*a^2*b^2*e^(6*d*x + 6*c) - 13*a*b^3*e^(6*d*x + 6*c) + b^4*e^(6*d*x + 6*c) + 27*a^3*b*e^(4*d*x + 4*c) - 21*a^2*b^2*e^(4*d*x + 4*c) + 29*a*b^3*e^(4*d*x + 4*c) - 3*b^4*e^(4*d*x + 4*c) + 27*a^3*b*e^(2*d*x + 2*c) + a^2*b^2*e^(2*d*x + 2*c) - 23*a*b^3*e^(2*d*x + 2*c) + 3*b^4*e^(2*d*x + 2*c) + 9*a^3*b + 17*a^2*b^2 + 7*a*b^3 - b^4)/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
44,1,1718,0,0.615161," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(2 \, {\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left(2 \, a b^{2} + {\left(a b - b^{2}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\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} - 2 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(2 \, a^{8} b + 10 \, a^{7} b^{2} + 18 \, a^{6} b^{3} + 10 \, a^{5} b^{4} - 10 \, a^{4} b^{5} - 18 \, a^{3} b^{6} - 10 \, a^{2} b^{7} - 2 \, a b^{8} + {\left(a^{8} + 4 \, a^{7} b + 4 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 10 \, a^{4} b^{4} - 4 \, a^{3} b^{5} + 4 \, a^{2} b^{6} + 4 \, a b^{7} + b^{8}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|}} + \frac{15 \, {\left(2 \, {\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left(2 \, a b^{2} - {\left(a b - b^{2}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\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} + 2 \, {\left(a^{4} b + 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 4 \, a b^{4} + b^{5}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(2 \, a^{8} b + 10 \, a^{7} b^{2} + 18 \, a^{6} b^{3} + 10 \, a^{5} b^{4} - 10 \, a^{4} b^{5} - 18 \, a^{3} b^{6} - 10 \, a^{2} b^{7} - 2 \, a b^{8} - {\left(a^{8} + 4 \, a^{7} b + 4 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 10 \, a^{4} b^{4} - 4 \, a^{3} b^{5} + 4 \, a^{2} b^{6} + 4 \, a b^{7} + b^{8}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - 3 \, a^{2} b e^{\left(2 \, c\right)} - 3 \, a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} \right|}} - \frac{4 \, e^{\left(d x + 14 \, c\right)}}{a^{3} e^{\left(13 \, c\right)} + 3 \, a^{2} b e^{\left(13 \, c\right)} + 3 \, a b^{2} e^{\left(13 \, c\right)} + b^{3} e^{\left(13 \, c\right)}} - \frac{4 \, e^{\left(-d x\right)}}{a^{3} e^{c} + 3 \, a^{2} b e^{c} + 3 \, a b^{2} e^{c} + b^{3} e^{c}} + \frac{2 \, {\left(9 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 9 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 27 \, a b e^{\left(5 \, d x + 5 \, c\right)} - b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 27 \, a b e^{\left(3 \, d x + 3 \, c\right)} - b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 9 \, a b e^{\left(d x + c\right)} + 9 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(15*(2*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))^2*(2*a*b^2 + (a*b - b^2)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)) + (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 - 2*(a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5)*sqrt(-a*b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (2*a^8*b + 10*a^7*b^2 + 18*a^6*b^3 + 10*a^5*b^4 - 10*a^4*b^5 - 18*a^3*b^6 - 10*a^2*b^7 - 2*a*b^8 + (a^8 + 4*a^7*b + 4*a^6*b^2 - 4*a^5*b^3 - 10*a^4*b^4 - 4*a^3*b^5 + 4*a^2*b^6 + 4*a*b^7 + b^8)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c) + sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))^2 - (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)))/(a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))))*e^(-4*c)/((a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))) + 15*(2*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))^2*(2*a*b^2 - (a*b - b^2)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)) + (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 + 2*(a^4*b + 4*a^3*b^2 + 6*a^2*b^3 + 4*a*b^4 + b^5)*sqrt(-a*b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (2*a^8*b + 10*a^7*b^2 + 18*a^6*b^3 + 10*a^5*b^4 - 10*a^4*b^5 - 18*a^3*b^6 - 10*a^2*b^7 - 2*a*b^8 - (a^8 + 4*a^7*b + 4*a^6*b^2 - 4*a^5*b^3 - 10*a^4*b^4 - 4*a^3*b^5 + 4*a^2*b^6 + 4*a*b^7 + b^8)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c) - sqrt((a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))^2 - (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)))/(a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))))*e^(-4*c)/((a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - 3*a^2*b*e^(2*c) - 3*a*b^2*e^(2*c) - b^3*e^(2*c))) - 4*e^(d*x + 14*c)/(a^3*e^(13*c) + 3*a^2*b*e^(13*c) + 3*a*b^2*e^(13*c) + b^3*e^(13*c)) - 4*e^(-d*x)/(a^3*e^c + 3*a^2*b*e^c + 3*a*b^2*e^c + b^3*e^c) + 2*(9*a*b*e^(7*d*x + 7*c) + 9*b^2*e^(7*d*x + 7*c) + 27*a*b*e^(5*d*x + 5*c) - b^2*e^(5*d*x + 5*c) + 27*a*b*e^(3*d*x + 3*c) - b^2*e^(3*d*x + 3*c) + 9*a*b*e^(d*x + c) + 9*b^2*e^(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
45,1,2033,0,0.501532," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)}\right)}^{2} {\left(30 \, a^{3} b^{2} + 40 \, a^{2} b^{3} + 16 \, a b^{4} - {\left(15 \, a^{3} b + 5 \, a^{2} b^{2} - 12 \, a b^{3} - 8 \, b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(15 \, a^{9} b + 50 \, a^{8} b^{2} + 48 \, a^{7} b^{3} - 14 \, a^{6} b^{4} - 55 \, a^{5} b^{5} - 36 \, a^{4} b^{6} - 8 \, a^{3} b^{7} + 2 \, {\left(15 \, a^{8} b + 65 \, a^{7} b^{2} + 113 \, a^{6} b^{3} + 99 \, a^{5} b^{4} + 44 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(30 \, a^{14} b + 130 \, a^{13} b^{2} + 196 \, a^{12} b^{3} + 68 \, a^{11} b^{4} - 138 \, a^{10} b^{5} - 182 \, a^{9} b^{6} - 88 \, a^{8} b^{7} - 16 \, a^{7} b^{8} - {\left(15 \, a^{14} + 50 \, a^{13} b + 33 \, a^{12} b^{2} - 64 \, a^{11} b^{3} - 103 \, a^{10} b^{4} - 22 \, a^{9} b^{5} + 47 \, a^{8} b^{6} + 36 \, a^{7} b^{7} + 8 \, a^{6} b^{8}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} + a^{5} b e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - a^{3} b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} + a^{5} b e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - a^{3} b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 3 \, a^{5} b e^{\left(4 \, c\right)} + 3 \, a^{4} b^{2} e^{\left(4 \, c\right)} + a^{3} b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 3 \, a^{5} b e^{\left(4 \, c\right)} + 3 \, a^{4} b^{2} e^{\left(4 \, c\right)} + a^{3} b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{15} + 7 \, a^{14} b + 20 \, a^{13} b^{2} + 28 \, a^{12} b^{3} + 14 \, a^{11} b^{4} - 14 \, a^{10} b^{5} - 28 \, a^{9} b^{6} - 20 \, a^{8} b^{7} - 7 \, a^{7} b^{8} - a^{6} b^{9} + 2 \, {\left(a^{14} + 8 \, a^{13} b + 28 \, a^{12} b^{2} + 56 \, a^{11} b^{3} + 70 \, a^{10} b^{4} + 56 \, a^{9} b^{5} + 28 \, a^{8} b^{6} + 8 \, a^{7} b^{7} + a^{6} b^{8}\right)} \sqrt{-a b}\right)} {\left| a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(60 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 48 \, a^{2} b^{4} - 32 \, a b^{5} + {\left(15 \, a^{4} b - 70 \, a^{3} b^{2} - 97 \, a^{2} b^{3} - 28 \, a b^{4} + 8 \, b^{5}\right)} \sqrt{-a b}\right)} {\left(a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(15 \, a^{10} b - 25 \, a^{9} b^{2} - 262 \, a^{8} b^{3} - 514 \, a^{7} b^{4} - 437 \, a^{6} b^{5} - 157 \, a^{5} b^{6} - 4 \, a^{4} b^{7} + 8 \, a^{3} b^{8} - 4 \, {\left(15 \, a^{9} b + 50 \, a^{8} b^{2} + 48 \, a^{7} b^{3} - 14 \, a^{6} b^{4} - 55 \, a^{5} b^{5} - 36 \, a^{4} b^{6} - 8 \, a^{3} b^{7}\right)} \sqrt{-a b}\right)} {\left| a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(60 \, a^{15} b + 200 \, a^{14} b^{2} + 132 \, a^{13} b^{3} - 256 \, a^{12} b^{4} - 412 \, a^{11} b^{5} - 88 \, a^{10} b^{6} + 188 \, a^{9} b^{7} + 144 \, a^{8} b^{8} + 32 \, a^{7} b^{9} + {\left(15 \, a^{15} - 25 \, a^{14} b - 277 \, a^{13} b^{2} - 489 \, a^{12} b^{3} - 175 \, a^{11} b^{4} + 357 \, a^{10} b^{5} + 433 \, a^{9} b^{6} + 165 \, a^{8} b^{7} + 4 \, a^{7} b^{8} - 8 \, a^{6} b^{9}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} + a^{5} b e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - a^{3} b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} + a^{5} b e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - a^{3} b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 3 \, a^{5} b e^{\left(4 \, c\right)} + 3 \, a^{4} b^{2} e^{\left(4 \, c\right)} + a^{3} b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 3 \, a^{5} b e^{\left(4 \, c\right)} + 3 \, a^{4} b^{2} e^{\left(4 \, c\right)} + a^{3} b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{14} + 6 \, a^{13} b + 14 \, a^{12} b^{2} + 14 \, a^{11} b^{3} - 14 \, a^{9} b^{5} - 14 \, a^{8} b^{6} - 6 \, a^{7} b^{7} - a^{6} b^{8} - 2 \, {\left(a^{13} + 7 \, a^{12} b + 21 \, a^{11} b^{2} + 35 \, a^{10} b^{3} + 35 \, a^{9} b^{4} + 21 \, a^{8} b^{5} + 7 \, a^{7} b^{6} + a^{6} b^{7}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} + a^{3} b^{2} e^{\left(2 \, c\right)} \right|}} - \frac{2 \, {\left(9 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 13 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 4 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 27 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 11 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 4 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 27 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 11 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 4 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 9 \, a^{2} b e^{\left(d x + c\right)} + 13 \, a b^{2} e^{\left(d x + c\right)} + 4 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}} + \frac{8 \, \log\left(e^{\left(d x + c\right)} + 1\right)}{a^{3}} - \frac{8 \, \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a^{3}}}{8 \, d}"," ",0,"-1/8*((2*(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))^2*(30*a^3*b^2 + 40*a^2*b^3 + 16*a*b^4 - (15*a^3*b + 5*a^2*b^2 - 12*a*b^3 - 8*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) - (15*a^9*b + 50*a^8*b^2 + 48*a^7*b^3 - 14*a^6*b^4 - 55*a^5*b^5 - 36*a^4*b^6 - 8*a^3*b^7 + 2*(15*a^8*b + 65*a^7*b^2 + 113*a^6*b^3 + 99*a^5*b^4 + 44*a^4*b^5 + 8*a^3*b^6)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (30*a^14*b + 130*a^13*b^2 + 196*a^12*b^3 + 68*a^11*b^4 - 138*a^10*b^5 - 182*a^9*b^6 - 88*a^8*b^7 - 16*a^7*b^8 - (15*a^14 + 50*a^13*b + 33*a^12*b^2 - 64*a^11*b^3 - 103*a^10*b^4 - 22*a^9*b^5 + 47*a^8*b^6 + 36*a^7*b^7 + 8*a^6*b^8)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) + a^5*b*e^(2*c) - a^4*b^2*e^(2*c) - a^3*b^3*e^(2*c) + sqrt((a^6*e^(2*c) + a^5*b*e^(2*c) - a^4*b^2*e^(2*c) - a^3*b^3*e^(2*c))^2 - (a^6*e^(4*c) + 3*a^5*b*e^(4*c) + 3*a^4*b^2*e^(4*c) + a^3*b^3*e^(4*c))*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)))/(a^6*e^(4*c) + 3*a^5*b*e^(4*c) + 3*a^4*b^2*e^(4*c) + a^3*b^3*e^(4*c))))*e^(-4*c)/((a^15 + 7*a^14*b + 20*a^13*b^2 + 28*a^12*b^3 + 14*a^11*b^4 - 14*a^10*b^5 - 28*a^9*b^6 - 20*a^8*b^7 - 7*a^7*b^8 - a^6*b^9 + 2*(a^14 + 8*a^13*b + 28*a^12*b^2 + 56*a^11*b^3 + 70*a^10*b^4 + 56*a^9*b^5 + 28*a^8*b^6 + 8*a^7*b^7 + a^6*b^8)*sqrt(-a*b))*abs(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))) + (2*(60*a^4*b^2 + 20*a^3*b^3 - 48*a^2*b^4 - 32*a*b^5 + (15*a^4*b - 70*a^3*b^2 - 97*a^2*b^3 - 28*a*b^4 + 8*b^5)*sqrt(-a*b))*(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (15*a^10*b - 25*a^9*b^2 - 262*a^8*b^3 - 514*a^7*b^4 - 437*a^6*b^5 - 157*a^5*b^6 - 4*a^4*b^7 + 8*a^3*b^8 - 4*(15*a^9*b + 50*a^8*b^2 + 48*a^7*b^3 - 14*a^6*b^4 - 55*a^5*b^5 - 36*a^4*b^6 - 8*a^3*b^7)*sqrt(-a*b))*abs(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (60*a^15*b + 200*a^14*b^2 + 132*a^13*b^3 - 256*a^12*b^4 - 412*a^11*b^5 - 88*a^10*b^6 + 188*a^9*b^7 + 144*a^8*b^8 + 32*a^7*b^9 + (15*a^15 - 25*a^14*b - 277*a^13*b^2 - 489*a^12*b^3 - 175*a^11*b^4 + 357*a^10*b^5 + 433*a^9*b^6 + 165*a^8*b^7 + 4*a^7*b^8 - 8*a^6*b^9)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) + a^5*b*e^(2*c) - a^4*b^2*e^(2*c) - a^3*b^3*e^(2*c) - sqrt((a^6*e^(2*c) + a^5*b*e^(2*c) - a^4*b^2*e^(2*c) - a^3*b^3*e^(2*c))^2 - (a^6*e^(4*c) + 3*a^5*b*e^(4*c) + 3*a^4*b^2*e^(4*c) + a^3*b^3*e^(4*c))*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)))/(a^6*e^(4*c) + 3*a^5*b*e^(4*c) + 3*a^4*b^2*e^(4*c) + a^3*b^3*e^(4*c))))*e^(-4*c)/((a^14 + 6*a^13*b + 14*a^12*b^2 + 14*a^11*b^3 - 14*a^9*b^5 - 14*a^8*b^6 - 6*a^7*b^7 - a^6*b^8 - 2*(a^13 + 7*a^12*b + 21*a^11*b^2 + 35*a^10*b^3 + 35*a^9*b^4 + 21*a^8*b^5 + 7*a^7*b^6 + a^6*b^7)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a^5*e^(2*c) + 2*a^4*b*e^(2*c) + a^3*b^2*e^(2*c))) - 2*(9*a^2*b*e^(7*d*x + 7*c) + 13*a*b^2*e^(7*d*x + 7*c) + 4*b^3*e^(7*d*x + 7*c) + 27*a^2*b*e^(5*d*x + 5*c) + 11*a*b^2*e^(5*d*x + 5*c) - 4*b^3*e^(5*d*x + 5*c) + 27*a^2*b*e^(3*d*x + 3*c) + 11*a*b^2*e^(3*d*x + 3*c) - 4*b^3*e^(3*d*x + 3*c) + 9*a^2*b*e^(d*x + c) + 13*a*b^2*e^(d*x + c) + 4*b^3*e^(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2) + 8*log(e^(d*x + c) + 1)/a^3 - 8*log(abs(e^(d*x + c) - 1))/a^3)/d","B",0
46,1,351,0,0.801906," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{15 \, b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{2 \, {\left(9 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 13 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} - 7 \, b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 27 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 13 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 21 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} + 25 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 23 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} - 21 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a^{3} b + 25 \, a^{2} b^{2} + 23 \, a b^{3} + 7 \, b^{4}\right)}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}} + \frac{16}{a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}}}{8 \, d}"," ",0,"-1/8*(15*b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3) - 2*(9*a^3*b*e^(6*d*x + 6*c) + 3*a^2*b^2*e^(6*d*x + 6*c) - 13*a*b^3*e^(6*d*x + 6*c) - 7*b^4*e^(6*d*x + 6*c) + 27*a^3*b*e^(4*d*x + 4*c) + 3*a^2*b^2*e^(4*d*x + 4*c) + 13*a*b^3*e^(4*d*x + 4*c) + 21*b^4*e^(4*d*x + 4*c) + 27*a^3*b*e^(2*d*x + 2*c) + 25*a^2*b^2*e^(2*d*x + 2*c) - 23*a*b^3*e^(2*d*x + 2*c) - 21*b^4*e^(2*d*x + 2*c) + 9*a^3*b + 25*a^2*b^2 + 23*a*b^3 + 7*b^4)/((a^5 + 2*a^4*b + a^3*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2) + 16/(a^3*(e^(2*d*x + 2*c) - 1)))/d","B",0
47,1,1877,0,1.026304," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)}\right)}^{2} {\left(30 \, a^{3} b^{2} + 80 \, a^{2} b^{3} + 48 \, a b^{4} - {\left(15 \, a^{3} b + 25 \, a^{2} b^{2} - 16 \, a b^{3} - 24 \, b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(15 \, a^{9} b + 55 \, a^{8} b^{2} + 49 \, a^{7} b^{3} - 31 \, a^{6} b^{4} - 64 \, a^{5} b^{5} - 24 \, a^{4} b^{6} + 2 \, {\left(15 \, a^{8} b + 70 \, a^{7} b^{2} + 119 \, a^{6} b^{3} + 88 \, a^{5} b^{4} + 24 \, a^{4} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{5} e^{\left(2 \, c\right)} - a^{4} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(30 \, a^{14} b + 110 \, a^{13} b^{2} + 98 \, a^{12} b^{3} - 62 \, a^{11} b^{4} - 128 \, a^{10} b^{5} - 48 \, a^{9} b^{6} - {\left(15 \, a^{14} + 40 \, a^{13} b - 6 \, a^{12} b^{2} - 80 \, a^{11} b^{3} - 33 \, a^{10} b^{4} + 40 \, a^{9} b^{5} + 24 \, a^{8} b^{6}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 2 \, a^{5} b e^{\left(4 \, c\right)} + a^{4} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 2 \, a^{5} b e^{\left(4 \, c\right)} + a^{4} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{15} + 5 \, a^{14} b + 9 \, a^{13} b^{2} + 5 \, a^{12} b^{3} - 5 \, a^{11} b^{4} - 9 \, a^{10} b^{5} - 5 \, a^{9} b^{6} - a^{8} b^{7} + 2 \, {\left(a^{14} + 6 \, a^{13} b + 15 \, a^{12} b^{2} + 20 \, a^{11} b^{3} + 15 \, a^{10} b^{4} + 6 \, a^{9} b^{5} + a^{8} b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{5} e^{\left(2 \, c\right)} - a^{4} b e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(60 \, a^{4} b^{2} + 100 \, a^{3} b^{3} - 64 \, a^{2} b^{4} - 96 \, a b^{5} + {\left(15 \, a^{4} b - 50 \, a^{3} b^{2} - 201 \, a^{2} b^{3} - 104 \, a b^{4} + 24 \, b^{5}\right)} \sqrt{-a b}\right)} {\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(15 \, a^{10} b - 20 \, a^{9} b^{2} - 286 \, a^{8} b^{3} - 556 \, a^{7} b^{4} - 385 \, a^{6} b^{5} - 56 \, a^{5} b^{6} + 24 \, a^{4} b^{7} - 4 \, {\left(15 \, a^{9} b + 55 \, a^{8} b^{2} + 49 \, a^{7} b^{3} - 31 \, a^{6} b^{4} - 64 \, a^{5} b^{5} - 24 \, a^{4} b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{5} e^{\left(2 \, c\right)} - a^{4} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} + {\left(60 \, a^{15} b + 160 \, a^{14} b^{2} - 24 \, a^{13} b^{3} - 320 \, a^{12} b^{4} - 132 \, a^{11} b^{5} + 160 \, a^{10} b^{6} + 96 \, a^{9} b^{7} + {\left(15 \, a^{15} - 35 \, a^{14} b - 266 \, a^{13} b^{2} - 270 \, a^{12} b^{3} + 171 \, a^{11} b^{4} + 329 \, a^{10} b^{5} + 80 \, a^{9} b^{6} - 24 \, a^{8} b^{7}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 2 \, a^{5} b e^{\left(4 \, c\right)} + a^{4} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 2 \, a^{5} b e^{\left(4 \, c\right)} + a^{4} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{14} + 4 \, a^{13} b + 5 \, a^{12} b^{2} - 5 \, a^{10} b^{4} - 4 \, a^{9} b^{5} - a^{8} b^{6} - 2 \, {\left(a^{13} + 5 \, a^{12} b + 10 \, a^{11} b^{2} + 10 \, a^{10} b^{3} + 5 \, a^{9} b^{4} + a^{8} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{5} e^{\left(2 \, c\right)} - a^{4} b e^{\left(2 \, c\right)} \right|}} - \frac{4 \, {\left(a e^{c} + 6 \, b e^{c}\right)} e^{\left(-c\right)} \log\left(e^{\left(d x + c\right)} + 1\right)}{a^{4}} + \frac{4 \, {\left(a e^{c} + 6 \, b e^{c}\right)} e^{\left(-c\right)} \log\left({\left| -e^{\left(d x + c\right)} + 1 \right|}\right)}{a^{4}} + \frac{2 \, {\left(4 \, a^{3} e^{\left(11 \, d x + 11 \, c\right)} + 21 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} + 29 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 12 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 20 \, a^{3} e^{\left(9 \, d x + 9 \, c\right)} + 37 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} - 15 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} - 36 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} + 40 \, a^{3} e^{\left(7 \, d x + 7 \, c\right)} + 6 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} - 14 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 24 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 40 \, a^{3} e^{\left(5 \, d x + 5 \, c\right)} + 6 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 14 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 24 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} + 20 \, a^{3} e^{\left(3 \, d x + 3 \, c\right)} + 37 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} - 15 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 36 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 4 \, a^{3} e^{\left(d x + c\right)} + 21 \, a^{2} b e^{\left(d x + c\right)} + 29 \, a b^{2} e^{\left(d x + c\right)} + 12 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a^{4} + a^{3} b\right)} {\left(a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((2*(a^5*e^(2*c) + a^4*b*e^(2*c))^2*(30*a^3*b^2 + 80*a^2*b^3 + 48*a*b^4 - (15*a^3*b + 25*a^2*b^2 - 16*a*b^3 - 24*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) + (15*a^9*b + 55*a^8*b^2 + 49*a^7*b^3 - 31*a^6*b^4 - 64*a^5*b^5 - 24*a^4*b^6 + 2*(15*a^8*b + 70*a^7*b^2 + 119*a^6*b^3 + 88*a^5*b^4 + 24*a^4*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^5*e^(2*c) - a^4*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (30*a^14*b + 110*a^13*b^2 + 98*a^12*b^3 - 62*a^11*b^4 - 128*a^10*b^5 - 48*a^9*b^6 - (15*a^14 + 40*a^13*b - 6*a^12*b^2 - 80*a^11*b^3 - 33*a^10*b^4 + 40*a^9*b^5 + 24*a^8*b^6)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) - a^4*b^2*e^(2*c) - sqrt((a^6*e^(2*c) - a^4*b^2*e^(2*c))^2 - (a^6*e^(4*c) + 2*a^5*b*e^(4*c) + a^4*b^2*e^(4*c))*(a^6 + 2*a^5*b + a^4*b^2)))/(a^6*e^(4*c) + 2*a^5*b*e^(4*c) + a^4*b^2*e^(4*c))))*e^(-4*c)/((a^15 + 5*a^14*b + 9*a^13*b^2 + 5*a^12*b^3 - 5*a^11*b^4 - 9*a^10*b^5 - 5*a^9*b^6 - a^8*b^7 + 2*(a^14 + 6*a^13*b + 15*a^12*b^2 + 20*a^11*b^3 + 15*a^10*b^4 + 6*a^9*b^5 + a^8*b^6)*sqrt(-a*b))*abs(-a^5*e^(2*c) - a^4*b*e^(2*c))) + (2*(60*a^4*b^2 + 100*a^3*b^3 - 64*a^2*b^4 - 96*a*b^5 + (15*a^4*b - 50*a^3*b^2 - 201*a^2*b^3 - 104*a*b^4 + 24*b^5)*sqrt(-a*b))*(a^5*e^(2*c) + a^4*b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (15*a^10*b - 20*a^9*b^2 - 286*a^8*b^3 - 556*a^7*b^4 - 385*a^6*b^5 - 56*a^5*b^6 + 24*a^4*b^7 - 4*(15*a^9*b + 55*a^8*b^2 + 49*a^7*b^3 - 31*a^6*b^4 - 64*a^5*b^5 - 24*a^4*b^6)*sqrt(-a*b))*abs(-a^5*e^(2*c) - a^4*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) + (60*a^15*b + 160*a^14*b^2 - 24*a^13*b^3 - 320*a^12*b^4 - 132*a^11*b^5 + 160*a^10*b^6 + 96*a^9*b^7 + (15*a^15 - 35*a^14*b - 266*a^13*b^2 - 270*a^12*b^3 + 171*a^11*b^4 + 329*a^10*b^5 + 80*a^9*b^6 - 24*a^8*b^7)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) - a^4*b^2*e^(2*c) + sqrt((a^6*e^(2*c) - a^4*b^2*e^(2*c))^2 - (a^6*e^(4*c) + 2*a^5*b*e^(4*c) + a^4*b^2*e^(4*c))*(a^6 + 2*a^5*b + a^4*b^2)))/(a^6*e^(4*c) + 2*a^5*b*e^(4*c) + a^4*b^2*e^(4*c))))*e^(-4*c)/((a^14 + 4*a^13*b + 5*a^12*b^2 - 5*a^10*b^4 - 4*a^9*b^5 - a^8*b^6 - 2*(a^13 + 5*a^12*b + 10*a^11*b^2 + 10*a^10*b^3 + 5*a^9*b^4 + a^8*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^5*e^(2*c) - a^4*b*e^(2*c))) - 4*(a*e^c + 6*b*e^c)*e^(-c)*log(e^(d*x + c) + 1)/a^4 + 4*(a*e^c + 6*b*e^c)*e^(-c)*log(abs(-e^(d*x + c) + 1))/a^4 + 2*(4*a^3*e^(11*d*x + 11*c) + 21*a^2*b*e^(11*d*x + 11*c) + 29*a*b^2*e^(11*d*x + 11*c) + 12*b^3*e^(11*d*x + 11*c) + 20*a^3*e^(9*d*x + 9*c) + 37*a^2*b*e^(9*d*x + 9*c) - 15*a*b^2*e^(9*d*x + 9*c) - 36*b^3*e^(9*d*x + 9*c) + 40*a^3*e^(7*d*x + 7*c) + 6*a^2*b*e^(7*d*x + 7*c) - 14*a*b^2*e^(7*d*x + 7*c) + 24*b^3*e^(7*d*x + 7*c) + 40*a^3*e^(5*d*x + 5*c) + 6*a^2*b*e^(5*d*x + 5*c) - 14*a*b^2*e^(5*d*x + 5*c) + 24*b^3*e^(5*d*x + 5*c) + 20*a^3*e^(3*d*x + 3*c) + 37*a^2*b*e^(3*d*x + 3*c) - 15*a*b^2*e^(3*d*x + 3*c) - 36*b^3*e^(3*d*x + 3*c) + 4*a^3*e^(d*x + c) + 21*a^2*b*e^(d*x + c) + 29*a*b^2*e^(d*x + c) + 12*b^3*e^(d*x + c))/((a^4 + a^3*b)*(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) - a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) - a - b)^2))/d","B",0
48,1,407,0,0.847047," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(3 \, a b e^{\left(2 \, c\right)} + 7 \, b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a^{4}} - \frac{6 \, {\left(9 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} + 7 \, a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 13 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} - 11 \, b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 27 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} + 15 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 5 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 33 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} + 37 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 23 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} - 33 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a^{3} b + 29 \, a^{2} b^{2} + 31 \, a b^{3} + 11 \, b^{4}\right)}}{{\left(a^{5} + a^{4} b\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}} + \frac{16 \, {\left(9 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} - 18 \, b e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a + 9 \, b\right)}}{a^{4} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(15*(3*a*b*e^(2*c) + 7*b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a^4) - 6*(9*a^3*b*e^(6*d*x + 6*c) + 7*a^2*b^2*e^(6*d*x + 6*c) - 13*a*b^3*e^(6*d*x + 6*c) - 11*b^4*e^(6*d*x + 6*c) + 27*a^3*b*e^(4*d*x + 4*c) + 15*a^2*b^2*e^(4*d*x + 4*c) + 5*a*b^3*e^(4*d*x + 4*c) + 33*b^4*e^(4*d*x + 4*c) + 27*a^3*b*e^(2*d*x + 2*c) + 37*a^2*b^2*e^(2*d*x + 2*c) - 23*a*b^3*e^(2*d*x + 2*c) - 33*b^4*e^(2*d*x + 2*c) + 9*a^3*b + 29*a^2*b^2 + 31*a*b^3 + 11*b^4)/((a^5 + a^4*b)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2) + 16*(9*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) - 18*b*e^(2*d*x + 2*c) + 2*a + 9*b)/(a^4*(e^(2*d*x + 2*c) - 1)^3))/d","B",0
49,1,206,0,0.251313," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{24 \, {\left(a - 8 \, b\right)} d x + {\left(a e^{\left(4 \, d x + 24 \, c\right)} + b e^{\left(4 \, d x + 24 \, c\right)} - 8 \, a e^{\left(2 \, d x + 22 \, c\right)} - 20 \, b e^{\left(2 \, d x + 22 \, c\right)}\right)} e^{\left(-20 \, c\right)} + 192 \, b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{{\left(9 \, a e^{\left(8 \, d x + 8 \, c\right)} + 72 \, b e^{\left(8 \, d x + 8 \, c\right)} + 10 \, a e^{\left(6 \, d x + 6 \, c\right)} + 36 \, b e^{\left(6 \, d x + 6 \, c\right)} - 6 \, a e^{\left(4 \, d x + 4 \, c\right)} + 111 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 18 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b\right)} e^{\left(-4 \, c\right)}}{{\left(e^{\left(2 \, d x\right)} + e^{\left(4 \, d x + 2 \, c\right)}\right)}^{2}}}{64 \, d}"," ",0,"1/64*(24*(a - 8*b)*d*x + (a*e^(4*d*x + 24*c) + b*e^(4*d*x + 24*c) - 8*a*e^(2*d*x + 22*c) - 20*b*e^(2*d*x + 22*c))*e^(-20*c) + 192*b*log(e^(2*d*x + 2*c) + 1) - (9*a*e^(8*d*x + 8*c) + 72*b*e^(8*d*x + 8*c) + 10*a*e^(6*d*x + 6*c) + 36*b*e^(6*d*x + 6*c) - 6*a*e^(4*d*x + 4*c) + 111*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) + 18*b*e^(2*d*x + 2*c) + a - b)*e^(-4*c)/(e^(2*d*x) + e^(4*d*x + 2*c))^2)/d","A",0
50,1,142,0,0.192335," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{120 \, b \arctan\left(e^{\left(d x + c\right)}\right) - {\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} - 27 \, b e^{\left(2 \, d x + 2 \, c\right)} - a + b\right)} e^{\left(-3 \, d x - 3 \, c\right)} + {\left(a e^{\left(3 \, d x + 30 \, c\right)} + b e^{\left(3 \, d x + 30 \, c\right)} - 9 \, a e^{\left(d x + 28 \, c\right)} - 27 \, b e^{\left(d x + 28 \, c\right)}\right)} e^{\left(-27 \, c\right)} - \frac{24 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{24 \, d}"," ",0,"1/24*(120*b*arctan(e^(d*x + c)) - (9*a*e^(2*d*x + 2*c) - 27*b*e^(2*d*x + 2*c) - a + b)*e^(-3*d*x - 3*c) + (a*e^(3*d*x + 30*c) + b*e^(3*d*x + 30*c) - 9*a*e^(d*x + 28*c) - 27*b*e^(d*x + 28*c))*e^(-27*c) - 24*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
51,1,142,0,0.176951," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{4 \, {\left(a - 4 \, b\right)} d x - {\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 8 \, b e^{\left(2 \, d x + 2 \, c\right)} - a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a e^{\left(2 \, d x + 10 \, c\right)} + b e^{\left(2 \, d x + 10 \, c\right)}\right)} e^{\left(-8 \, c\right)} + 16 \, b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{8 \, {\left(3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(4*(a - 4*b)*d*x - (2*a*e^(2*d*x + 2*c) - 8*b*e^(2*d*x + 2*c) - a + b)*e^(-2*d*x - 2*c) - (a*e^(2*d*x + 10*c) + b*e^(2*d*x + 10*c))*e^(-8*c) + 16*b*log(e^(2*d*x + 2*c) + 1) - 8*(3*b*e^(4*d*x + 4*c) + 4*b*e^(2*d*x + 2*c) + 3*b)/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
52,1,95,0,0.171990," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{6 \, b \arctan\left(e^{\left(d x + c\right)}\right) - {\left(a - b\right)} e^{\left(-d x - c\right)} - {\left(a e^{\left(d x + 8 \, c\right)} + b e^{\left(d x + 8 \, c\right)}\right)} e^{\left(-7 \, c\right)} - \frac{2 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(6*b*arctan(e^(d*x + c)) - (a - b)*e^(-d*x - c) - (a*e^(d*x + 8*c) + b*e^(d*x + 8*c))*e^(-7*c) - 2*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
53,1,74,0,0.158798," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{b \arctan\left(e^{\left(d x + c\right)}\right) - a \log\left(e^{\left(d x + c\right)} + 1\right) + a \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{d}"," ",0,"(b*arctan(e^(d*x + c)) - a*log(e^(d*x + c) + 1) + a*log(abs(e^(d*x + c) - 1)) - (b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
54,1,45,0,0.188538," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{a}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{b e^{\left(2 \, d x + 2 \, c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}\right)}}{d}"," ",0,"-2*(a/(e^(2*d*x + 2*c) - 1) + b*e^(2*d*x + 2*c)/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
55,1,143,0,0.165223," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{2 \, b \arctan\left(e^{\left(d x + c\right)}\right) + a \log\left(e^{\left(d x + c\right)} + 1\right) - a \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{2 \, {\left(a e^{\left(7 \, d x + 7 \, c\right)} - b e^{\left(7 \, d x + 7 \, c\right)} + 3 \, a e^{\left(5 \, d x + 5 \, c\right)} + 3 \, b e^{\left(5 \, d x + 5 \, c\right)} + 3 \, a e^{\left(3 \, d x + 3 \, c\right)} - 3 \, b e^{\left(3 \, d x + 3 \, c\right)} + a e^{\left(d x + c\right)} + b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(4 \, d x + 4 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*b*arctan(e^(d*x + c)) + a*log(e^(d*x + c) + 1) - a*log(abs(e^(d*x + c) - 1)) - 2*(a*e^(7*d*x + 7*c) - b*e^(7*d*x + 7*c) + 3*a*e^(5*d*x + 5*c) + 3*b*e^(5*d*x + 5*c) + 3*a*e^(3*d*x + 3*c) - 3*b*e^(3*d*x + 3*c) + a*e^(d*x + c) + b*e^(d*x + c))/(e^(4*d*x + 4*c) - 1)^2)/d","B",0
56,1,149,0,0.178031," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{6 \, b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 6 \, b \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) - \frac{3 \, {\left(3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 10 \, b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}} + \frac{11 \, b e^{\left(6 \, d x + 6 \, c\right)} - 33 \, b e^{\left(4 \, d x + 4 \, c\right)} + 24 \, a e^{\left(2 \, d x + 2 \, c\right)} + 33 \, b e^{\left(2 \, d x + 2 \, c\right)} - 8 \, a - 11 \, b}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*b*log(e^(2*d*x + 2*c) + 1) - 6*b*log(abs(e^(2*d*x + 2*c) - 1)) - 3*(3*b*e^(4*d*x + 4*c) + 10*b*e^(2*d*x + 2*c) + 3*b)/(e^(2*d*x + 2*c) + 1)^2 + (11*b*e^(6*d*x + 6*c) - 33*b*e^(4*d*x + 4*c) + 24*a*e^(2*d*x + 2*c) + 33*b*e^(2*d*x + 2*c) - 8*a - 11*b)/(e^(2*d*x + 2*c) - 1)^3)/d","B",0
57,1,376,0,0.711443," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{120 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 1920 \, a b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 5 \, {\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 288 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 378 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 40 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 32 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} - 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 5 \, {\left(a^{2} e^{\left(4 \, d x + 36 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 36 \, c\right)} + b^{2} e^{\left(4 \, d x + 36 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 34 \, c\right)} - 40 \, a b e^{\left(2 \, d x + 34 \, c\right)} - 32 \, b^{2} e^{\left(2 \, d x + 34 \, c\right)}\right)} e^{\left(-32 \, c\right)} - \frac{32 \, {\left(137 \, a b e^{\left(10 \, d x + 10 \, c\right)} + 645 \, a b e^{\left(8 \, d x + 8 \, c\right)} - 200 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 1250 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 600 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 1250 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 840 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 645 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 520 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 137 \, a b - 144 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{320 \, d}"," ",0,"1/320*(120*(a^2 - 16*a*b + 21*b^2)*d*x + 1920*a*b*log(e^(2*d*x + 2*c) + 1) - 5*(18*a^2*e^(4*d*x + 4*c) - 288*a*b*e^(4*d*x + 4*c) + 378*b^2*e^(4*d*x + 4*c) - 8*a^2*e^(2*d*x + 2*c) + 40*a*b*e^(2*d*x + 2*c) - 32*b^2*e^(2*d*x + 2*c) + a^2 - 2*a*b + b^2)*e^(-4*d*x - 4*c) + 5*(a^2*e^(4*d*x + 36*c) + 2*a*b*e^(4*d*x + 36*c) + b^2*e^(4*d*x + 36*c) - 8*a^2*e^(2*d*x + 34*c) - 40*a*b*e^(2*d*x + 34*c) - 32*b^2*e^(2*d*x + 34*c))*e^(-32*c) - 32*(137*a*b*e^(10*d*x + 10*c) + 645*a*b*e^(8*d*x + 8*c) - 200*b^2*e^(8*d*x + 8*c) + 1250*a*b*e^(6*d*x + 6*c) - 600*b^2*e^(6*d*x + 6*c) + 1250*a*b*e^(4*d*x + 4*c) - 840*b^2*e^(4*d*x + 4*c) + 645*a*b*e^(2*d*x + 2*c) - 520*b^2*e^(2*d*x + 2*c) + 137*a*b - 144*b^2)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
58,1,300,0,0.484912," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{1200 \, a b \arctan\left(e^{\left(d x + c\right)}\right) - 5 \, {\left(9 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 54 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 45 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2} + 2 \, a b - b^{2}\right)} e^{\left(-3 \, d x - 3 \, c\right)} + 5 \, {\left(a^{2} e^{\left(3 \, d x + 48 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 48 \, c\right)} + b^{2} e^{\left(3 \, d x + 48 \, c\right)} - 9 \, a^{2} e^{\left(d x + 46 \, c\right)} - 54 \, a b e^{\left(d x + 46 \, c\right)} - 45 \, b^{2} e^{\left(d x + 46 \, c\right)}\right)} e^{\left(-45 \, c\right)} - \frac{16 \, {\left(15 \, a b e^{\left(9 \, d x + 9 \, c\right)} + 90 \, b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 30 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 280 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 428 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 30 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 280 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 15 \, a b e^{\left(d x + c\right)} + 90 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(1200*a*b*arctan(e^(d*x + c)) - 5*(9*a^2*e^(2*d*x + 2*c) - 54*a*b*e^(2*d*x + 2*c) + 45*b^2*e^(2*d*x + 2*c) - a^2 + 2*a*b - b^2)*e^(-3*d*x - 3*c) + 5*(a^2*e^(3*d*x + 48*c) + 2*a*b*e^(3*d*x + 48*c) + b^2*e^(3*d*x + 48*c) - 9*a^2*e^(d*x + 46*c) - 54*a*b*e^(d*x + 46*c) - 45*b^2*e^(d*x + 46*c))*e^(-45*c) - 16*(15*a*b*e^(9*d*x + 9*c) + 90*b^2*e^(9*d*x + 9*c) + 30*a*b*e^(7*d*x + 7*c) + 280*b^2*e^(7*d*x + 7*c) + 428*b^2*e^(5*d*x + 5*c) - 30*a*b*e^(3*d*x + 3*c) + 280*b^2*e^(3*d*x + 3*c) - 15*a*b*e^(d*x + c) + 90*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
59,1,298,0,0.444424," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 480 \, a b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 15 \, {\left(2 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 16 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 14 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2} + 2 \, a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, {\left(a^{2} e^{\left(2 \, d x + 16 \, c\right)} + 2 \, a b e^{\left(2 \, d x + 16 \, c\right)} + b^{2} e^{\left(2 \, d x + 16 \, c\right)}\right)} e^{\left(-14 \, c\right)} - \frac{8 \, {\left(137 \, a b e^{\left(10 \, d x + 10 \, c\right)} + 625 \, a b e^{\left(8 \, d x + 8 \, c\right)} - 180 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 1190 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 480 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 1190 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 680 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 625 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 400 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 137 \, a b - 116 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(60*(a^2 - 8*a*b + 7*b^2)*d*x + 480*a*b*log(e^(2*d*x + 2*c) + 1) - 15*(2*a^2*e^(2*d*x + 2*c) - 16*a*b*e^(2*d*x + 2*c) + 14*b^2*e^(2*d*x + 2*c) - a^2 + 2*a*b - b^2)*e^(-2*d*x - 2*c) - 15*(a^2*e^(2*d*x + 16*c) + 2*a*b*e^(2*d*x + 16*c) + b^2*e^(2*d*x + 16*c))*e^(-14*c) - 8*(137*a*b*e^(10*d*x + 10*c) + 625*a*b*e^(8*d*x + 8*c) - 180*b^2*e^(8*d*x + 8*c) + 1190*a*b*e^(6*d*x + 6*c) - 480*b^2*e^(6*d*x + 6*c) + 1190*a*b*e^(4*d*x + 4*c) - 680*b^2*e^(4*d*x + 4*c) + 625*a*b*e^(2*d*x + 2*c) - 400*b^2*e^(2*d*x + 2*c) + 137*a*b - 116*b^2)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
60,1,214,0,0.312808," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{60 \, a b \arctan\left(e^{\left(d x + c\right)}\right) - 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} e^{\left(-d x - c\right)} - 5 \, {\left(a^{2} e^{\left(d x + 14 \, c\right)} + 2 \, a b e^{\left(d x + 14 \, c\right)} + b^{2} e^{\left(d x + 14 \, c\right)}\right)} e^{\left(-13 \, c\right)} - \frac{4 \, {\left(5 \, a b e^{\left(9 \, d x + 9 \, c\right)} + 15 \, b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 10 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 40 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 66 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 10 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 40 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 5 \, a b e^{\left(d x + c\right)} + 15 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{10 \, d}"," ",0,"-1/10*(60*a*b*arctan(e^(d*x + c)) - 5*(a^2 - 2*a*b + b^2)*e^(-d*x - c) - 5*(a^2*e^(d*x + 14*c) + 2*a*b*e^(d*x + 14*c) + b^2*e^(d*x + 14*c))*e^(-13*c) - 4*(5*a*b*e^(9*d*x + 9*c) + 15*b^2*e^(9*d*x + 9*c) + 10*a*b*e^(7*d*x + 7*c) + 40*b^2*e^(7*d*x + 7*c) + 66*b^2*e^(5*d*x + 5*c) - 10*a*b*e^(3*d*x + 3*c) + 40*b^2*e^(3*d*x + 3*c) - 5*a*b*e^(d*x + c) + 15*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
61,1,178,0,0.285129," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{30 \, a b \arctan\left(e^{\left(d x + c\right)}\right) - 15 \, a^{2} \log\left(e^{\left(d x + c\right)} + 1\right) + 15 \, a^{2} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{2 \, {\left(15 \, a b e^{\left(9 \, d x + 9 \, c\right)} + 15 \, b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 30 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 20 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 58 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 30 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 20 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 15 \, a b e^{\left(d x + c\right)} + 15 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(30*a*b*arctan(e^(d*x + c)) - 15*a^2*log(e^(d*x + c) + 1) + 15*a^2*log(abs(e^(d*x + c) - 1)) - 2*(15*a*b*e^(9*d*x + 9*c) + 15*b^2*e^(9*d*x + 9*c) + 30*a*b*e^(7*d*x + 7*c) + 20*b^2*e^(7*d*x + 7*c) + 58*b^2*e^(5*d*x + 5*c) - 30*a*b*e^(3*d*x + 3*c) + 20*b^2*e^(3*d*x + 3*c) - 15*a*b*e^(d*x + c) + 15*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
62,1,122,0,0.321795," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, a^{2}}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{10 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 5 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 30 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 30 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 10 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 10 \, a b e^{\left(2 \, d x + 2 \, c\right)} + b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}\right)}}{5 \, d}"," ",0,"-2/5*(5*a^2/(e^(2*d*x + 2*c) - 1) + (10*a*b*e^(8*d*x + 8*c) + 5*b^2*e^(8*d*x + 8*c) + 30*a*b*e^(6*d*x + 6*c) + 30*a*b*e^(4*d*x + 4*c) + 10*b^2*e^(4*d*x + 4*c) + 10*a*b*e^(2*d*x + 2*c) + b^2)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
63,1,192,0,0.312303," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{60 \, a b \arctan\left(e^{\left(d x + c\right)}\right) + 15 \, a^{2} \log\left(e^{\left(d x + c\right)} + 1\right) - 15 \, a^{2} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - \frac{30 \, {\left(a^{2} e^{\left(3 \, d x + 3 \, c\right)} + a^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}} + \frac{4 \, {\left(15 \, a b e^{\left(9 \, d x + 9 \, c\right)} + 30 \, a b e^{\left(7 \, d x + 7 \, c\right)} - 20 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 8 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 30 \, a b e^{\left(3 \, d x + 3 \, c\right)} - 20 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 15 \, a b e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*arctan(e^(d*x + c)) + 15*a^2*log(e^(d*x + c) + 1) - 15*a^2*log(abs(e^(d*x + c) - 1)) - 30*(a^2*e^(3*d*x + 3*c) + a^2*e^(d*x + c))/(e^(2*d*x + 2*c) - 1)^2 + 4*(15*a*b*e^(9*d*x + 9*c) + 30*a*b*e^(7*d*x + 7*c) - 20*b^2*e^(7*d*x + 7*c) + 8*b^2*e^(5*d*x + 5*c) - 30*a*b*e^(3*d*x + 3*c) - 20*b^2*e^(3*d*x + 3*c) - 15*a*b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
64,1,249,0,0.331001," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{60 \, a b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 60 \, a b \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{10 \, {\left(11 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 33 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 12 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 33 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 4 \, a^{2} - 11 \, a b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}} - \frac{137 \, a b e^{\left(10 \, d x + 10 \, c\right)} + 805 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 1730 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 120 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 1730 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 40 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 805 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 40 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 137 \, a b - 8 \, b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{30 \, d}"," ",0,"-1/30*(60*a*b*log(e^(2*d*x + 2*c) + 1) - 60*a*b*log(abs(e^(2*d*x + 2*c) - 1)) + 10*(11*a*b*e^(6*d*x + 6*c) - 33*a*b*e^(4*d*x + 4*c) + 12*a^2*e^(2*d*x + 2*c) + 33*a*b*e^(2*d*x + 2*c) - 4*a^2 - 11*a*b)/(e^(2*d*x + 2*c) - 1)^3 - (137*a*b*e^(10*d*x + 10*c) + 805*a*b*e^(8*d*x + 8*c) + 1730*a*b*e^(6*d*x + 6*c) - 120*b^2*e^(6*d*x + 6*c) + 1730*a*b*e^(4*d*x + 4*c) + 40*b^2*e^(4*d*x + 4*c) + 805*a*b*e^(2*d*x + 2*c) - 40*b^2*e^(2*d*x + 2*c) + 137*a*b - 8*b^2)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
65,1,708,0,1.632856," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{840 \, {\left(a^{3} - 24 \, a^{2} b + 63 \, a b^{2} - 40 \, b^{3}\right)} d x + 6720 \, {\left(3 \, a^{2} b e^{\left(2 \, c\right)} + 5 \, b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(-2 \, c\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 35 \, {\left(18 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - 432 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 1134 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 720 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 60 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 96 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 44 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 35 \, {\left(a^{3} e^{\left(4 \, d x + 48 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, d x + 48 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, d x + 48 \, c\right)} + b^{3} e^{\left(4 \, d x + 48 \, c\right)} - 8 \, a^{3} e^{\left(2 \, d x + 46 \, c\right)} - 60 \, a^{2} b e^{\left(2 \, d x + 46 \, c\right)} - 96 \, a b^{2} e^{\left(2 \, d x + 46 \, c\right)} - 44 \, b^{3} e^{\left(2 \, d x + 46 \, c\right)}\right)} e^{\left(-44 \, c\right)} - \frac{8 \, {\left(6849 \, a^{2} b e^{\left(16 \, d x + 16 \, c\right)} + 11415 \, b^{3} e^{\left(16 \, d x + 16 \, c\right)} + 53112 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} - 16800 \, a b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 80120 \, b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 181692 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} - 100800 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 269220 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 358344 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} - 272160 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 520520 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 445830 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} - 423360 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 648970 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 358344 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 405216 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 520520 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 181692 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 237888 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 269220 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 53112 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 79968 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 80120 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 6849 \, a^{2} b - 12096 \, a b^{2} + 11415 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{2240 \, d}"," ",0,"1/2240*(840*(a^3 - 24*a^2*b + 63*a*b^2 - 40*b^3)*d*x + 6720*(3*a^2*b*e^(2*c) + 5*b^3*e^(2*c))*e^(-2*c)*log(e^(2*d*x + 2*c) + 1) - 35*(18*a^3*e^(4*d*x + 4*c) - 432*a^2*b*e^(4*d*x + 4*c) + 1134*a*b^2*e^(4*d*x + 4*c) - 720*b^3*e^(4*d*x + 4*c) - 8*a^3*e^(2*d*x + 2*c) + 60*a^2*b*e^(2*d*x + 2*c) - 96*a*b^2*e^(2*d*x + 2*c) + 44*b^3*e^(2*d*x + 2*c) + a^3 - 3*a^2*b + 3*a*b^2 - b^3)*e^(-4*d*x - 4*c) + 35*(a^3*e^(4*d*x + 48*c) + 3*a^2*b*e^(4*d*x + 48*c) + 3*a*b^2*e^(4*d*x + 48*c) + b^3*e^(4*d*x + 48*c) - 8*a^3*e^(2*d*x + 46*c) - 60*a^2*b*e^(2*d*x + 46*c) - 96*a*b^2*e^(2*d*x + 46*c) - 44*b^3*e^(2*d*x + 46*c))*e^(-44*c) - 8*(6849*a^2*b*e^(16*d*x + 16*c) + 11415*b^3*e^(16*d*x + 16*c) + 53112*a^2*b*e^(14*d*x + 14*c) - 16800*a*b^2*e^(14*d*x + 14*c) + 80120*b^3*e^(14*d*x + 14*c) + 181692*a^2*b*e^(12*d*x + 12*c) - 100800*a*b^2*e^(12*d*x + 12*c) + 269220*b^3*e^(12*d*x + 12*c) + 358344*a^2*b*e^(10*d*x + 10*c) - 272160*a*b^2*e^(10*d*x + 10*c) + 520520*b^3*e^(10*d*x + 10*c) + 445830*a^2*b*e^(8*d*x + 8*c) - 423360*a*b^2*e^(8*d*x + 8*c) + 648970*b^3*e^(8*d*x + 8*c) + 358344*a^2*b*e^(6*d*x + 6*c) - 405216*a*b^2*e^(6*d*x + 6*c) + 520520*b^3*e^(6*d*x + 6*c) + 181692*a^2*b*e^(4*d*x + 4*c) - 237888*a*b^2*e^(4*d*x + 4*c) + 269220*b^3*e^(4*d*x + 4*c) + 53112*a^2*b*e^(2*d*x + 2*c) - 79968*a*b^2*e^(2*d*x + 2*c) + 80120*b^3*e^(2*d*x + 2*c) + 6849*a^2*b - 12096*a*b^2 + 11415*b^3)/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
66,1,601,0,1.247526," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{225 \, {\left(64 \, a^{2} b e^{c} + 77 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - 40 \, {\left(9 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 81 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 135 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 63 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} - a^{3} + 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} e^{\left(-3 \, d x - 3 \, c\right)} + 40 \, {\left(a^{3} e^{\left(3 \, d x + 66 \, c\right)} + 3 \, a^{2} b e^{\left(3 \, d x + 66 \, c\right)} + 3 \, a b^{2} e^{\left(3 \, d x + 66 \, c\right)} + b^{3} e^{\left(3 \, d x + 66 \, c\right)} - 9 \, a^{3} e^{\left(d x + 64 \, c\right)} - 81 \, a^{2} b e^{\left(d x + 64 \, c\right)} - 135 \, a b^{2} e^{\left(d x + 64 \, c\right)} - 63 \, b^{3} e^{\left(d x + 64 \, c\right)}\right)} e^{\left(-63 \, c\right)} - \frac{2880 \, a^{2} b e^{\left(15 \, d x + 15 \, c\right)} + 34560 \, a b^{2} e^{\left(15 \, d x + 15 \, c\right)} + 11475 \, b^{3} e^{\left(15 \, d x + 15 \, c\right)} + 14400 \, a^{2} b e^{\left(13 \, d x + 13 \, c\right)} + 211200 \, a b^{2} e^{\left(13 \, d x + 13 \, c\right)} + 36775 \, b^{3} e^{\left(13 \, d x + 13 \, c\right)} + 25920 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} + 590592 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 67715 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 14400 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 957696 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 27055 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} - 14400 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 957696 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 27055 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 25920 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 590592 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 67715 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 14400 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 211200 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 36775 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 2880 \, a^{2} b e^{\left(d x + c\right)} + 34560 \, a b^{2} e^{\left(d x + c\right)} - 11475 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{960 \, d}"," ",0,"1/960*(225*(64*a^2*b*e^c + 77*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) - 40*(9*a^3*e^(2*d*x + 2*c) - 81*a^2*b*e^(2*d*x + 2*c) + 135*a*b^2*e^(2*d*x + 2*c) - 63*b^3*e^(2*d*x + 2*c) - a^3 + 3*a^2*b - 3*a*b^2 + b^3)*e^(-3*d*x - 3*c) + 40*(a^3*e^(3*d*x + 66*c) + 3*a^2*b*e^(3*d*x + 66*c) + 3*a*b^2*e^(3*d*x + 66*c) + b^3*e^(3*d*x + 66*c) - 9*a^3*e^(d*x + 64*c) - 81*a^2*b*e^(d*x + 64*c) - 135*a*b^2*e^(d*x + 64*c) - 63*b^3*e^(d*x + 64*c))*e^(-63*c) - (2880*a^2*b*e^(15*d*x + 15*c) + 34560*a*b^2*e^(15*d*x + 15*c) + 11475*b^3*e^(15*d*x + 15*c) + 14400*a^2*b*e^(13*d*x + 13*c) + 211200*a*b^2*e^(13*d*x + 13*c) + 36775*b^3*e^(13*d*x + 13*c) + 25920*a^2*b*e^(11*d*x + 11*c) + 590592*a*b^2*e^(11*d*x + 11*c) + 67715*b^3*e^(11*d*x + 11*c) + 14400*a^2*b*e^(9*d*x + 9*c) + 957696*a*b^2*e^(9*d*x + 9*c) + 27055*b^3*e^(9*d*x + 9*c) - 14400*a^2*b*e^(7*d*x + 7*c) + 957696*a*b^2*e^(7*d*x + 7*c) - 27055*b^3*e^(7*d*x + 7*c) - 25920*a^2*b*e^(5*d*x + 5*c) + 590592*a*b^2*e^(5*d*x + 5*c) - 67715*b^3*e^(5*d*x + 5*c) - 14400*a^2*b*e^(3*d*x + 3*c) + 211200*a*b^2*e^(3*d*x + 3*c) - 36775*b^3*e^(3*d*x + 3*c) - 2880*a^2*b*e^(d*x + c) + 34560*a*b^2*e^(d*x + c) - 11475*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^8)/d","A",0
67,1,592,0,1.275906," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{420 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 840 \, {\left(6 \, a^{2} b e^{\left(2 \, c\right)} + 5 \, b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(-2 \, c\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 105 \, {\left(2 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 24 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 42 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 20 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} - a^{3} + 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 105 \, {\left(a^{3} e^{\left(2 \, d x + 22 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, d x + 22 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, d x + 22 \, c\right)} + b^{3} e^{\left(2 \, d x + 22 \, c\right)}\right)} e^{\left(-20 \, c\right)} - \frac{13698 \, a^{2} b e^{\left(16 \, d x + 16 \, c\right)} + 11415 \, b^{3} e^{\left(16 \, d x + 16 \, c\right)} + 104544 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} - 30240 \, a b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 74520 \, b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 353304 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} - 171360 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 252420 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 691488 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} - 446880 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 476840 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 858060 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} - 682080 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 601930 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 691488 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 644448 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 476840 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 353304 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 374304 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 252420 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 104544 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 125664 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 74520 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 13698 \, a^{2} b - 19488 \, a b^{2} + 11415 \, b^{3}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{840 \, d}"," ",0,"-1/840*(420*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 840*(6*a^2*b*e^(2*c) + 5*b^3*e^(2*c))*e^(-2*c)*log(e^(2*d*x + 2*c) + 1) - 105*(2*a^3*e^(2*d*x + 2*c) - 24*a^2*b*e^(2*d*x + 2*c) + 42*a*b^2*e^(2*d*x + 2*c) - 20*b^3*e^(2*d*x + 2*c) - a^3 + 3*a^2*b - 3*a*b^2 + b^3)*e^(-2*d*x - 2*c) - 105*(a^3*e^(2*d*x + 22*c) + 3*a^2*b*e^(2*d*x + 22*c) + 3*a*b^2*e^(2*d*x + 22*c) + b^3*e^(2*d*x + 22*c))*e^(-20*c) - (13698*a^2*b*e^(16*d*x + 16*c) + 11415*b^3*e^(16*d*x + 16*c) + 104544*a^2*b*e^(14*d*x + 14*c) - 30240*a*b^2*e^(14*d*x + 14*c) + 74520*b^3*e^(14*d*x + 14*c) + 353304*a^2*b*e^(12*d*x + 12*c) - 171360*a*b^2*e^(12*d*x + 12*c) + 252420*b^3*e^(12*d*x + 12*c) + 691488*a^2*b*e^(10*d*x + 10*c) - 446880*a*b^2*e^(10*d*x + 10*c) + 476840*b^3*e^(10*d*x + 10*c) + 858060*a^2*b*e^(8*d*x + 8*c) - 682080*a*b^2*e^(8*d*x + 8*c) + 601930*b^3*e^(8*d*x + 8*c) + 691488*a^2*b*e^(6*d*x + 6*c) - 644448*a*b^2*e^(6*d*x + 6*c) + 476840*b^3*e^(6*d*x + 6*c) + 353304*a^2*b*e^(4*d*x + 4*c) - 374304*a*b^2*e^(4*d*x + 4*c) + 252420*b^3*e^(4*d*x + 4*c) + 104544*a^2*b*e^(2*d*x + 2*c) - 125664*a*b^2*e^(2*d*x + 2*c) + 74520*b^3*e^(2*d*x + 2*c) + 13698*a^2*b - 19488*a*b^2 + 11415*b^3)/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
68,1,485,0,0.677814," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{45 \, {\left(64 \, a^{2} b e^{c} + 35 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - 160 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} e^{\left(-d x - c\right)} - 160 \, {\left(a^{3} e^{\left(d x + 20 \, c\right)} + 3 \, a^{2} b e^{\left(d x + 20 \, c\right)} + 3 \, a b^{2} e^{\left(d x + 20 \, c\right)} + b^{3} e^{\left(d x + 20 \, c\right)}\right)} e^{\left(-19 \, c\right)} - \frac{960 \, a^{2} b e^{\left(15 \, d x + 15 \, c\right)} + 5760 \, a b^{2} e^{\left(15 \, d x + 15 \, c\right)} + 1625 \, b^{3} e^{\left(15 \, d x + 15 \, c\right)} + 4800 \, a^{2} b e^{\left(13 \, d x + 13 \, c\right)} + 32640 \, a b^{2} e^{\left(13 \, d x + 13 \, c\right)} + 3925 \, b^{3} e^{\left(13 \, d x + 13 \, c\right)} + 8640 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} + 88704 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 9065 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 4800 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 143232 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 1645 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} - 4800 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 143232 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 1645 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 8640 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 88704 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 9065 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 4800 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 32640 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 3925 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 960 \, a^{2} b e^{\left(d x + c\right)} + 5760 \, a b^{2} e^{\left(d x + c\right)} - 1625 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{320 \, d}"," ",0,"-1/320*(45*(64*a^2*b*e^c + 35*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) - 160*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*e^(-d*x - c) - 160*(a^3*e^(d*x + 20*c) + 3*a^2*b*e^(d*x + 20*c) + 3*a*b^2*e^(d*x + 20*c) + b^3*e^(d*x + 20*c))*e^(-19*c) - (960*a^2*b*e^(15*d*x + 15*c) + 5760*a*b^2*e^(15*d*x + 15*c) + 1625*b^3*e^(15*d*x + 15*c) + 4800*a^2*b*e^(13*d*x + 13*c) + 32640*a*b^2*e^(13*d*x + 13*c) + 3925*b^3*e^(13*d*x + 13*c) + 8640*a^2*b*e^(11*d*x + 11*c) + 88704*a*b^2*e^(11*d*x + 11*c) + 9065*b^3*e^(11*d*x + 11*c) + 4800*a^2*b*e^(9*d*x + 9*c) + 143232*a*b^2*e^(9*d*x + 9*c) + 1645*b^3*e^(9*d*x + 9*c) - 4800*a^2*b*e^(7*d*x + 7*c) + 143232*a*b^2*e^(7*d*x + 7*c) - 1645*b^3*e^(7*d*x + 7*c) - 8640*a^2*b*e^(5*d*x + 5*c) + 88704*a*b^2*e^(5*d*x + 5*c) - 9065*b^3*e^(5*d*x + 5*c) - 4800*a^2*b*e^(3*d*x + 3*c) + 32640*a*b^2*e^(3*d*x + 3*c) - 3925*b^3*e^(3*d*x + 3*c) - 960*a^2*b*e^(d*x + c) + 5760*a*b^2*e^(d*x + c) - 1625*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^8)/d","A",0
69,1,422,0,0.597534," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{960 \, a^{3} \log\left(e^{\left(d x + c\right)} + 1\right) - 960 \, a^{3} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) - 15 \, {\left(192 \, a^{2} b e^{c} + 35 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + \frac{2880 \, a^{2} b e^{\left(15 \, d x + 15 \, c\right)} + 5760 \, a b^{2} e^{\left(15 \, d x + 15 \, c\right)} + 1395 \, b^{3} e^{\left(15 \, d x + 15 \, c\right)} + 14400 \, a^{2} b e^{\left(13 \, d x + 13 \, c\right)} + 24960 \, a b^{2} e^{\left(13 \, d x + 13 \, c\right)} + 455 \, b^{3} e^{\left(13 \, d x + 13 \, c\right)} + 25920 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} + 62592 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 8995 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 14400 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 103296 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} - 5425 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} - 14400 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 103296 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 5425 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 25920 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 62592 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 8995 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 14400 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 24960 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 455 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 2880 \, a^{2} b e^{\left(d x + c\right)} + 5760 \, a b^{2} e^{\left(d x + c\right)} - 1395 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{960 \, d}"," ",0,"-1/960*(960*a^3*log(e^(d*x + c) + 1) - 960*a^3*log(abs(e^(d*x + c) - 1)) - 15*(192*a^2*b*e^c + 35*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) + (2880*a^2*b*e^(15*d*x + 15*c) + 5760*a*b^2*e^(15*d*x + 15*c) + 1395*b^3*e^(15*d*x + 15*c) + 14400*a^2*b*e^(13*d*x + 13*c) + 24960*a*b^2*e^(13*d*x + 13*c) + 455*b^3*e^(13*d*x + 13*c) + 25920*a^2*b*e^(11*d*x + 11*c) + 62592*a*b^2*e^(11*d*x + 11*c) + 8995*b^3*e^(11*d*x + 11*c) + 14400*a^2*b*e^(9*d*x + 9*c) + 103296*a*b^2*e^(9*d*x + 9*c) - 5425*b^3*e^(9*d*x + 9*c) - 14400*a^2*b*e^(7*d*x + 7*c) + 103296*a*b^2*e^(7*d*x + 7*c) + 5425*b^3*e^(7*d*x + 7*c) - 25920*a^2*b*e^(5*d*x + 5*c) + 62592*a*b^2*e^(5*d*x + 5*c) - 8995*b^3*e^(5*d*x + 5*c) - 14400*a^2*b*e^(3*d*x + 3*c) + 24960*a*b^2*e^(3*d*x + 3*c) - 455*b^3*e^(3*d*x + 3*c) - 2880*a^2*b*e^(d*x + c) + 5760*a*b^2*e^(d*x + c) - 1395*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
70,1,311,0,0.765087," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, a^{3}}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{15 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} + 15 \, a b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 5 \, b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 90 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} + 45 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 225 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} + 75 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 35 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 300 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 105 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 225 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 93 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 35 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 90 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 39 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 15 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 5 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}\right)}}{5 \, d}"," ",0,"-2/5*(5*a^3/(e^(2*d*x + 2*c) - 1) + (15*a^2*b*e^(14*d*x + 14*c) + 15*a*b^2*e^(14*d*x + 14*c) + 5*b^3*e^(14*d*x + 14*c) + 90*a^2*b*e^(12*d*x + 12*c) + 45*a*b^2*e^(12*d*x + 12*c) + 225*a^2*b*e^(10*d*x + 10*c) + 75*a*b^2*e^(10*d*x + 10*c) + 35*b^3*e^(10*d*x + 10*c) + 300*a^2*b*e^(8*d*x + 8*c) + 105*a*b^2*e^(8*d*x + 8*c) + 225*a^2*b*e^(6*d*x + 6*c) + 93*a*b^2*e^(6*d*x + 6*c) + 35*b^3*e^(6*d*x + 6*c) + 90*a^2*b*e^(4*d*x + 4*c) + 39*a*b^2*e^(4*d*x + 4*c) + 15*a^2*b*e^(2*d*x + 2*c) + 9*a*b^2*e^(2*d*x + 2*c) + 5*b^3*e^(2*d*x + 2*c) + 3*a*b^2)/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
71,1,434,0,0.841220," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{480 \, a^{3} \log\left(e^{\left(d x + c\right)} + 1\right) - 480 \, a^{3} \log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right) + 15 \, {\left(192 \, a^{2} b e^{c} + 5 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - \frac{960 \, {\left(a^{3} e^{\left(3 \, d x + 3 \, c\right)} + a^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}} + \frac{2880 \, a^{2} b e^{\left(15 \, d x + 15 \, c\right)} + 75 \, b^{3} e^{\left(15 \, d x + 15 \, c\right)} + 14400 \, a^{2} b e^{\left(13 \, d x + 13 \, c\right)} - 7680 \, a b^{2} e^{\left(13 \, d x + 13 \, c\right)} - 1985 \, b^{3} e^{\left(13 \, d x + 13 \, c\right)} + 25920 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} - 19968 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 4475 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 14400 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} - 21504 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} - 8825 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} - 14400 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} - 21504 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 8825 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 25920 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 19968 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 4475 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 14400 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} - 7680 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 1985 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 2880 \, a^{2} b e^{\left(d x + c\right)} - 75 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{960 \, d}"," ",0,"1/960*(480*a^3*log(e^(d*x + c) + 1) - 480*a^3*log(abs(e^(d*x + c) - 1)) + 15*(192*a^2*b*e^c + 5*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) - 960*(a^3*e^(3*d*x + 3*c) + a^3*e^(d*x + c))/(e^(2*d*x + 2*c) - 1)^2 + (2880*a^2*b*e^(15*d*x + 15*c) + 75*b^3*e^(15*d*x + 15*c) + 14400*a^2*b*e^(13*d*x + 13*c) - 7680*a*b^2*e^(13*d*x + 13*c) - 1985*b^3*e^(13*d*x + 13*c) + 25920*a^2*b*e^(11*d*x + 11*c) - 19968*a*b^2*e^(11*d*x + 11*c) + 4475*b^3*e^(11*d*x + 11*c) + 14400*a^2*b*e^(9*d*x + 9*c) - 21504*a*b^2*e^(9*d*x + 9*c) - 8825*b^3*e^(9*d*x + 9*c) - 14400*a^2*b*e^(7*d*x + 7*c) - 21504*a*b^2*e^(7*d*x + 7*c) + 8825*b^3*e^(7*d*x + 7*c) - 25920*a^2*b*e^(5*d*x + 5*c) - 19968*a*b^2*e^(5*d*x + 5*c) - 4475*b^3*e^(5*d*x + 5*c) - 14400*a^2*b*e^(3*d*x + 3*c) - 7680*a*b^2*e^(3*d*x + 3*c) + 1985*b^3*e^(3*d*x + 3*c) - 2880*a^2*b*e^(d*x + c) - 75*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
72,1,437,0,0.824524," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2520 \, a^{2} b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - 2520 \, a^{2} b \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{140 \, {\left(33 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 99 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 24 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 99 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 8 \, a^{3} - 33 \, a^{2} b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}} - \frac{6849 \, a^{2} b e^{\left(16 \, d x + 16 \, c\right)} + 59832 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} + 222012 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} - 10080 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} - 3360 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 459144 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} - 26880 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 4480 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 580230 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} - 23520 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} - 11200 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 459144 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 10752 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 4480 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 222012 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 8736 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 3360 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 59832 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 5376 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 6849 \, a^{2} b - 672 \, a b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{840 \, d}"," ",0,"-1/840*(2520*a^2*b*log(e^(2*d*x + 2*c) + 1) - 2520*a^2*b*log(abs(e^(2*d*x + 2*c) - 1)) + 140*(33*a^2*b*e^(6*d*x + 6*c) - 99*a^2*b*e^(4*d*x + 4*c) + 24*a^3*e^(2*d*x + 2*c) + 99*a^2*b*e^(2*d*x + 2*c) - 8*a^3 - 33*a^2*b)/(e^(2*d*x + 2*c) - 1)^3 - (6849*a^2*b*e^(16*d*x + 16*c) + 59832*a^2*b*e^(14*d*x + 14*c) + 222012*a^2*b*e^(12*d*x + 12*c) - 10080*a*b^2*e^(12*d*x + 12*c) - 3360*b^3*e^(12*d*x + 12*c) + 459144*a^2*b*e^(10*d*x + 10*c) - 26880*a*b^2*e^(10*d*x + 10*c) + 4480*b^3*e^(10*d*x + 10*c) + 580230*a^2*b*e^(8*d*x + 8*c) - 23520*a*b^2*e^(8*d*x + 8*c) - 11200*b^3*e^(8*d*x + 8*c) + 459144*a^2*b*e^(6*d*x + 6*c) - 10752*a*b^2*e^(6*d*x + 6*c) + 4480*b^3*e^(6*d*x + 6*c) + 222012*a^2*b*e^(4*d*x + 4*c) - 8736*a*b^2*e^(4*d*x + 4*c) - 3360*b^3*e^(4*d*x + 4*c) + 59832*a^2*b*e^(2*d*x + 2*c) - 5376*a*b^2*e^(2*d*x + 2*c) + 6849*a^2*b - 672*a*b^2)/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
73,1,362,0,0.759100," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{2} + 5 \, a b\right)} d x}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 90 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 4 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} - 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x\right)}}{a^{3} e^{\left(4 \, c\right)} - 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} - b^{3} e^{\left(4 \, c\right)}} - \frac{64 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{a e^{\left(4 \, d x + 24 \, c\right)} + b e^{\left(4 \, d x + 24 \, c\right)} - 8 \, a e^{\left(2 \, d x + 22 \, c\right)} + 4 \, b e^{\left(2 \, d x + 22 \, c\right)}}{a^{2} e^{\left(20 \, c\right)} + 2 \, a b e^{\left(20 \, c\right)} + b^{2} e^{\left(20 \, c\right)}}}{64 \, d}"," ",0,"1/64*(24*(a^2 + 5*a*b)*d*x/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (18*a^2*e^(4*d*x + 4*c) + 90*a*b*e^(4*d*x + 4*c) - 8*a^2*e^(2*d*x + 2*c) + 4*a*b*e^(2*d*x + 2*c) + 4*b^2*e^(2*d*x + 2*c) + a^2 - 2*a*b + b^2)*e^(-4*d*x)/(a^3*e^(4*c) - 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) - b^3*e^(4*c)) - 64*(a^4*b + 2*a^2*b^3)*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (a*e^(4*d*x + 24*c) + b*e^(4*d*x + 24*c) - 8*a*e^(2*d*x + 22*c) + 4*b*e^(2*d*x + 22*c))/(a^2*e^(20*c) + 2*a*b*e^(20*c) + b^2*e^(20*c)))/d","A",0
74,1,344,0,3.163925," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{\frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} + 9 \, b e^{\left(2 \, d x + 2 \, c\right)} - a + b\right)} e^{\left(-3 \, d x\right)}}{a^{2} e^{\left(3 \, c\right)} - 2 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}} - \frac{a^{2} e^{\left(3 \, d x + 30 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 30 \, c\right)} + b^{2} e^{\left(3 \, d x + 30 \, c\right)} - 9 \, a^{2} e^{\left(d x + 28 \, c\right)} + 9 \, b^{2} e^{\left(d x + 28 \, c\right)}}{a^{3} e^{\left(27 \, c\right)} + 3 \, a^{2} b e^{\left(27 \, c\right)} + 3 \, a b^{2} e^{\left(27 \, c\right)} + b^{3} e^{\left(27 \, c\right)}}}{24 \, d} - \frac{\frac{6 \, {\left(a^{3} b e^{c} + a^{2} b^{2} e^{c} + a b^{3} e^{c}\right)} d x}{a - b} - \frac{{\left(a^{3} b e^{c} + a^{2} b^{2} e^{c} + a b^{3} e^{c}\right)} \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a - b}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}"," ",0,"-1/24*((9*a*e^(2*d*x + 2*c) + 9*b*e^(2*d*x + 2*c) - a + b)*e^(-3*d*x)/(a^2*e^(3*c) - 2*a*b*e^(3*c) + b^2*e^(3*c)) - (a^2*e^(3*d*x + 30*c) + 2*a*b*e^(3*d*x + 30*c) + b^2*e^(3*d*x + 30*c) - 9*a^2*e^(d*x + 28*c) + 9*b^2*e^(d*x + 28*c))/(a^3*e^(27*c) + 3*a^2*b*e^(27*c) + 3*a*b^2*e^(27*c) + b^3*e^(27*c)))/d - (6*(a^3*b*e^c + a^2*b^2*e^c + a*b^3*e^c)*d*x/(a - b) - (a^3*b*e^c + a^2*b^2*e^c + a*b^3*e^c)*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/(a - b))/((a^4 - 2*a^2*b^2 + b^4)*d^2)","B",0
75,1,223,0,0.365316," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a + 2 \, b\right)} d x}{a^{2} - 2 \, a b + b^{2}} - \frac{3 \, {\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} + 4 \, b e^{\left(2 \, d x + 2 \, c\right)} - a + b\right)} e^{\left(-2 \, d x\right)}}{a^{2} e^{\left(2 \, c\right)} - 2 \, a b e^{\left(2 \, c\right)} + b^{2} e^{\left(2 \, c\right)}} - \frac{8 \, {\left(2 \, a^{2} b + b^{3}\right)} \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{3 \, e^{\left(2 \, d x + 10 \, c\right)}}{a e^{\left(8 \, c\right)} + b e^{\left(8 \, c\right)}}}{24 \, d}"," ",0,"-1/24*(12*(a + 2*b)*d*x/(a^2 - 2*a*b + b^2) - 3*(2*a*e^(2*d*x + 2*c) + 4*b*e^(2*d*x + 2*c) - a + b)*e^(-2*d*x)/(a^2*e^(2*c) - 2*a*b*e^(2*c) + b^2*e^(2*c)) - 8*(2*a^2*b + b^3)*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/(a^4 - 2*a^2*b^2 + b^4) - 3*e^(2*d*x + 10*c)/(a*e^(8*c) + b*e^(8*c)))/d","A",0
76,1,189,0,1.841223," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{\frac{e^{\left(d x + 8 \, c\right)}}{a e^{\left(7 \, c\right)} + b e^{\left(7 \, c\right)}} + \frac{e^{\left(-d x\right)}}{a e^{c} - b e^{c}}}{2 \, d} + \frac{\frac{6 \, {\left(2 \, a b e^{c} + b^{2} e^{c}\right)} d x}{a - b} - \frac{{\left(2 \, a b e^{c} + b^{2} e^{c}\right)} \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a - b}}{3 \, {\left(a^{2} - b^{2}\right)} d^{2}}"," ",0,"1/2*(e^(d*x + 8*c)/(a*e^(7*c) + b*e^(7*c)) + e^(-d*x)/(a*e^c - b*e^c))/d + 1/3*(6*(2*a*b*e^c + b^2*e^c)*d*x/(a - b) - (2*a*b*e^c + b^2*e^c)*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/(a - b))/((a^2 - b^2)*d^2)","B",0
77,1,147,0,1.398410," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{\frac{\log\left(e^{\left(d x + c\right)} + 1\right)}{a} - \frac{\log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a}}{d} - \frac{\frac{6 \, b d x e^{c}}{a - b} - \frac{b e^{c} \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a - b}}{3 \, a d^{2}}"," ",0,"-(log(e^(d*x + c) + 1)/a - log(abs(e^(d*x + c) - 1))/a)/d - 1/3*(6*b*d*x*e^c/(a - b) - b*e^c*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/(a - b))/(a*d^2)","B",0
78,1,21,0,0.251935," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","-\frac{2}{a d {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}}"," ",0,"-2/(a*d*(e^(2*d*x + 2*c) - 1))","A",0
79,1,68,0,0.788413," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{\frac{\log\left(e^{\left(d x + c\right)} + 1\right)}{a} - \frac{\log\left({\left| e^{\left(d x + c\right)} - 1 \right|}\right)}{a} - \frac{2 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}\right)}}{a {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(log(e^(d*x + c) + 1)/a - log(abs(e^(d*x + c) - 1))/a - 2*(e^(3*d*x + 3*c) + e^(d*x + c))/(a*(e^(2*d*x + 2*c) - 1)^2))/d","B",0
80,1,180,0,0.285021," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""giac"")","\frac{\frac{2 \, b \log\left({\left| a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a - b \right|}\right)}{a^{2}} - \frac{6 \, b \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{2}} + \frac{11 \, b e^{\left(6 \, d x + 6 \, c\right)} - 33 \, b e^{\left(4 \, d x + 4 \, c\right)} - 24 \, a e^{\left(2 \, d x + 2 \, c\right)} + 33 \, b e^{\left(2 \, d x + 2 \, c\right)} + 8 \, a - 11 \, b}{a^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(2*b*log(abs(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) + a - b))/a^2 - 6*b*log(abs(e^(2*d*x + 2*c) - 1))/a^2 + (11*b*e^(6*d*x + 6*c) - 33*b*e^(4*d*x + 4*c) - 24*a*e^(2*d*x + 2*c) + 33*b*e^(2*d*x + 2*c) + 8*a - 11*b)/(a^2*(e^(2*d*x + 2*c) - 1)^3))/d","A",0
81,1,107,0,0.176543," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{8 \, {\left(3 \, a - b\right)} d x - {\left(18 \, a e^{\left(4 \, d x + 4 \, c\right)} - 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 8 \, a e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a e^{\left(4 \, d x + 12 \, c\right)} + b e^{\left(4 \, d x + 12 \, c\right)} + 8 \, a e^{\left(2 \, d x + 10 \, c\right)}\right)} e^{\left(-8 \, c\right)}}{64 \, d}"," ",0,"1/64*(8*(3*a - b)*d*x - (18*a*e^(4*d*x + 4*c) - 6*b*e^(4*d*x + 4*c) + 8*a*e^(2*d*x + 2*c) + a + b)*e^(-4*d*x - 4*c) + (a*e^(4*d*x + 12*c) + b*e^(4*d*x + 12*c) + 8*a*e^(2*d*x + 10*c))*e^(-8*c))/d","A",0
82,1,94,0,0.159274," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} - 3 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-3 \, d x - 3 \, c\right)} - {\left(a e^{\left(3 \, d x + 12 \, c\right)} + b e^{\left(3 \, d x + 12 \, c\right)} + 9 \, a e^{\left(d x + 10 \, c\right)} - 3 \, b e^{\left(d x + 10 \, c\right)}\right)} e^{\left(-9 \, c\right)}}{24 \, d}"," ",0,"-1/24*((9*a*e^(2*d*x + 2*c) - 3*b*e^(2*d*x + 2*c) + a + b)*e^(-3*d*x - 3*c) - (a*e^(3*d*x + 12*c) + b*e^(3*d*x + 12*c) + 9*a*e^(d*x + 10*c) - 3*b*e^(d*x + 10*c))*e^(-9*c))/d","B",0
83,1,81,0,0.140191," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{4 \, {\left(a - b\right)} d x - {\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a e^{\left(2 \, d x + 4 \, c\right)} + b e^{\left(2 \, d x + 4 \, c\right)}\right)} e^{\left(-2 \, c\right)}}{8 \, d}"," ",0,"1/8*(4*(a - b)*d*x - (2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*e^(-2*d*x - 2*c) + (a*e^(2*d*x + 4*c) + b*e^(2*d*x + 4*c))*e^(-2*c))/d","B",0
84,1,56,0,0.143079," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{4 \, b \arctan\left(e^{\left(d x + c\right)}\right) + {\left(a + b\right)} e^{\left(-d x - c\right)} - {\left(a e^{\left(d x + 4 \, c\right)} + b e^{\left(d x + 4 \, c\right)}\right)} e^{\left(-3 \, c\right)}}{2 \, d}"," ",0,"-1/2*(4*b*arctan(e^(d*x + c)) + (a + b)*e^(-d*x - c) - (a*e^(d*x + 4*c) + b*e^(d*x + 4*c))*e^(-3*c))/d","B",0
85,1,63,0,0.144801," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(2 \, a e^{c} + b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - \frac{b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{d}"," ",0,"((2*a*e^c + b*e^c)*arctan(e^(d*x + c))*e^(-c) - (b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
86,1,59,0,0.156244," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a + b\right)}}{3 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}"," ",0,"-2/3*(3*a*e^(4*d*x + 4*c) + 3*b*e^(4*d*x + 4*c) + 6*a*e^(2*d*x + 2*c) + 3*a + b)/(d*(e^(2*d*x + 2*c) + 1)^3)","B",0
87,1,132,0,0.154097," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(4 \, a e^{c} + b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + \frac{4 \, a e^{\left(7 \, d x + 7 \, c\right)} + b e^{\left(7 \, d x + 7 \, c\right)} + 4 \, a e^{\left(5 \, d x + 5 \, c\right)} - 7 \, b e^{\left(5 \, d x + 5 \, c\right)} - 4 \, a e^{\left(3 \, d x + 3 \, c\right)} + 7 \, b e^{\left(3 \, d x + 3 \, c\right)} - 4 \, a e^{\left(d x + c\right)} - b e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{4}}}{4 \, d}"," ",0,"1/4*((4*a*e^c + b*e^c)*arctan(e^(d*x + c))*e^(-c) + (4*a*e^(7*d*x + 7*c) + b*e^(7*d*x + 7*c) + 4*a*e^(5*d*x + 5*c) - 7*b*e^(5*d*x + 5*c) - 4*a*e^(3*d*x + 3*c) + 7*b*e^(3*d*x + 3*c) - 4*a*e^(d*x + c) - b*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^4)/d","B",0
88,1,95,0,0.159463," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{4 \, {\left(15 \, a e^{\left(6 \, d x + 6 \, c\right)} + 15 \, b e^{\left(6 \, d x + 6 \, c\right)} + 35 \, a e^{\left(4 \, d x + 4 \, c\right)} - 5 \, b e^{\left(4 \, d x + 4 \, c\right)} + 25 \, a e^{\left(2 \, d x + 2 \, c\right)} + 5 \, b e^{\left(2 \, d x + 2 \, c\right)} + 5 \, a + b\right)}}{15 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}"," ",0,"-4/15*(15*a*e^(6*d*x + 6*c) + 15*b*e^(6*d*x + 6*c) + 35*a*e^(4*d*x + 4*c) - 5*b*e^(4*d*x + 4*c) + 25*a*e^(2*d*x + 2*c) + 5*b*e^(2*d*x + 2*c) + 5*a + b)/(d*(e^(2*d*x + 2*c) + 1)^5)","B",0
89,1,189,0,0.387568," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{8 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - {\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 12 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 18 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 8 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{2} e^{\left(4 \, d x + 12 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 12 \, c\right)} + b^{2} e^{\left(4 \, d x + 12 \, c\right)} + 8 \, a^{2} e^{\left(2 \, d x + 10 \, c\right)} - 8 \, b^{2} e^{\left(2 \, d x + 10 \, c\right)}\right)} e^{\left(-8 \, c\right)}}{64 \, d}"," ",0,"1/64*(8*(3*a^2 - 2*a*b + 3*b^2)*d*x - (18*a^2*e^(4*d*x + 4*c) - 12*a*b*e^(4*d*x + 4*c) + 18*b^2*e^(4*d*x + 4*c) + 8*a^2*e^(2*d*x + 2*c) - 8*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) + (a^2*e^(4*d*x + 12*c) + 2*a*b*e^(4*d*x + 12*c) + b^2*e^(4*d*x + 12*c) + 8*a^2*e^(2*d*x + 10*c) - 8*b^2*e^(2*d*x + 10*c))*e^(-8*c))/d","B",0
90,1,164,0,0.364321," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{48 \, b^{2} \arctan\left(e^{\left(d x + c\right)}\right) - {\left(9 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 15 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-3 \, d x - 3 \, c\right)} + {\left(a^{2} e^{\left(3 \, d x + 18 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 18 \, c\right)} + b^{2} e^{\left(3 \, d x + 18 \, c\right)} + 9 \, a^{2} e^{\left(d x + 16 \, c\right)} - 6 \, a b e^{\left(d x + 16 \, c\right)} - 15 \, b^{2} e^{\left(d x + 16 \, c\right)}\right)} e^{\left(-15 \, c\right)}}{24 \, d}"," ",0,"1/24*(48*b^2*arctan(e^(d*x + c)) - (9*a^2*e^(2*d*x + 2*c) - 6*a*b*e^(2*d*x + 2*c) - 15*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-3*d*x - 3*c) + (a^2*e^(3*d*x + 18*c) + 2*a*b*e^(3*d*x + 18*c) + b^2*e^(3*d*x + 18*c) + 9*a^2*e^(d*x + 16*c) - 6*a*b*e^(d*x + 16*c) - 15*b^2*e^(d*x + 16*c))*e^(-15*c))/d","B",0
91,1,170,0,0.276498," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{4 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x + {\left(a^{2} e^{\left(2 \, d x + 8 \, c\right)} + 2 \, a b e^{\left(2 \, d x + 8 \, c\right)} + b^{2} e^{\left(2 \, d x + 8 \, c\right)}\right)} e^{\left(-6 \, c\right)} - \frac{{\left(a^{2} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 14 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, c\right)}}{e^{\left(2 \, d x\right)} + e^{\left(4 \, d x + 2 \, c\right)}}}{8 \, d}"," ",0,"1/8*(4*(a^2 - 2*a*b - 3*b^2)*d*x + (a^2*e^(2*d*x + 8*c) + 2*a*b*e^(2*d*x + 8*c) + b^2*e^(2*d*x + 8*c))*e^(-6*c) - (a^2*e^(4*d*x + 4*c) - 2*a*b*e^(4*d*x + 4*c) - 3*b^2*e^(4*d*x + 4*c) + 2*a^2*e^(2*d*x + 2*c) + 14*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-2*c)/(e^(2*d*x) + e^(4*d*x + 2*c)))/d","B",0
92,1,137,0,0.248191," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(4 \, a b e^{c} + 3 \, b^{2} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-d x - c\right)} - {\left(a^{2} e^{\left(d x + 8 \, c\right)} + 2 \, a b e^{\left(d x + 8 \, c\right)} + b^{2} e^{\left(d x + 8 \, c\right)}\right)} e^{\left(-7 \, c\right)} - \frac{2 \, {\left(b^{2} e^{\left(3 \, d x + 3 \, c\right)} - b^{2} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(4*a*b*e^c + 3*b^2*e^c)*arctan(e^(d*x + c))*e^(-c) + (a^2 + 2*a*b + b^2)*e^(-d*x - c) - (a^2*e^(d*x + 8*c) + 2*a*b*e^(d*x + 8*c) + b^2*e^(d*x + 8*c))*e^(-7*c) - 2*(b^2*e^(3*d*x + 3*c) - b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","B",0
93,1,157,0,0.203128," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{{\left(8 \, a^{2} e^{c} + 8 \, a b e^{c} + 3 \, b^{2} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - \frac{8 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 5 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 8 \, a b e^{\left(5 \, d x + 5 \, c\right)} - 3 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 8 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 3 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 8 \, a b e^{\left(d x + c\right)} - 5 \, b^{2} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{4}}}{4 \, d}"," ",0,"1/4*((8*a^2*e^c + 8*a*b*e^c + 3*b^2*e^c)*arctan(e^(d*x + c))*e^(-c) - (8*a*b*e^(7*d*x + 7*c) + 5*b^2*e^(7*d*x + 7*c) + 8*a*b*e^(5*d*x + 5*c) - 3*b^2*e^(5*d*x + 5*c) - 8*a*b*e^(3*d*x + 3*c) + 3*b^2*e^(3*d*x + 3*c) - 8*a*b*e^(d*x + c) - 5*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^4)/d","A",0
94,1,169,0,0.228792," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 30 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 15 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} + 60 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 90 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 40 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 30 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 60 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 20 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 15 \, a^{2} + 10 \, a b + 3 \, b^{2}\right)}}{15 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}"," ",0,"-2/15*(15*a^2*e^(8*d*x + 8*c) + 30*a*b*e^(8*d*x + 8*c) + 15*b^2*e^(8*d*x + 8*c) + 60*a^2*e^(6*d*x + 6*c) + 60*a*b*e^(6*d*x + 6*c) + 90*a^2*e^(4*d*x + 4*c) + 40*a*b*e^(4*d*x + 4*c) + 30*b^2*e^(4*d*x + 4*c) + 60*a^2*e^(2*d*x + 2*c) + 20*a*b*e^(2*d*x + 2*c) + 15*a^2 + 10*a*b + 3*b^2)/(d*(e^(2*d*x + 2*c) + 1)^5)","B",0
95,1,291,0,0.215182," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(8 \, a^{2} e^{c} + 4 \, a b e^{c} + b^{2} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + \frac{24 \, a^{2} e^{\left(11 \, d x + 11 \, c\right)} + 12 \, a b e^{\left(11 \, d x + 11 \, c\right)} + 3 \, b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 72 \, a^{2} e^{\left(9 \, d x + 9 \, c\right)} - 60 \, a b e^{\left(9 \, d x + 9 \, c\right)} - 47 \, b^{2} e^{\left(9 \, d x + 9 \, c\right)} + 48 \, a^{2} e^{\left(7 \, d x + 7 \, c\right)} - 72 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 78 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 48 \, a^{2} e^{\left(5 \, d x + 5 \, c\right)} + 72 \, a b e^{\left(5 \, d x + 5 \, c\right)} - 78 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 72 \, a^{2} e^{\left(3 \, d x + 3 \, c\right)} + 60 \, a b e^{\left(3 \, d x + 3 \, c\right)} + 47 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 24 \, a^{2} e^{\left(d x + c\right)} - 12 \, a b e^{\left(d x + c\right)} - 3 \, b^{2} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{6}}}{24 \, d}"," ",0,"1/24*(3*(8*a^2*e^c + 4*a*b*e^c + b^2*e^c)*arctan(e^(d*x + c))*e^(-c) + (24*a^2*e^(11*d*x + 11*c) + 12*a*b*e^(11*d*x + 11*c) + 3*b^2*e^(11*d*x + 11*c) + 72*a^2*e^(9*d*x + 9*c) - 60*a*b*e^(9*d*x + 9*c) - 47*b^2*e^(9*d*x + 9*c) + 48*a^2*e^(7*d*x + 7*c) - 72*a*b*e^(7*d*x + 7*c) + 78*b^2*e^(7*d*x + 7*c) - 48*a^2*e^(5*d*x + 5*c) + 72*a*b*e^(5*d*x + 5*c) - 78*b^2*e^(5*d*x + 5*c) - 72*a^2*e^(3*d*x + 3*c) + 60*a*b*e^(3*d*x + 3*c) + 47*b^2*e^(3*d*x + 3*c) - 24*a^2*e^(d*x + c) - 12*a*b*e^(d*x + c) - 3*b^2*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^6)/d","B",0
96,1,238,0,0.244359," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, a^{2} e^{\left(10 \, d x + 10 \, c\right)} + 210 \, a b e^{\left(10 \, d x + 10 \, c\right)} + 105 \, b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 455 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 350 \, a b e^{\left(8 \, d x + 8 \, c\right)} - 105 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 770 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} + 140 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 210 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 630 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 84 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 42 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 245 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 98 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 21 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 35 \, a^{2} + 14 \, a b + 3 \, b^{2}\right)}}{105 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{7}}"," ",0,"-4/105*(105*a^2*e^(10*d*x + 10*c) + 210*a*b*e^(10*d*x + 10*c) + 105*b^2*e^(10*d*x + 10*c) + 455*a^2*e^(8*d*x + 8*c) + 350*a*b*e^(8*d*x + 8*c) - 105*b^2*e^(8*d*x + 8*c) + 770*a^2*e^(6*d*x + 6*c) + 140*a*b*e^(6*d*x + 6*c) + 210*b^2*e^(6*d*x + 6*c) + 630*a^2*e^(4*d*x + 4*c) + 84*a*b*e^(4*d*x + 4*c) - 42*b^2*e^(4*d*x + 4*c) + 245*a^2*e^(2*d*x + 2*c) + 98*a*b*e^(2*d*x + 2*c) + 21*b^2*e^(2*d*x + 2*c) + 35*a^2 + 14*a*b + 3*b^2)/(d*(e^(2*d*x + 2*c) + 1)^7)","B",0
97,1,285,0,0.755303," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{24 \, {\left(a^{3} - a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} d x + \frac{128 \, b^{3}}{e^{\left(2 \, d x + 2 \, c\right)} + 1} - {\left(18 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - 18 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 54 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 90 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 24 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 16 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} e^{\left(4 \, d x + 20 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, d x + 20 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, d x + 20 \, c\right)} + b^{3} e^{\left(4 \, d x + 20 \, c\right)} + 8 \, a^{3} e^{\left(2 \, d x + 18 \, c\right)} - 24 \, a b^{2} e^{\left(2 \, d x + 18 \, c\right)} - 16 \, b^{3} e^{\left(2 \, d x + 18 \, c\right)}\right)} e^{\left(-16 \, c\right)}}{64 \, d}"," ",0,"1/64*(24*(a^3 - a^2*b + 3*a*b^2 + 5*b^3)*d*x + 128*b^3/(e^(2*d*x + 2*c) + 1) - (18*a^3*e^(4*d*x + 4*c) - 18*a^2*b*e^(4*d*x + 4*c) + 54*a*b^2*e^(4*d*x + 4*c) + 90*b^3*e^(4*d*x + 4*c) + 8*a^3*e^(2*d*x + 2*c) - 24*a*b^2*e^(2*d*x + 2*c) - 16*b^3*e^(2*d*x + 2*c) + a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-4*d*x - 4*c) + (a^3*e^(4*d*x + 20*c) + 3*a^2*b*e^(4*d*x + 20*c) + 3*a*b^2*e^(4*d*x + 20*c) + b^3*e^(4*d*x + 20*c) + 8*a^3*e^(2*d*x + 18*c) - 24*a*b^2*e^(2*d*x + 18*c) - 16*b^3*e^(2*d*x + 18*c))*e^(-16*c))/d","B",0
98,1,279,0,0.656088," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{24 \, {\left(6 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - {\left(9 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 45 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 27 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-3 \, d x - 3 \, c\right)} + {\left(a^{3} e^{\left(3 \, d x + 30 \, c\right)} + 3 \, a^{2} b e^{\left(3 \, d x + 30 \, c\right)} + 3 \, a b^{2} e^{\left(3 \, d x + 30 \, c\right)} + b^{3} e^{\left(3 \, d x + 30 \, c\right)} + 9 \, a^{3} e^{\left(d x + 28 \, c\right)} - 9 \, a^{2} b e^{\left(d x + 28 \, c\right)} - 45 \, a b^{2} e^{\left(d x + 28 \, c\right)} - 27 \, b^{3} e^{\left(d x + 28 \, c\right)}\right)} e^{\left(-27 \, c\right)} - \frac{24 \, {\left(b^{3} e^{\left(3 \, d x + 3 \, c\right)} - b^{3} e^{\left(d x + c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{24 \, d}"," ",0,"1/24*(24*(6*a*b^2*e^c + 5*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) - (9*a^3*e^(2*d*x + 2*c) - 9*a^2*b*e^(2*d*x + 2*c) - 45*a*b^2*e^(2*d*x + 2*c) - 27*b^3*e^(2*d*x + 2*c) + a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-3*d*x - 3*c) + (a^3*e^(3*d*x + 30*c) + 3*a^2*b*e^(3*d*x + 30*c) + 3*a*b^2*e^(3*d*x + 30*c) + b^3*e^(3*d*x + 30*c) + 9*a^3*e^(d*x + 28*c) - 9*a^2*b*e^(d*x + 28*c) - 45*a*b^2*e^(d*x + 28*c) - 27*b^3*e^(d*x + 28*c))*e^(-27*c) - 24*(b^3*e^(3*d*x + 3*c) - b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^2)/d","B",0
99,1,267,0,0.598506," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{12 \, {\left(a^{3} - 3 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)} d x - 3 \, {\left(2 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 18 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 10 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a^{3} e^{\left(2 \, d x + 12 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, d x + 12 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, d x + 12 \, c\right)} + b^{3} e^{\left(2 \, d x + 12 \, c\right)}\right)} e^{\left(-10 \, c\right)} - \frac{16 \, {\left(9 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 18 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a b^{2} + 7 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(12*(a^3 - 3*a^2*b - 9*a*b^2 - 5*b^3)*d*x - 3*(2*a^3*e^(2*d*x + 2*c) - 6*a^2*b*e^(2*d*x + 2*c) - 18*a*b^2*e^(2*d*x + 2*c) - 10*b^3*e^(2*d*x + 2*c) + a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-2*d*x - 2*c) + 3*(a^3*e^(2*d*x + 12*c) + 3*a^2*b*e^(2*d*x + 12*c) + 3*a*b^2*e^(2*d*x + 12*c) + b^3*e^(2*d*x + 12*c))*e^(-10*c) - 16*(9*a*b^2*e^(4*d*x + 4*c) + 9*b^3*e^(4*d*x + 4*c) + 18*a*b^2*e^(2*d*x + 2*c) + 12*b^3*e^(2*d*x + 2*c) + 9*a*b^2 + 7*b^3)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
100,1,257,0,0.383526," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(8 \, a^{2} b e^{c} + 12 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(-d x - c\right)} - 2 \, {\left(a^{3} e^{\left(d x + 12 \, c\right)} + 3 \, a^{2} b e^{\left(d x + 12 \, c\right)} + 3 \, a b^{2} e^{\left(d x + 12 \, c\right)} + b^{3} e^{\left(d x + 12 \, c\right)}\right)} e^{\left(-11 \, c\right)} - \frac{12 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 9 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 12 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 12 \, a b^{2} e^{\left(d x + c\right)} - 9 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{4}}}{4 \, d}"," ",0,"-1/4*(3*(8*a^2*b*e^c + 12*a*b^2*e^c + 5*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) + 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-d*x - c) - 2*(a^3*e^(d*x + 12*c) + 3*a^2*b*e^(d*x + 12*c) + 3*a*b^2*e^(d*x + 12*c) + b^3*e^(d*x + 12*c))*e^(-11*c) - (12*a*b^2*e^(7*d*x + 7*c) + 9*b^3*e^(7*d*x + 7*c) + 12*a*b^2*e^(5*d*x + 5*c) + b^3*e^(5*d*x + 5*c) - 12*a*b^2*e^(3*d*x + 3*c) - b^3*e^(3*d*x + 3*c) - 12*a*b^2*e^(d*x + c) - 9*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^4)/d","B",0
101,1,321,0,0.309015," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(16 \, a^{3} e^{c} + 24 \, a^{2} b e^{c} + 18 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} - \frac{72 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} + 90 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 33 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 216 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 126 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} - 5 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} + 144 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 36 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 90 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 144 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 36 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 90 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 216 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} - 126 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 5 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 72 \, a^{2} b e^{\left(d x + c\right)} - 90 \, a b^{2} e^{\left(d x + c\right)} - 33 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{6}}}{24 \, d}"," ",0,"1/24*(3*(16*a^3*e^c + 24*a^2*b*e^c + 18*a*b^2*e^c + 5*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) - (72*a^2*b*e^(11*d*x + 11*c) + 90*a*b^2*e^(11*d*x + 11*c) + 33*b^3*e^(11*d*x + 11*c) + 216*a^2*b*e^(9*d*x + 9*c) + 126*a*b^2*e^(9*d*x + 9*c) - 5*b^3*e^(9*d*x + 9*c) + 144*a^2*b*e^(7*d*x + 7*c) + 36*a*b^2*e^(7*d*x + 7*c) + 90*b^3*e^(7*d*x + 7*c) - 144*a^2*b*e^(5*d*x + 5*c) - 36*a*b^2*e^(5*d*x + 5*c) - 90*b^3*e^(5*d*x + 5*c) - 216*a^2*b*e^(3*d*x + 3*c) - 126*a*b^2*e^(3*d*x + 3*c) + 5*b^3*e^(3*d*x + 3*c) - 72*a^2*b*e^(d*x + c) - 90*a*b^2*e^(d*x + c) - 33*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^6)/d","B",0
102,1,347,0,0.391951," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, a^{3} e^{\left(12 \, d x + 12 \, c\right)} + 105 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} + 105 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 35 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 210 \, a^{3} e^{\left(10 \, d x + 10 \, c\right)} + 420 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} + 210 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 525 \, a^{3} e^{\left(8 \, d x + 8 \, c\right)} + 665 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 315 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 175 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 700 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + 560 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 420 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 525 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 315 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 231 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 105 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 210 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 140 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 42 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 35 \, a^{3} + 35 \, a^{2} b + 21 \, a b^{2} + 5 \, b^{3}\right)}}{35 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{7}}"," ",0,"-2/35*(35*a^3*e^(12*d*x + 12*c) + 105*a^2*b*e^(12*d*x + 12*c) + 105*a*b^2*e^(12*d*x + 12*c) + 35*b^3*e^(12*d*x + 12*c) + 210*a^3*e^(10*d*x + 10*c) + 420*a^2*b*e^(10*d*x + 10*c) + 210*a*b^2*e^(10*d*x + 10*c) + 525*a^3*e^(8*d*x + 8*c) + 665*a^2*b*e^(8*d*x + 8*c) + 315*a*b^2*e^(8*d*x + 8*c) + 175*b^3*e^(8*d*x + 8*c) + 700*a^3*e^(6*d*x + 6*c) + 560*a^2*b*e^(6*d*x + 6*c) + 420*a*b^2*e^(6*d*x + 6*c) + 525*a^3*e^(4*d*x + 4*c) + 315*a^2*b*e^(4*d*x + 4*c) + 231*a*b^2*e^(4*d*x + 4*c) + 105*b^3*e^(4*d*x + 4*c) + 210*a^3*e^(2*d*x + 2*c) + 140*a^2*b*e^(2*d*x + 2*c) + 42*a*b^2*e^(2*d*x + 2*c) + 35*a^3 + 35*a^2*b + 21*a*b^2 + 5*b^3)/(d*(e^(2*d*x + 2*c) + 1)^7)","B",0
103,1,517,0,0.409862," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(64 \, a^{3} e^{c} + 48 \, a^{2} b e^{c} + 24 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)} + \frac{192 \, a^{3} e^{\left(15 \, d x + 15 \, c\right)} + 144 \, a^{2} b e^{\left(15 \, d x + 15 \, c\right)} + 72 \, a b^{2} e^{\left(15 \, d x + 15 \, c\right)} + 15 \, b^{3} e^{\left(15 \, d x + 15 \, c\right)} + 960 \, a^{3} e^{\left(13 \, d x + 13 \, c\right)} - 432 \, a^{2} b e^{\left(13 \, d x + 13 \, c\right)} - 984 \, a b^{2} e^{\left(13 \, d x + 13 \, c\right)} - 397 \, b^{3} e^{\left(13 \, d x + 13 \, c\right)} + 1728 \, a^{3} e^{\left(11 \, d x + 11 \, c\right)} - 2160 \, a^{2} b e^{\left(11 \, d x + 11 \, c\right)} - 312 \, a b^{2} e^{\left(11 \, d x + 11 \, c\right)} + 895 \, b^{3} e^{\left(11 \, d x + 11 \, c\right)} + 960 \, a^{3} e^{\left(9 \, d x + 9 \, c\right)} - 1584 \, a^{2} b e^{\left(9 \, d x + 9 \, c\right)} + 744 \, a b^{2} e^{\left(9 \, d x + 9 \, c\right)} - 1765 \, b^{3} e^{\left(9 \, d x + 9 \, c\right)} - 960 \, a^{3} e^{\left(7 \, d x + 7 \, c\right)} + 1584 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} - 744 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 1765 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} - 1728 \, a^{3} e^{\left(5 \, d x + 5 \, c\right)} + 2160 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} + 312 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 895 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 960 \, a^{3} e^{\left(3 \, d x + 3 \, c\right)} + 432 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 984 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 397 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 192 \, a^{3} e^{\left(d x + c\right)} - 144 \, a^{2} b e^{\left(d x + c\right)} - 72 \, a b^{2} e^{\left(d x + c\right)} - 15 \, b^{3} e^{\left(d x + c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{192 \, d}"," ",0,"1/192*(3*(64*a^3*e^c + 48*a^2*b*e^c + 24*a*b^2*e^c + 5*b^3*e^c)*arctan(e^(d*x + c))*e^(-c) + (192*a^3*e^(15*d*x + 15*c) + 144*a^2*b*e^(15*d*x + 15*c) + 72*a*b^2*e^(15*d*x + 15*c) + 15*b^3*e^(15*d*x + 15*c) + 960*a^3*e^(13*d*x + 13*c) - 432*a^2*b*e^(13*d*x + 13*c) - 984*a*b^2*e^(13*d*x + 13*c) - 397*b^3*e^(13*d*x + 13*c) + 1728*a^3*e^(11*d*x + 11*c) - 2160*a^2*b*e^(11*d*x + 11*c) - 312*a*b^2*e^(11*d*x + 11*c) + 895*b^3*e^(11*d*x + 11*c) + 960*a^3*e^(9*d*x + 9*c) - 1584*a^2*b*e^(9*d*x + 9*c) + 744*a*b^2*e^(9*d*x + 9*c) - 1765*b^3*e^(9*d*x + 9*c) - 960*a^3*e^(7*d*x + 7*c) + 1584*a^2*b*e^(7*d*x + 7*c) - 744*a*b^2*e^(7*d*x + 7*c) + 1765*b^3*e^(7*d*x + 7*c) - 1728*a^3*e^(5*d*x + 5*c) + 2160*a^2*b*e^(5*d*x + 5*c) + 312*a*b^2*e^(5*d*x + 5*c) - 895*b^3*e^(5*d*x + 5*c) - 960*a^3*e^(3*d*x + 3*c) + 432*a^2*b*e^(3*d*x + 3*c) + 984*a*b^2*e^(3*d*x + 3*c) + 397*b^3*e^(3*d*x + 3*c) - 192*a^3*e^(d*x + c) - 144*a^2*b*e^(d*x + c) - 72*a*b^2*e^(d*x + c) - 15*b^3*e^(d*x + c))/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
104,1,447,0,0.412140," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{4 \, {\left(315 \, a^{3} e^{\left(14 \, d x + 14 \, c\right)} + 945 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} + 945 \, a b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 315 \, b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 1995 \, a^{3} e^{\left(12 \, d x + 12 \, c\right)} + 3465 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} + 945 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} - 525 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 5355 \, a^{3} e^{\left(10 \, d x + 10 \, c\right)} + 4725 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} + 945 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1575 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 7875 \, a^{3} e^{\left(8 \, d x + 8 \, c\right)} + 3213 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 2457 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} - 945 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 6825 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + 1827 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 1323 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 945 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 3465 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 1323 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 135 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 945 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 567 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 243 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 45 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 105 \, a^{3} + 63 \, a^{2} b + 27 \, a b^{2} + 5 \, b^{3}\right)}}{315 \, d {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{9}}"," ",0,"-4/315*(315*a^3*e^(14*d*x + 14*c) + 945*a^2*b*e^(14*d*x + 14*c) + 945*a*b^2*e^(14*d*x + 14*c) + 315*b^3*e^(14*d*x + 14*c) + 1995*a^3*e^(12*d*x + 12*c) + 3465*a^2*b*e^(12*d*x + 12*c) + 945*a*b^2*e^(12*d*x + 12*c) - 525*b^3*e^(12*d*x + 12*c) + 5355*a^3*e^(10*d*x + 10*c) + 4725*a^2*b*e^(10*d*x + 10*c) + 945*a*b^2*e^(10*d*x + 10*c) + 1575*b^3*e^(10*d*x + 10*c) + 7875*a^3*e^(8*d*x + 8*c) + 3213*a^2*b*e^(8*d*x + 8*c) + 2457*a*b^2*e^(8*d*x + 8*c) - 945*b^3*e^(8*d*x + 8*c) + 6825*a^3*e^(6*d*x + 6*c) + 1827*a^2*b*e^(6*d*x + 6*c) + 1323*a*b^2*e^(6*d*x + 6*c) + 945*b^3*e^(6*d*x + 6*c) + 3465*a^3*e^(4*d*x + 4*c) + 1323*a^2*b*e^(4*d*x + 4*c) + 27*a*b^2*e^(4*d*x + 4*c) - 135*b^3*e^(4*d*x + 4*c) + 945*a^3*e^(2*d*x + 2*c) + 567*a^2*b*e^(2*d*x + 2*c) + 243*a*b^2*e^(2*d*x + 2*c) + 45*b^3*e^(2*d*x + 2*c) + 105*a^3 + 63*a^2*b + 27*a*b^2 + 5*b^3)/(d*(e^(2*d*x + 2*c) + 1)^9)","B",0
105,1,326,0,1.067887," ","integrate(cosh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{64 \, b^{3} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} + \frac{8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{{\left(18 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 60 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 90 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 24 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 16 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x\right)}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}} + \frac{a e^{\left(4 \, d x + 20 \, c\right)} + b e^{\left(4 \, d x + 20 \, c\right)} + 8 \, a e^{\left(2 \, d x + 18 \, c\right)} + 16 \, b e^{\left(2 \, d x + 18 \, c\right)}}{a^{2} e^{\left(16 \, c\right)} + 2 \, a b e^{\left(16 \, c\right)} + b^{2} e^{\left(16 \, c\right)}}}{64 \, d}"," ",0,"1/64*(64*b^3*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) + 8*(3*a^2 + 10*a*b + 15*b^2)*d*x/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (18*a^2*e^(4*d*x + 4*c) + 60*a*b*e^(4*d*x + 4*c) + 90*b^2*e^(4*d*x + 4*c) + 8*a^2*e^(2*d*x + 2*c) + 24*a*b*e^(2*d*x + 2*c) + 16*b^2*e^(2*d*x + 2*c) + a^2 + 2*a*b + b^2)*e^(-4*d*x)/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c)) + (a*e^(4*d*x + 20*c) + b*e^(4*d*x + 20*c) + 8*a*e^(2*d*x + 18*c) + 16*b*e^(2*d*x + 18*c))/(a^2*e^(16*c) + 2*a*b*e^(16*c) + b^2*e^(16*c)))/d","B",0
106,1,829,0,0.486621," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a b^{2} + \sqrt{-a b} b^{2}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} + 2 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{-a b}} + \frac{24 \, {\left(a^{2} b^{2} - 3 \, a b^{3} - {\left(3 \, a b^{2} - b^{3}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4} - 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}}} - \frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} + 21 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-3 \, d x\right)}}{a^{2} e^{\left(3 \, c\right)} + 2 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}} + \frac{a^{2} e^{\left(3 \, d x + 24 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 24 \, c\right)} + b^{2} e^{\left(3 \, d x + 24 \, c\right)} + 9 \, a^{2} e^{\left(d x + 22 \, c\right)} + 30 \, a b e^{\left(d x + 22 \, c\right)} + 21 \, b^{2} e^{\left(d x + 22 \, c\right)}}{a^{3} e^{\left(21 \, c\right)} + 3 \, a^{2} b e^{\left(21 \, c\right)} + 3 \, a b^{2} e^{\left(21 \, c\right)} + b^{3} e^{\left(21 \, c\right)}}}{24 \, d}"," ",0,"1/24*(24*(a*b^2 + sqrt(-a*b)*b^2)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) + sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 + 2*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sqrt(-a*b)) + 24*(a^2*b^2 - 3*a*b^3 - (3*a*b^2 - b^3)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c) - sqrt((a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))/(a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/((a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4 - 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))) - (9*a*e^(2*d*x + 2*c) + 21*b*e^(2*d*x + 2*c) + a + b)*e^(-3*d*x)/(a^2*e^(3*c) + 2*a*b*e^(3*c) + b^2*e^(3*c)) + (a^2*e^(3*d*x + 24*c) + 2*a*b*e^(3*d*x + 24*c) + b^2*e^(3*d*x + 24*c) + 9*a^2*e^(d*x + 22*c) + 30*a*b*e^(d*x + 22*c) + 21*b^2*e^(d*x + 22*c))/(a^3*e^(21*c) + 3*a^2*b*e^(21*c) + 3*a*b^2*e^(21*c) + b^3*e^(21*c)))/d","B",0
107,1,172,0,0.563873," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{4 \, {\left(a + 3 \, b\right)} d x}{a^{2} + 2 \, a b + b^{2}} + \frac{8 \, b^{2} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{{\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-2 \, d x\right)}}{a^{2} e^{\left(2 \, c\right)} + 2 \, a b e^{\left(2 \, c\right)} + b^{2} e^{\left(2 \, c\right)}} + \frac{e^{\left(2 \, d x + 8 \, c\right)}}{a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}}}{8 \, d}"," ",0,"1/8*(4*(a + 3*b)*d*x/(a^2 + 2*a*b + b^2) + 8*b^2*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) - (2*a*e^(2*d*x + 2*c) + 6*b*e^(2*d*x + 2*c) + a + b)*e^(-2*d*x)/(a^2*e^(2*c) + 2*a*b*e^(2*c) + b^2*e^(2*c)) + e^(2*d*x + 8*c)/(a*e^(6*c) + b*e^(6*c)))/d","B",0
108,1,1117,0,0.267593," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} - {\left(a^{2} b - a b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4} + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(2 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 2 \, a b^{5} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{8} + 5 \, a^{7} b + 9 \, a^{6} b^{2} + 5 \, a^{5} b^{3} - 5 \, a^{4} b^{4} - 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} - a b^{7} + 2 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} \sqrt{-a b}\right)} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|}} + \frac{2 \, {\left(2 \, {\left(4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + {\left(a^{3} b - 6 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{-a b}\right)} {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{5} b - 4 \, a^{4} b^{2} - 10 \, a^{3} b^{3} - 4 \, a^{2} b^{4} + a b^{5} - 4 \, {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(4 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 4 \, a b^{6} + {\left(a^{5} b - 5 \, a^{4} b^{2} - 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 5 \, a b^{5} - b^{6}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6} - 2 \, {\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)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} \right|}} - \frac{e^{\left(d x + 6 \, c\right)}}{a e^{\left(5 \, c\right)} + b e^{\left(5 \, c\right)}} + \frac{e^{\left(-d x\right)}}{a e^{c} + b e^{c}}}{2 \, d}"," ",0,"-1/2*(2*(2*(2*a^2*b^2 - (a^2*b - a*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*(a*e^(2*c) + b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^4*b + a^3*b^2 - a^2*b^3 - a*b^4 + 2*(a^3*b + 2*a^2*b^2 + a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(-a*e^(2*c) - b*e^(2*c))*e^(2*c) - (2*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 2*a*b^5 - (a^4*b - 2*a^2*b^3 + b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - b^2*e^(2*c) - sqrt((a^2*e^(2*c) - b^2*e^(2*c))^2 - (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*(a^2 + 2*a*b + b^2)))/(a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))))*e^(-4*c)/((a^8 + 5*a^7*b + 9*a^6*b^2 + 5*a^5*b^3 - 5*a^4*b^4 - 9*a^3*b^5 - 5*a^2*b^6 - a*b^7 + 2*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*sqrt(-a*b))*abs(-a*e^(2*c) - b*e^(2*c))) + 2*(2*(4*a^3*b^2 - 4*a^2*b^3 + (a^3*b - 6*a^2*b^2 + a*b^3)*sqrt(-a*b))*(a*e^(2*c) + b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^5*b - 4*a^4*b^2 - 10*a^3*b^3 - 4*a^2*b^4 + a*b^5 - 4*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*abs(-a*e^(2*c) - b*e^(2*c))*e^(2*c) - (4*a^5*b^2 - 8*a^3*b^4 + 4*a*b^6 + (a^5*b - 5*a^4*b^2 - 6*a^3*b^3 + 6*a^2*b^4 + 5*a*b^5 - b^6)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - b^2*e^(2*c) + sqrt((a^2*e^(2*c) - b^2*e^(2*c))^2 - (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*(a^2 + 2*a*b + b^2)))/(a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))))*e^(-4*c)/((a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6 - 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)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a*e^(2*c) - b*e^(2*c))) - e^(d*x + 6*c)/(a*e^(5*c) + b*e^(5*c)) + e^(-d*x)/(a*e^c + b*e^c))/d","B",0
109,1,480,0,0.182234," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{{\left(a^{3} - 10 \, a^{2} b + 5 \, a b^{2} + {\left(5 \, a^{2} - 10 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} + \sqrt{{\left(a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a e^{\left(4 \, c\right)} + b e^{\left(4 \, c\right)}\right)} {\left(a + b\right)}}}{a e^{\left(4 \, c\right)} + b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{6} - 13 \, a^{5} b - 14 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 13 \, a^{2} b^{4} - a b^{5} + 2 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 14 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sqrt{-a b}} + \frac{{\left(a^{3} - 10 \, a^{2} b + 5 \, a b^{2} - {\left(5 \, a^{2} - 10 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)} - \sqrt{{\left(a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a e^{\left(4 \, c\right)} + b e^{\left(4 \, c\right)}\right)} {\left(a + b\right)}}}{a e^{\left(4 \, c\right)} + b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{6} - 13 \, a^{5} b - 14 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 13 \, a^{2} b^{4} - a b^{5} - 2 \, {\left(3 \, a^{5} - 4 \, a^{4} b - 14 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sqrt{-a b}}}{d}"," ",0,"((a^3 - 10*a^2*b + 5*a*b^2 + (5*a^2 - 10*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a*e^(2*c) - b*e^(2*c) + sqrt((a*e^(2*c) - b*e^(2*c))^2 - (a*e^(4*c) + b*e^(4*c))*(a + b)))/(a*e^(4*c) + b*e^(4*c))))*e^(-2*c)/(a^6 - 13*a^5*b - 14*a^4*b^2 + 14*a^3*b^3 + 13*a^2*b^4 - a*b^5 + 2*(3*a^5 - 4*a^4*b - 14*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*sqrt(-a*b)) + (a^3 - 10*a^2*b + 5*a*b^2 - (5*a^2 - 10*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a*e^(2*c) - b*e^(2*c) - sqrt((a*e^(2*c) - b*e^(2*c))^2 - (a*e^(4*c) + b*e^(4*c))*(a + b)))/(a*e^(4*c) + b*e^(4*c))))*e^(-2*c)/(a^6 - 13*a^5*b - 14*a^4*b^2 + 14*a^3*b^3 + 13*a^2*b^4 - a*b^5 - 2*(3*a^5 - 4*a^4*b - 14*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*sqrt(-a*b)))/d","B",0
110,1,44,0,0.329252," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} d}"," ",0,"arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*d)","A",0
111,1,563,0,0.397405," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} a b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left(a + b\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| b \right|} - {\left(a b^{2} - b^{3}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a b + b^{2}\right)}}}{a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-a b} {\left| b \right|}} - \frac{{\left(2 \, \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} a b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left(a + b\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| b \right|} - {\left(a b^{2} - b^{3}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} {\left(a b + b^{2}\right)}}}{a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{-a b} {\left| b \right|}} - \frac{2 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b}}{d}"," ",0,"((2*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*a*b^2*abs(a*e^(2*c) + b*e^(2*c)) + sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*(a + b)*abs(a*e^(2*c) + b*e^(2*c))*abs(b) - (a*b^2 - b^3)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a*b*e^(2*c) - b^2*e^(2*c) + sqrt((a*b*e^(2*c) - b^2*e^(2*c))^2 - (a*b*e^(4*c) + b^2*e^(4*c))*(a*b + b^2)))/(a*b*e^(4*c) + b^2*e^(4*c))))*e^(-2*c)/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-a*b)*abs(b)) - (2*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*a*b^2*abs(a*e^(2*c) + b*e^(2*c)) - sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*(a + b)*abs(a*e^(2*c) + b*e^(2*c))*abs(b) - (a*b^2 - b^3)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a*b*e^(2*c) - b^2*e^(2*c) - sqrt((a*b*e^(2*c) - b^2*e^(2*c))^2 - (a*b*e^(4*c) + b^2*e^(4*c))*(a*b + b^2)))/(a*b*e^(4*c) + b^2*e^(4*c))))*e^(-2*c)/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(-a*b)*abs(b)) - 2*arctan(e^(d*x + c))/b)/d","B",0
112,1,84,0,0.341527," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{{\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} b} + \frac{2}{b {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}}}{d}"," ",0,"((a*e^(2*c) + b*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*b) + 2/(b*(e^(2*d*x + 2*c) + 1)))/d","A",0
113,1,428,0,0.401974," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{\sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(a + \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a b^{2} + b^{3}\right)}}}{a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{2} b^{2} - a b^{3} + 2 \, \sqrt{-a b} a b^{2}} + \frac{\sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(a - \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} {\left(a b^{2} + b^{3}\right)}}}{a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{2} b^{2} - a b^{3} - 2 \, \sqrt{-a b} a b^{2}} - \frac{{\left(2 \, a e^{c} + 3 \, b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)}}{b^{2}} - \frac{e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(d x + c\right)}}{b {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{d}"," ",0,"(sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*(a + sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a*b^2*e^(2*c) - b^3*e^(2*c) + sqrt((a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a*b^2*e^(4*c) + b^3*e^(4*c))*(a*b^2 + b^3)))/(a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^2*b^2 - a*b^3 + 2*sqrt(-a*b)*a*b^2) + sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*(a - sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a*b^2*e^(2*c) - b^3*e^(2*c) - sqrt((a*b^2*e^(2*c) - b^3*e^(2*c))^2 - (a*b^2*e^(4*c) + b^3*e^(4*c))*(a*b^2 + b^3)))/(a*b^2*e^(4*c) + b^3*e^(4*c))))*e^(-2*c)/(a^2*b^2 - a*b^3 - 2*sqrt(-a*b)*a*b^2) - (2*a*e^c + 3*b*e^c)*arctan(e^(d*x + c))*e^(-c)/b^2 - (e^(3*d*x + 3*c) - e^(d*x + c))/(b*(e^(2*d*x + 2*c) + 1)^2))/d","B",0
114,1,153,0,0.360971," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{2} e^{\left(2 \, c\right)} + 2 \, a b e^{\left(2 \, c\right)} + b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} b^{2}} + \frac{2 \, {\left(3 \, a e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 12 \, b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a + 5 \, b\right)}}{b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^2*e^(2*c) + 2*a*b*e^(2*c) + b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*b^2) + 2*(3*a*e^(4*d*x + 4*c) + 3*b*e^(4*d*x + 4*c) + 6*a*e^(2*d*x + 2*c) + 12*b*e^(2*d*x + 2*c) + 3*a + 5*b)/(b^2*(e^(2*d*x + 2*c) + 1)^3))/d","B",0
115,1,2074,0,0.937490," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(9 \, a e^{\left(2 \, d x + 2 \, c\right)} + 33 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-3 \, d x\right)}}{a^{3} e^{\left(3 \, c\right)} + 3 \, a^{2} b e^{\left(3 \, c\right)} + 3 \, a b^{2} e^{\left(3 \, c\right)} + b^{3} e^{\left(3 \, c\right)}} + \frac{12 \, {\left(2 \, {\left(12 \, a^{2} b^{3} + 2 \, a b^{4} + {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \sqrt{-a b}\right)} {\left(a^{4} e^{\left(2 \, c\right)} + 3 \, a^{3} b e^{\left(2 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} + a b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(6 \, a^{7} b^{2} + 19 \, a^{6} b^{3} + 15 \, a^{5} b^{4} - 10 \, a^{4} b^{5} - 20 \, a^{3} b^{6} - 9 \, a^{2} b^{7} - a b^{8} - 2 \, {\left(6 \, a^{6} b^{2} + 25 \, a^{5} b^{3} + 40 \, a^{4} b^{4} + 30 \, a^{3} b^{5} + 10 \, a^{2} b^{6} + a b^{7}\right)} \sqrt{-a b}\right)} {\left| -a^{4} e^{\left(2 \, c\right)} - 3 \, a^{3} b e^{\left(2 \, c\right)} - 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(12 \, a^{10} b^{3} + 62 \, a^{9} b^{4} + 118 \, a^{8} b^{5} + 78 \, a^{7} b^{6} - 50 \, a^{6} b^{7} - 118 \, a^{5} b^{8} - 78 \, a^{4} b^{9} - 22 \, a^{3} b^{10} - 2 \, a^{2} b^{11} + {\left(6 \, a^{10} b^{2} + 25 \, a^{9} b^{3} + 28 \, a^{8} b^{4} - 20 \, a^{7} b^{5} - 64 \, a^{6} b^{6} - 34 \, a^{5} b^{7} + 20 \, a^{4} b^{8} + 28 \, a^{3} b^{9} + 10 \, a^{2} b^{10} + a b^{11}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 4 \, a^{4} b e^{\left(4 \, c\right)} + 6 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 4 \, a^{4} b e^{\left(4 \, c\right)} + 6 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{11} + 9 \, a^{10} b + 36 \, a^{9} b^{2} + 84 \, a^{8} b^{3} + 126 \, a^{7} b^{4} + 126 \, a^{6} b^{5} + 84 \, a^{5} b^{6} + 36 \, a^{4} b^{7} + 9 \, a^{3} b^{8} + a^{2} b^{9}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{4} e^{\left(2 \, c\right)} - 3 \, a^{3} b e^{\left(2 \, c\right)} - 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} \right|}} + \frac{12 \, {\left(2 \, {\left(12 \, a^{2} b^{3} + 2 \, a b^{4} - {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \sqrt{-a b}\right)} {\left(a^{4} e^{\left(2 \, c\right)} + 3 \, a^{3} b e^{\left(2 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} + a b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(6 \, a^{7} b^{2} + 19 \, a^{6} b^{3} + 15 \, a^{5} b^{4} - 10 \, a^{4} b^{5} - 20 \, a^{3} b^{6} - 9 \, a^{2} b^{7} - a b^{8} + 2 \, {\left(6 \, a^{6} b^{2} + 25 \, a^{5} b^{3} + 40 \, a^{4} b^{4} + 30 \, a^{3} b^{5} + 10 \, a^{2} b^{6} + a b^{7}\right)} \sqrt{-a b}\right)} {\left| -a^{4} e^{\left(2 \, c\right)} - 3 \, a^{3} b e^{\left(2 \, c\right)} - 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(12 \, a^{10} b^{3} + 62 \, a^{9} b^{4} + 118 \, a^{8} b^{5} + 78 \, a^{7} b^{6} - 50 \, a^{6} b^{7} - 118 \, a^{5} b^{8} - 78 \, a^{4} b^{9} - 22 \, a^{3} b^{10} - 2 \, a^{2} b^{11} - {\left(6 \, a^{10} b^{2} + 25 \, a^{9} b^{3} + 28 \, a^{8} b^{4} - 20 \, a^{7} b^{5} - 64 \, a^{6} b^{6} - 34 \, a^{5} b^{7} + 20 \, a^{4} b^{8} + 28 \, a^{3} b^{9} + 10 \, a^{2} b^{10} + a b^{11}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 4 \, a^{4} b e^{\left(4 \, c\right)} + 6 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 4 \, a^{4} b e^{\left(4 \, c\right)} + 6 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{11} + 9 \, a^{10} b + 36 \, a^{9} b^{2} + 84 \, a^{8} b^{3} + 126 \, a^{7} b^{4} + 126 \, a^{6} b^{5} + 84 \, a^{5} b^{6} + 36 \, a^{4} b^{7} + 9 \, a^{3} b^{8} + a^{2} b^{9}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{4} e^{\left(2 \, c\right)} - 3 \, a^{3} b e^{\left(2 \, c\right)} - 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} \right|}} - \frac{a^{4} e^{\left(3 \, d x + 36 \, c\right)} + 4 \, a^{3} b e^{\left(3 \, d x + 36 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(3 \, d x + 36 \, c\right)} + 4 \, a b^{3} e^{\left(3 \, d x + 36 \, c\right)} + b^{4} e^{\left(3 \, d x + 36 \, c\right)} + 9 \, a^{4} e^{\left(d x + 34 \, c\right)} + 60 \, a^{3} b e^{\left(d x + 34 \, c\right)} + 126 \, a^{2} b^{2} e^{\left(d x + 34 \, c\right)} + 108 \, a b^{3} e^{\left(d x + 34 \, c\right)} + 33 \, b^{4} e^{\left(d x + 34 \, c\right)}}{a^{6} e^{\left(33 \, c\right)} + 6 \, a^{5} b e^{\left(33 \, c\right)} + 15 \, a^{4} b^{2} e^{\left(33 \, c\right)} + 20 \, a^{3} b^{3} e^{\left(33 \, c\right)} + 15 \, a^{2} b^{4} e^{\left(33 \, c\right)} + 6 \, a b^{5} e^{\left(33 \, c\right)} + b^{6} e^{\left(33 \, c\right)}} - \frac{24 \, {\left(b^{3} e^{\left(3 \, d x + 3 \, c\right)} - b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{24 \, d}"," ",0,"-1/24*((9*a*e^(2*d*x + 2*c) + 33*b*e^(2*d*x + 2*c) + a + b)*e^(-3*d*x)/(a^3*e^(3*c) + 3*a^2*b*e^(3*c) + 3*a*b^2*e^(3*c) + b^3*e^(3*c)) + 12*(2*(12*a^2*b^3 + 2*a*b^4 + (6*a^2*b^2 - 5*a*b^3 - b^4)*sqrt(-a*b))*(a^4*e^(2*c) + 3*a^3*b*e^(2*c) + 3*a^2*b^2*e^(2*c) + a*b^3*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (6*a^7*b^2 + 19*a^6*b^3 + 15*a^5*b^4 - 10*a^4*b^5 - 20*a^3*b^6 - 9*a^2*b^7 - a*b^8 - 2*(6*a^6*b^2 + 25*a^5*b^3 + 40*a^4*b^4 + 30*a^3*b^5 + 10*a^2*b^6 + a*b^7)*sqrt(-a*b))*abs(-a^4*e^(2*c) - 3*a^3*b*e^(2*c) - 3*a^2*b^2*e^(2*c) - a*b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (12*a^10*b^3 + 62*a^9*b^4 + 118*a^8*b^5 + 78*a^7*b^6 - 50*a^6*b^7 - 118*a^5*b^8 - 78*a^4*b^9 - 22*a^3*b^10 - 2*a^2*b^11 + (6*a^10*b^2 + 25*a^9*b^3 + 28*a^8*b^4 - 20*a^7*b^5 - 64*a^6*b^6 - 34*a^5*b^7 + 20*a^4*b^8 + 28*a^3*b^9 + 10*a^2*b^10 + a*b^11)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + 2*a^4*b*e^(2*c) - 2*a^2*b^3*e^(2*c) - a*b^4*e^(2*c) + sqrt((a^5*e^(2*c) + 2*a^4*b*e^(2*c) - 2*a^2*b^3*e^(2*c) - a*b^4*e^(2*c))^2 - (a^5*e^(4*c) + 4*a^4*b*e^(4*c) + 6*a^3*b^2*e^(4*c) + 4*a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)))/(a^5*e^(4*c) + 4*a^4*b*e^(4*c) + 6*a^3*b^2*e^(4*c) + 4*a^2*b^3*e^(4*c) + a*b^4*e^(4*c))))*e^(-4*c)/((a^11 + 9*a^10*b + 36*a^9*b^2 + 84*a^8*b^3 + 126*a^7*b^4 + 126*a^6*b^5 + 84*a^5*b^6 + 36*a^4*b^7 + 9*a^3*b^8 + a^2*b^9)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^4*e^(2*c) - 3*a^3*b*e^(2*c) - 3*a^2*b^2*e^(2*c) - a*b^3*e^(2*c))) + 12*(2*(12*a^2*b^3 + 2*a*b^4 - (6*a^2*b^2 - 5*a*b^3 - b^4)*sqrt(-a*b))*(a^4*e^(2*c) + 3*a^3*b*e^(2*c) + 3*a^2*b^2*e^(2*c) + a*b^3*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (6*a^7*b^2 + 19*a^6*b^3 + 15*a^5*b^4 - 10*a^4*b^5 - 20*a^3*b^6 - 9*a^2*b^7 - a*b^8 + 2*(6*a^6*b^2 + 25*a^5*b^3 + 40*a^4*b^4 + 30*a^3*b^5 + 10*a^2*b^6 + a*b^7)*sqrt(-a*b))*abs(-a^4*e^(2*c) - 3*a^3*b*e^(2*c) - 3*a^2*b^2*e^(2*c) - a*b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (12*a^10*b^3 + 62*a^9*b^4 + 118*a^8*b^5 + 78*a^7*b^6 - 50*a^6*b^7 - 118*a^5*b^8 - 78*a^4*b^9 - 22*a^3*b^10 - 2*a^2*b^11 - (6*a^10*b^2 + 25*a^9*b^3 + 28*a^8*b^4 - 20*a^7*b^5 - 64*a^6*b^6 - 34*a^5*b^7 + 20*a^4*b^8 + 28*a^3*b^9 + 10*a^2*b^10 + a*b^11)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + 2*a^4*b*e^(2*c) - 2*a^2*b^3*e^(2*c) - a*b^4*e^(2*c) - sqrt((a^5*e^(2*c) + 2*a^4*b*e^(2*c) - 2*a^2*b^3*e^(2*c) - a*b^4*e^(2*c))^2 - (a^5*e^(4*c) + 4*a^4*b*e^(4*c) + 6*a^3*b^2*e^(4*c) + 4*a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)))/(a^5*e^(4*c) + 4*a^4*b*e^(4*c) + 6*a^3*b^2*e^(4*c) + 4*a^2*b^3*e^(4*c) + a*b^4*e^(4*c))))*e^(-4*c)/((a^11 + 9*a^10*b + 36*a^9*b^2 + 84*a^8*b^3 + 126*a^7*b^4 + 126*a^6*b^5 + 84*a^5*b^6 + 36*a^4*b^7 + 9*a^3*b^8 + a^2*b^9)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^4*e^(2*c) - 3*a^3*b*e^(2*c) - 3*a^2*b^2*e^(2*c) - a*b^3*e^(2*c))) - (a^4*e^(3*d*x + 36*c) + 4*a^3*b*e^(3*d*x + 36*c) + 6*a^2*b^2*e^(3*d*x + 36*c) + 4*a*b^3*e^(3*d*x + 36*c) + b^4*e^(3*d*x + 36*c) + 9*a^4*e^(d*x + 34*c) + 60*a^3*b*e^(d*x + 34*c) + 126*a^2*b^2*e^(d*x + 34*c) + 108*a*b^3*e^(d*x + 34*c) + 33*b^4*e^(d*x + 34*c))/(a^6*e^(33*c) + 6*a^5*b*e^(33*c) + 15*a^4*b^2*e^(33*c) + 20*a^3*b^3*e^(33*c) + 15*a^2*b^4*e^(33*c) + 6*a*b^5*e^(33*c) + b^6*e^(33*c)) - 24*(b^3*e^(3*d*x + 3*c) - b^3*e^(d*x + c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
116,1,449,0,1.095879," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a + 5 \, b\right)} d x}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{12 \, {\left(5 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b}} + \frac{3 \, e^{\left(2 \, d x + 12 \, c\right)}}{a^{2} e^{\left(10 \, c\right)} + 2 \, a b e^{\left(10 \, c\right)} + b^{2} e^{\left(10 \, c\right)}} - \frac{2 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + 12 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 10 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 7 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 22 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 7 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 24 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 28 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 24 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2}}{{\left(a^{4} e^{\left(2 \, c\right)} + 3 \, a^{3} b e^{\left(2 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(2 \, c\right)} + a b^{3} e^{\left(2 \, c\right)}\right)} {\left(a e^{\left(2 \, d x\right)} + b e^{\left(2 \, d x\right)} + a e^{\left(6 \, d x + 4 \, c\right)} + b e^{\left(6 \, d x + 4 \, c\right)} + 2 \, a e^{\left(4 \, d x + 2 \, c\right)} - 2 \, b e^{\left(4 \, d x + 2 \, c\right)}\right)}}}{24 \, d}"," ",0,"1/24*(12*(a + 5*b)*d*x/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 12*(5*a*b^2*e^(2*c) + b^3*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)) + 3*e^(2*d*x + 12*c)/(a^2*e^(10*c) + 2*a*b*e^(10*c) + b^2*e^(10*c)) - (2*a^3*e^(6*d*x + 6*c) + 12*a^2*b*e^(6*d*x + 6*c) + 10*a*b^2*e^(6*d*x + 6*c) + 7*a^3*e^(4*d*x + 4*c) + 22*a^2*b*e^(4*d*x + 4*c) + 7*a*b^2*e^(4*d*x + 4*c) - 24*b^3*e^(4*d*x + 4*c) + 8*a^3*e^(2*d*x + 2*c) + 12*a^2*b*e^(2*d*x + 2*c) + 28*a*b^2*e^(2*d*x + 2*c) + 24*b^3*e^(2*d*x + 2*c) + 3*a^3 + 6*a^2*b + 3*a*b^2)/((a^4*e^(2*c) + 3*a^3*b*e^(2*c) + 3*a^2*b^2*e^(2*c) + a*b^3*e^(2*c))*(a*e^(2*d*x) + b*e^(2*d*x) + a*e^(6*d*x + 4*c) + b*e^(6*d*x + 4*c) + 2*a*e^(4*d*x + 2*c) - 2*b*e^(4*d*x + 2*c))))/d","B",0
117,1,1838,0,0.452760," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(8 \, a^{2} b^{2} + 2 \, a b^{3} - {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)}\right)}^{2} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(4 \, a^{6} b + 9 \, a^{5} b^{2} + 2 \, a^{4} b^{3} - 8 \, a^{3} b^{4} - 6 \, a^{2} b^{5} - a b^{6} + 2 \, {\left(4 \, a^{5} b + 13 \, a^{4} b^{2} + 15 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + a b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(8 \, a^{8} b^{2} + 26 \, a^{7} b^{3} + 22 \, a^{6} b^{4} - 12 \, a^{5} b^{5} - 28 \, a^{4} b^{6} - 14 \, a^{3} b^{7} - 2 \, a^{2} b^{8} - {\left(4 \, a^{8} b + 9 \, a^{7} b^{2} - 2 \, a^{6} b^{3} - 17 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + 6 \, a^{2} b^{7} + a b^{8}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + a^{3} b e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + a^{3} b e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 3 \, a^{3} b e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 3 \, a^{3} b e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{11} + 7 \, a^{10} b + 20 \, a^{9} b^{2} + 28 \, a^{8} b^{3} + 14 \, a^{7} b^{4} - 14 \, a^{6} b^{5} - 28 \, a^{5} b^{6} - 20 \, a^{4} b^{7} - 7 \, a^{3} b^{8} - a^{2} b^{9} + 2 \, {\left(a^{10} + 8 \, a^{9} b + 28 \, a^{8} b^{2} + 56 \, a^{7} b^{3} + 70 \, a^{6} b^{4} + 56 \, a^{5} b^{5} + 28 \, a^{4} b^{6} + 8 \, a^{3} b^{7} + a^{2} b^{8}\right)} \sqrt{-a b}\right)} {\left| a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(16 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 4 \, a b^{4} + {\left(4 \, a^{3} b - 23 \, a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(4 \, a^{7} b - 11 \, a^{6} b^{2} - 59 \, a^{5} b^{3} - 70 \, a^{4} b^{4} - 26 \, a^{3} b^{5} + a^{2} b^{6} + a b^{7} - 4 \, {\left(4 \, a^{6} b + 9 \, a^{5} b^{2} + 2 \, a^{4} b^{3} - 8 \, a^{3} b^{4} - 6 \, a^{2} b^{5} - a b^{6}\right)} \sqrt{-a b}\right)} {\left| a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(16 \, a^{9} b^{2} + 36 \, a^{8} b^{3} - 8 \, a^{7} b^{4} - 68 \, a^{6} b^{5} - 32 \, a^{5} b^{6} + 28 \, a^{4} b^{7} + 24 \, a^{3} b^{8} + 4 \, a^{2} b^{9} + {\left(4 \, a^{9} b - 11 \, a^{8} b^{2} - 63 \, a^{7} b^{3} - 59 \, a^{6} b^{4} + 33 \, a^{5} b^{5} + 71 \, a^{4} b^{6} + 27 \, a^{3} b^{7} - a^{2} b^{8} - a b^{9}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} + a^{3} b e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} + a^{3} b e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 3 \, a^{3} b e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 3 \, a^{3} b e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{10} + 6 \, a^{9} b + 14 \, a^{8} b^{2} + 14 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 14 \, a^{4} b^{6} - 6 \, a^{3} b^{7} - a^{2} b^{8} - 2 \, {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)} + a b^{2} e^{\left(2 \, c\right)} \right|}} + \frac{e^{\left(d x + 10 \, c\right)}}{a^{2} e^{\left(9 \, c\right)} + 2 \, a b e^{\left(9 \, c\right)} + b^{2} e^{\left(9 \, c\right)}} - \frac{a^{2} e^{\left(4 \, d x + 4 \, c\right)} + a b e^{\left(4 \, d x + 4 \, c\right)} - 2 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 2 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + a b}{{\left(a^{3} e^{c} + 2 \, a^{2} b e^{c} + a b^{2} e^{c}\right)} {\left(a e^{\left(5 \, d x + 4 \, c\right)} + b e^{\left(5 \, d x + 4 \, c\right)} + 2 \, a e^{\left(3 \, d x + 2 \, c\right)} - 2 \, b e^{\left(3 \, d x + 2 \, c\right)} + a e^{\left(d x\right)} + b e^{\left(d x\right)}\right)}}}{2 \, d}"," ",0,"1/2*((2*(8*a^2*b^2 + 2*a*b^3 - (4*a^2*b - 3*a*b^2 - b^3)*sqrt(-a*b))*(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))^2*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) + (4*a^6*b + 9*a^5*b^2 + 2*a^4*b^3 - 8*a^3*b^4 - 6*a^2*b^5 - a*b^6 + 2*(4*a^5*b + 13*a^4*b^2 + 15*a^3*b^3 + 7*a^2*b^4 + a*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (8*a^8*b^2 + 26*a^7*b^3 + 22*a^6*b^4 - 12*a^5*b^5 - 28*a^4*b^6 - 14*a^3*b^7 - 2*a^2*b^8 - (4*a^8*b + 9*a^7*b^2 - 2*a^6*b^3 - 17*a^5*b^4 - 8*a^4*b^5 + 7*a^3*b^6 + 6*a^2*b^7 + a*b^8)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + a^3*b*e^(2*c) - a^2*b^2*e^(2*c) - a*b^3*e^(2*c) + sqrt((a^4*e^(2*c) + a^3*b*e^(2*c) - a^2*b^2*e^(2*c) - a*b^3*e^(2*c))^2 - (a^4*e^(4*c) + 3*a^3*b*e^(4*c) + 3*a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)))/(a^4*e^(4*c) + 3*a^3*b*e^(4*c) + 3*a^2*b^2*e^(4*c) + a*b^3*e^(4*c))))*e^(-4*c)/((a^11 + 7*a^10*b + 20*a^9*b^2 + 28*a^8*b^3 + 14*a^7*b^4 - 14*a^6*b^5 - 28*a^5*b^6 - 20*a^4*b^7 - 7*a^3*b^8 - a^2*b^9 + 2*(a^10 + 8*a^9*b + 28*a^8*b^2 + 56*a^7*b^3 + 70*a^6*b^4 + 56*a^5*b^5 + 28*a^4*b^6 + 8*a^3*b^7 + a^2*b^8)*sqrt(-a*b))*abs(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))) + (2*(16*a^3*b^2 - 12*a^2*b^3 - 4*a*b^4 + (4*a^3*b - 23*a^2*b^2 - 2*a*b^3 + b^4)*sqrt(-a*b))*(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) + (4*a^7*b - 11*a^6*b^2 - 59*a^5*b^3 - 70*a^4*b^4 - 26*a^3*b^5 + a^2*b^6 + a*b^7 - 4*(4*a^6*b + 9*a^5*b^2 + 2*a^4*b^3 - 8*a^3*b^4 - 6*a^2*b^5 - a*b^6)*sqrt(-a*b))*abs(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (16*a^9*b^2 + 36*a^8*b^3 - 8*a^7*b^4 - 68*a^6*b^5 - 32*a^5*b^6 + 28*a^4*b^7 + 24*a^3*b^8 + 4*a^2*b^9 + (4*a^9*b - 11*a^8*b^2 - 63*a^7*b^3 - 59*a^6*b^4 + 33*a^5*b^5 + 71*a^4*b^6 + 27*a^3*b^7 - a^2*b^8 - a*b^9)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) + a^3*b*e^(2*c) - a^2*b^2*e^(2*c) - a*b^3*e^(2*c) - sqrt((a^4*e^(2*c) + a^3*b*e^(2*c) - a^2*b^2*e^(2*c) - a*b^3*e^(2*c))^2 - (a^4*e^(4*c) + 3*a^3*b*e^(4*c) + 3*a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)))/(a^4*e^(4*c) + 3*a^3*b*e^(4*c) + 3*a^2*b^2*e^(4*c) + a*b^3*e^(4*c))))*e^(-4*c)/((a^10 + 6*a^9*b + 14*a^8*b^2 + 14*a^7*b^3 - 14*a^5*b^5 - 14*a^4*b^6 - 6*a^3*b^7 - a^2*b^8 - 2*(a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a^3*e^(2*c) + 2*a^2*b*e^(2*c) + a*b^2*e^(2*c))) + e^(d*x + 10*c)/(a^2*e^(9*c) + 2*a*b*e^(9*c) + b^2*e^(9*c)) - (a^2*e^(4*d*x + 4*c) + a*b*e^(4*d*x + 4*c) - 2*b^2*e^(4*d*x + 4*c) + 2*a^2*e^(2*d*x + 2*c) - 2*a*b*e^(2*d*x + 2*c) + 2*b^2*e^(2*d*x + 2*c) + a^2 + a*b)/((a^3*e^c + 2*a^2*b*e^c + a*b^2*e^c)*(a*e^(5*d*x + 4*c) + b*e^(5*d*x + 4*c) + 2*a*e^(3*d*x + 2*c) - 2*b*e^(3*d*x + 2*c) + a*e^(d*x) + b*e^(d*x))))/d","B",0
118,1,1309,0,0.324045," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(4 \, a^{2} b + 2 \, a b^{2} - {\left(2 \, a^{2} - a b - b^{2}\right)} \sqrt{-a b}\right)} {\left(a^{2} e^{\left(2 \, c\right)} + a b e^{\left(2 \, c\right)}\right)}^{2} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(2 \, a^{5} + 3 \, a^{4} b - a^{3} b^{2} - 3 \, a^{2} b^{3} - a b^{4} + 2 \, {\left(2 \, a^{4} + 5 \, a^{3} b + 4 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(4 \, a^{6} b + 6 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 6 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - {\left(2 \, a^{6} + a^{5} b - 4 \, a^{4} b^{2} - 2 \, a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b e^{\left(4 \, c\right)} + a b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b e^{\left(4 \, c\right)} + a b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 5 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 9 \, a^{4} b^{5} - 5 \, a^{3} b^{6} - a^{2} b^{7} + 2 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(8 \, a^{3} b - 4 \, a^{2} b^{2} - 4 \, a b^{3} + {\left(2 \, a^{3} - 11 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{2} e^{\left(2 \, c\right)} + a b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(2 \, a^{6} - 7 \, a^{5} b - 24 \, a^{4} b^{2} - 18 \, a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5} - 4 \, {\left(2 \, a^{5} + 3 \, a^{4} b - a^{3} b^{2} - 3 \, a^{2} b^{3} - a b^{4}\right)} \sqrt{-a b}\right)} {\left| -a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(8 \, a^{7} b + 4 \, a^{6} b^{2} - 16 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 8 \, a^{3} b^{5} + 4 \, a^{2} b^{6} + {\left(2 \, a^{7} - 9 \, a^{6} b - 17 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 3 \, a^{2} b^{5} - a b^{6}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b e^{\left(4 \, c\right)} + a b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)}}}{a^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b e^{\left(4 \, c\right)} + a b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6} - 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)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} \right|}} - \frac{2 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{{\left(a^{2} + a b\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{2 \, d}"," ",0,"-1/2*((2*(4*a^2*b + 2*a*b^2 - (2*a^2 - a*b - b^2)*sqrt(-a*b))*(a^2*e^(2*c) + a*b*e^(2*c))^2*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) - (2*a^5 + 3*a^4*b - a^3*b^2 - 3*a^2*b^3 - a*b^4 + 2*(2*a^4 + 5*a^3*b + 4*a^2*b^2 + a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^2*e^(2*c) - a*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (4*a^6*b + 6*a^5*b^2 - 2*a^4*b^3 - 6*a^3*b^4 - 2*a^2*b^5 - (2*a^6 + a^5*b - 4*a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a*b^2*e^(2*c) - sqrt((a^3*e^(2*c) - a*b^2*e^(2*c))^2 - (a^3*e^(4*c) + 2*a^2*b*e^(4*c) + a*b^2*e^(4*c))*(a^3 + 2*a^2*b + a*b^2)))/(a^3*e^(4*c) + 2*a^2*b*e^(4*c) + a*b^2*e^(4*c))))*e^(-4*c)/((a^9 + 5*a^8*b + 9*a^7*b^2 + 5*a^6*b^3 - 5*a^5*b^4 - 9*a^4*b^5 - 5*a^3*b^6 - a^2*b^7 + 2*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*sqrt(-a*b))*abs(-a^2*e^(2*c) - a*b*e^(2*c))) + (2*(8*a^3*b - 4*a^2*b^2 - 4*a*b^3 + (2*a^3 - 11*a^2*b - 4*a*b^2 + b^3)*sqrt(-a*b))*(a^2*e^(2*c) + a*b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (2*a^6 - 7*a^5*b - 24*a^4*b^2 - 18*a^3*b^3 - 2*a^2*b^4 + a*b^5 - 4*(2*a^5 + 3*a^4*b - a^3*b^2 - 3*a^2*b^3 - a*b^4)*sqrt(-a*b))*abs(-a^2*e^(2*c) - a*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (8*a^7*b + 4*a^6*b^2 - 16*a^5*b^3 - 8*a^4*b^4 + 8*a^3*b^5 + 4*a^2*b^6 + (2*a^7 - 9*a^6*b - 17*a^5*b^2 + 6*a^4*b^3 + 16*a^3*b^4 + 3*a^2*b^5 - a*b^6)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a*b^2*e^(2*c) + sqrt((a^3*e^(2*c) - a*b^2*e^(2*c))^2 - (a^3*e^(4*c) + 2*a^2*b*e^(4*c) + a*b^2*e^(4*c))*(a^3 + 2*a^2*b + a*b^2)))/(a^3*e^(4*c) + 2*a^2*b*e^(4*c) + a*b^2*e^(4*c))))*e^(-4*c)/((a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6 - 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)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^2*e^(2*c) - a*b*e^(2*c))) - 2*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/((a^2 + a*b)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
119,1,138,0,0.558375," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{\arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{2 \, {\left(a e^{\left(2 \, d x + 2 \, c\right)} - b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}{{\left(a^{2} + a b\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{2 \, d}"," ",0,"1/2*(arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a) - 2*(a*e^(2*d*x + 2*c) - b*e^(2*d*x + 2*c) + a + b)/((a^2 + a*b)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
120,1,978,0,0.599002," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(4 \, a^{2} b - 4 \, a b^{2} + {\left(a^{2} - 6 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{4} - 5 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3} - 4 \, {\left(a^{3} - a b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} - {\left(4 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + {\left(a^{4} - 7 \, a^{3} b + 7 \, a^{2} b^{2} - a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} {\left(a^{2} + a b\right)}}}{a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} - 2 \, a^{7} b - 17 \, a^{6} b^{2} - 28 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6} - 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)} \sqrt{-a b}\right)} {\left| a \right|}} + \frac{{\left(2 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - {\left(a^{2} - 6 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(a^{4} - 5 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3} + 4 \, {\left(a^{3} - a b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} - {\left(4 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - {\left(a^{4} - 7 \, a^{3} b + 7 \, a^{2} b^{2} - a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} {\left(a^{2} + a b\right)}}}{a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{8} - 2 \, a^{7} b - 17 \, a^{6} b^{2} - 28 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6} + 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)} \sqrt{-a b}\right)} {\left| a \right|}} - \frac{2 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a}}{2 \, d}"," ",0,"-1/2*((2*(4*a^2*b - 4*a*b^2 + (a^2 - 6*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^4 - 5*a^3*b - 5*a^2*b^2 + a*b^3 - 4*(a^3 - a*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) - (4*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 + (a^4 - 7*a^3*b + 7*a^2*b^2 - a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - a*b*e^(2*c) + sqrt((a^2*e^(2*c) - a*b*e^(2*c))^2 - (a^2*e^(4*c) + a*b*e^(4*c))*(a^2 + a*b)))/(a^2*e^(4*c) + a*b*e^(4*c))))*e^(-2*c)/((a^8 - 2*a^7*b - 17*a^6*b^2 - 28*a^5*b^3 - 17*a^4*b^4 - 2*a^3*b^5 + a^2*b^6 - 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)*sqrt(-a*b))*abs(a)) + (2*(4*a^2*b - 4*a*b^2 - (a^2 - 6*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (a^4 - 5*a^3*b - 5*a^2*b^2 + a*b^3 + 4*(a^3 - a*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) - (4*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 - (a^4 - 7*a^3*b + 7*a^2*b^2 - a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*e^(2*c) - a*b*e^(2*c) - sqrt((a^2*e^(2*c) - a*b*e^(2*c))^2 - (a^2*e^(4*c) + a*b*e^(4*c))*(a^2 + a*b)))/(a^2*e^(4*c) + a*b*e^(4*c))))*e^(-2*c)/((a^8 - 2*a^7*b - 17*a^6*b^2 - 28*a^5*b^3 - 17*a^4*b^4 - 2*a^3*b^5 + a^2*b^6 + 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)*sqrt(-a*b))*abs(a)) - 2*(e^(3*d*x + 3*c) - e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a))/d","B",0
121,1,156,0,0.554234," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a b} + \frac{2 \, {\left(a e^{\left(2 \, d x + 2 \, c\right)} - b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a b}}{2 \, d}"," ",0,"-1/2*((a*e^(2*c) - b*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a*b) + 2*(a*e^(2*d*x + 2*c) - b*e^(2*d*x + 2*c) + a + b)/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a*b))/d","B",0
122,1,1035,0,0.674800," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(4 \, a^{2} b - 2 \, a b^{2} - {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(2 \, a^{4} - a^{3} b - 2 \, a^{2} b^{2} + a b^{3} + 2 \, {\left(2 \, a^{3} + a^{2} b - a b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} - {\left(4 \, a^{4} b - 6 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{2} b^{2} + a b^{3}\right)}}}{a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{3} b^{5} - a^{2} b^{6} + 2 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} \sqrt{-a b}\right)} {\left| a \right|}} + \frac{{\left(2 \, {\left(8 \, a^{3} b - 12 \, a^{2} b^{2} + 4 \, a b^{3} + {\left(2 \, a^{3} - 13 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \sqrt{-a b}\right)} a^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(2 \, a^{5} - 11 \, a^{4} b - 5 \, a^{3} b^{2} + 7 \, a^{2} b^{3} - a b^{4} - 4 \, {\left(2 \, a^{4} - a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} - {\left(8 \, a^{5} b - 20 \, a^{4} b^{2} + 16 \, a^{3} b^{3} - 4 \, a^{2} b^{4} + {\left(2 \, a^{5} - 15 \, a^{4} b + 21 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{2} b^{2} + a b^{3}\right)}}}{a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} b^{2} + a^{4} b^{3} - a^{3} b^{4} - a^{2} b^{5} - 2 \, {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a \right|}} + \frac{4 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b^{2}} + \frac{2 \, {\left(a e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(3 \, d x + 3 \, c\right)} - a e^{\left(d x + c\right)} - b e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a b}}{2 \, d}"," ",0,"1/2*((2*(4*a^2*b - 2*a*b^2 - (2*a^2 - 3*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (2*a^4 - a^3*b - 2*a^2*b^2 + a*b^3 + 2*(2*a^3 + a^2*b - a*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) - (4*a^4*b - 6*a^3*b^2 + 2*a^2*b^3 - (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*b^2*e^(2*c) - a*b^3*e^(2*c) - sqrt((a^2*b^2*e^(2*c) - a*b^3*e^(2*c))^2 - (a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*(a^2*b^2 + a*b^3)))/(a^2*b^2*e^(4*c) + a*b^3*e^(4*c))))*e^(-2*c)/((a^6*b^2 + 2*a^5*b^3 - 2*a^3*b^5 - a^2*b^6 + 2*(a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*sqrt(-a*b))*abs(a)) + (2*(8*a^3*b - 12*a^2*b^2 + 4*a*b^3 + (2*a^3 - 13*a^2*b + 8*a*b^2 - b^3)*sqrt(-a*b))*a^2*abs(a*e^(2*c) + b*e^(2*c)) - (2*a^5 - 11*a^4*b - 5*a^3*b^2 + 7*a^2*b^3 - a*b^4 - 4*(2*a^4 - a^3*b - 2*a^2*b^2 + a*b^3)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*abs(a) - (8*a^5*b - 20*a^4*b^2 + 16*a^3*b^3 - 4*a^2*b^4 + (2*a^5 - 15*a^4*b + 21*a^3*b^2 - 9*a^2*b^3 + a*b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*b^2*e^(2*c) - a*b^3*e^(2*c) + sqrt((a^2*b^2*e^(2*c) - a*b^3*e^(2*c))^2 - (a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*(a^2*b^2 + a*b^3)))/(a^2*b^2*e^(4*c) + a*b^3*e^(4*c))))*e^(-2*c)/((a^5*b^2 + a^4*b^3 - a^3*b^4 - a^2*b^5 - 2*(a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a)) + 4*arctan(e^(d*x + c))/b^2 + 2*(a*e^(3*d*x + 3*c) + b*e^(3*d*x + 3*c) - a*e^(d*x + c) - b*e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a*b))/d","B",0
123,1,248,0,0.596192," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{2} e^{\left(2 \, c\right)} + 2 \, a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a b^{2}} + \frac{2 \, {\left(3 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a b e^{\left(4 \, d x + 4 \, c\right)} - b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{2} + 4 \, a b + b^{2}\right)}}{{\left(a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a e^{\left(4 \, d x + 4 \, c\right)} - b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a e^{\left(2 \, d x + 2 \, c\right)} - b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a b^{2}}}{2 \, d}"," ",0,"-1/2*((3*a^2*e^(2*c) + 2*a*b*e^(2*c) - b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a*b^2) + 2*(3*a^2*e^(4*d*x + 4*c) + 2*a*b*e^(4*d*x + 4*c) - b^2*e^(4*d*x + 4*c) + 6*a^2*e^(2*d*x + 2*c) - 2*a*b*e^(2*d*x + 2*c) + 3*a^2 + 4*a*b + b^2)/((a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + 3*a*e^(4*d*x + 4*c) - b*e^(4*d*x + 4*c) + 3*a*e^(2*d*x + 2*c) - b*e^(2*d*x + 2*c) + a + b)*a*b^2))/d","B",0
124,1,870,0,0.686890," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(4 \, a e^{c} + 5 \, b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)}}{b^{3}} - \frac{{\left(2 \, \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(4 \, a - b\right)} a^{2} b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(4 \, a^{2} + 3 \, a b - b^{2}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} {\left| b \right|} - {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{2} b^{3} + a b^{4}\right)}}}{a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} \sqrt{-a b} {\left| a \right|} {\left| b \right|}} + \frac{{\left(2 \, \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left(4 \, a - b\right)} a^{2} b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(4 \, a^{2} + 3 \, a b - b^{2}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| a \right|} {\left| b \right|} - {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{2} b^{3} + a b^{4}\right)}}}{a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5}\right)} \sqrt{-a b} {\left| a \right|} {\left| b \right|}} + \frac{2 \, {\left(a^{2} e^{\left(3 \, d x + 3 \, c\right)} + 2 \, a b e^{\left(3 \, d x + 3 \, c\right)} + b^{2} e^{\left(3 \, d x + 3 \, c\right)} - a^{2} e^{\left(d x + c\right)} - 2 \, a b e^{\left(d x + c\right)} - b^{2} e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} a b^{2}} + \frac{2 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(d x + c\right)}\right)}}{b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(4*a*e^c + 5*b*e^c)*arctan(e^(d*x + c))*e^(-c)/b^3 - (2*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*(4*a - b)*a^2*b^2*abs(a*e^(2*c) + b*e^(2*c)) + (4*a^2 + 3*a*b - b^2)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*abs(a*e^(2*c) + b*e^(2*c))*abs(a)*abs(b) - (4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*b^3*e^(2*c) - a*b^4*e^(2*c) + sqrt((a^2*b^3*e^(2*c) - a*b^4*e^(2*c))^2 - (a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*(a^2*b^3 + a*b^4)))/(a^2*b^3*e^(4*c) + a*b^4*e^(4*c))))*e^(-2*c)/((a^3*b^3 + 2*a^2*b^4 + a*b^5)*sqrt(-a*b)*abs(a)*abs(b)) + (2*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*(4*a - b)*a^2*b^2*abs(a*e^(2*c) + b*e^(2*c)) - (4*a^2 + 3*a*b - b^2)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*abs(a*e^(2*c) + b*e^(2*c))*abs(a)*abs(b) - (4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^2*b^3*e^(2*c) - a*b^4*e^(2*c) - sqrt((a^2*b^3*e^(2*c) - a*b^4*e^(2*c))^2 - (a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*(a^2*b^3 + a*b^4)))/(a^2*b^3*e^(4*c) + a*b^4*e^(4*c))))*e^(-2*c)/((a^3*b^3 + 2*a^2*b^4 + a*b^5)*sqrt(-a*b)*abs(a)*abs(b)) + 2*(a^2*e^(3*d*x + 3*c) + 2*a*b*e^(3*d*x + 3*c) + b^2*e^(3*d*x + 3*c) - a^2*e^(d*x + c) - 2*a*b*e^(d*x + c) - b^2*e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*a*b^2) + 2*(e^(3*d*x + 3*c) - e^(d*x + c))/(b^2*(e^(2*d*x + 2*c) + 1)^2))/d","B",0
125,1,595,0,1.913331," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(a + 7 \, b\right)} d x}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{{\left(35 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 14 \, a b^{3} e^{\left(2 \, c\right)} + 3 \, b^{4} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b}} - \frac{{\left(2 \, a e^{\left(2 \, d x + 2 \, c\right)} + 14 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} e^{\left(-2 \, d x\right)}}{a^{4} e^{\left(2 \, c\right)} + 4 \, a^{3} b e^{\left(2 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 4 \, a b^{3} e^{\left(2 \, c\right)} + b^{4} e^{\left(2 \, c\right)}} + \frac{e^{\left(2 \, d x + 16 \, c\right)}}{a^{3} e^{\left(14 \, c\right)} + 3 \, a^{2} b e^{\left(14 \, c\right)} + 3 \, a b^{2} e^{\left(14 \, c\right)} + b^{3} e^{\left(14 \, c\right)}} - \frac{2 \, {\left(13 \, a^{3} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - a^{2} b^{3} e^{\left(6 \, d x + 6 \, c\right)} - 17 \, a b^{4} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, b^{5} e^{\left(6 \, d x + 6 \, c\right)} + 39 \, a^{3} b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 17 \, a^{2} b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 33 \, a b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{5} e^{\left(4 \, d x + 4 \, c\right)} + 39 \, a^{3} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{2} b^{3} e^{\left(2 \, d x + 2 \, c\right)} - 35 \, a b^{4} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, b^{5} e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{3} b^{2} + 29 \, a^{2} b^{3} + 19 \, a b^{4} + 3 \, b^{5}\right)}}{{\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"1/8*(4*(a + 7*b)*d*x/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (35*a^2*b^2*e^(2*c) + 14*a*b^3*e^(2*c) + 3*b^4*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)) - (2*a*e^(2*d*x + 2*c) + 14*b*e^(2*d*x + 2*c) + a + b)*e^(-2*d*x)/(a^4*e^(2*c) + 4*a^3*b*e^(2*c) + 6*a^2*b^2*e^(2*c) + 4*a*b^3*e^(2*c) + b^4*e^(2*c)) + e^(2*d*x + 16*c)/(a^3*e^(14*c) + 3*a^2*b*e^(14*c) + 3*a*b^2*e^(14*c) + b^3*e^(14*c)) - 2*(13*a^3*b^2*e^(6*d*x + 6*c) - a^2*b^3*e^(6*d*x + 6*c) - 17*a*b^4*e^(6*d*x + 6*c) - 3*b^5*e^(6*d*x + 6*c) + 39*a^3*b^2*e^(4*d*x + 4*c) - 17*a^2*b^3*e^(4*d*x + 4*c) + 33*a*b^4*e^(4*d*x + 4*c) + 9*b^5*e^(4*d*x + 4*c) + 39*a^3*b^2*e^(2*d*x + 2*c) + 13*a^2*b^3*e^(2*d*x + 2*c) - 35*a*b^4*e^(2*d*x + 2*c) - 9*b^5*e^(2*d*x + 2*c) + 13*a^3*b^2 + 29*a^2*b^3 + 19*a*b^4 + 3*b^5)/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
126,1,2145,0,0.684265," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} + a^{2} b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left(16 \, a^{3} b^{2} + 8 \, a^{2} b^{3} + 2 \, a b^{4} + {\left(8 \, a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(8 \, a^{9} b + 28 \, a^{8} b^{2} + 29 \, a^{7} b^{3} - 5 \, a^{6} b^{4} - 30 \, a^{5} b^{5} - 22 \, a^{4} b^{6} - 7 \, a^{3} b^{7} - a^{2} b^{8} - 2 \, {\left(8 \, a^{8} b + 36 \, a^{7} b^{2} + 65 \, a^{6} b^{3} + 60 \, a^{5} b^{4} + 30 \, a^{4} b^{5} + 8 \, a^{3} b^{6} + a^{2} b^{7}\right)} \sqrt{-a b}\right)} {\left| -a^{5} e^{\left(2 \, c\right)} - 3 \, a^{4} b e^{\left(2 \, c\right)} - 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(16 \, a^{13} b^{2} + 88 \, a^{12} b^{3} + 186 \, a^{11} b^{4} + 162 \, a^{10} b^{5} - 22 \, a^{9} b^{6} - 174 \, a^{8} b^{7} - 162 \, a^{7} b^{8} - 74 \, a^{6} b^{9} - 18 \, a^{5} b^{10} - 2 \, a^{4} b^{11} + {\left(8 \, a^{13} b + 36 \, a^{12} b^{2} + 49 \, a^{11} b^{3} - 12 \, a^{10} b^{4} - 92 \, a^{9} b^{5} - 76 \, a^{8} b^{6} + 6 \, a^{7} b^{7} + 44 \, a^{6} b^{8} + 28 \, a^{5} b^{9} + 8 \, a^{4} b^{10} + a^{3} b^{11}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} + 2 \, a^{5} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} + 2 \, a^{5} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 4 \, a^{5} b e^{\left(4 \, c\right)} + 6 \, a^{4} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 4 \, a^{5} b e^{\left(4 \, c\right)} + 6 \, a^{4} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{13} + 9 \, a^{12} b + 36 \, a^{11} b^{2} + 84 \, a^{10} b^{3} + 126 \, a^{9} b^{4} + 126 \, a^{8} b^{5} + 84 \, a^{7} b^{6} + 36 \, a^{6} b^{7} + 9 \, a^{5} b^{8} + a^{4} b^{9}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{5} e^{\left(2 \, c\right)} - 3 \, a^{4} b e^{\left(2 \, c\right)} - 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} \right|}} + \frac{3 \, {\left(2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} + a^{2} b^{3} e^{\left(2 \, c\right)}\right)}^{2} {\left(16 \, a^{3} b^{2} + 8 \, a^{2} b^{3} + 2 \, a b^{4} - {\left(8 \, a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(8 \, a^{9} b + 28 \, a^{8} b^{2} + 29 \, a^{7} b^{3} - 5 \, a^{6} b^{4} - 30 \, a^{5} b^{5} - 22 \, a^{4} b^{6} - 7 \, a^{3} b^{7} - a^{2} b^{8} + 2 \, {\left(8 \, a^{8} b + 36 \, a^{7} b^{2} + 65 \, a^{6} b^{3} + 60 \, a^{5} b^{4} + 30 \, a^{4} b^{5} + 8 \, a^{3} b^{6} + a^{2} b^{7}\right)} \sqrt{-a b}\right)} {\left| -a^{5} e^{\left(2 \, c\right)} - 3 \, a^{4} b e^{\left(2 \, c\right)} - 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(16 \, a^{13} b^{2} + 88 \, a^{12} b^{3} + 186 \, a^{11} b^{4} + 162 \, a^{10} b^{5} - 22 \, a^{9} b^{6} - 174 \, a^{8} b^{7} - 162 \, a^{7} b^{8} - 74 \, a^{6} b^{9} - 18 \, a^{5} b^{10} - 2 \, a^{4} b^{11} - {\left(8 \, a^{13} b + 36 \, a^{12} b^{2} + 49 \, a^{11} b^{3} - 12 \, a^{10} b^{4} - 92 \, a^{9} b^{5} - 76 \, a^{8} b^{6} + 6 \, a^{7} b^{7} + 44 \, a^{6} b^{8} + 28 \, a^{5} b^{9} + 8 \, a^{4} b^{10} + a^{3} b^{11}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{6} e^{\left(2 \, c\right)} + 2 \, a^{5} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{6} e^{\left(2 \, c\right)} + 2 \, a^{5} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{6} e^{\left(4 \, c\right)} + 4 \, a^{5} b e^{\left(4 \, c\right)} + 6 \, a^{4} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)}}}{a^{6} e^{\left(4 \, c\right)} + 4 \, a^{5} b e^{\left(4 \, c\right)} + 6 \, a^{4} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{13} + 9 \, a^{12} b + 36 \, a^{11} b^{2} + 84 \, a^{10} b^{3} + 126 \, a^{9} b^{4} + 126 \, a^{8} b^{5} + 84 \, a^{7} b^{6} + 36 \, a^{6} b^{7} + 9 \, a^{5} b^{8} + a^{4} b^{9}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{5} e^{\left(2 \, c\right)} - 3 \, a^{4} b e^{\left(2 \, c\right)} - 3 \, a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} \right|}} - \frac{4 \, e^{\left(d x + 14 \, c\right)}}{a^{3} e^{\left(13 \, c\right)} + 3 \, a^{2} b e^{\left(13 \, c\right)} + 3 \, a b^{2} e^{\left(13 \, c\right)} + b^{3} e^{\left(13 \, c\right)}} + \frac{4 \, e^{\left(-d x\right)}}{a^{3} e^{c} + 3 \, a^{2} b e^{c} + 3 \, a b^{2} e^{c} + b^{3} e^{c}} - \frac{2 \, {\left(12 \, a^{2} b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 15 \, a b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 3 \, b^{4} e^{\left(7 \, d x + 7 \, c\right)} + 12 \, a^{2} b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 25 \, a b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 9 \, b^{4} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, a^{2} b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 25 \, a b^{3} e^{\left(3 \, d x + 3 \, c\right)} + 9 \, b^{4} e^{\left(3 \, d x + 3 \, c\right)} - 12 \, a^{2} b^{2} e^{\left(d x + c\right)} - 15 \, a b^{3} e^{\left(d x + c\right)} - 3 \, b^{4} e^{\left(d x + c\right)}\right)}}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(3*(2*(a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 3*a^3*b^2*e^(2*c) + a^2*b^3*e^(2*c))^2*(16*a^3*b^2 + 8*a^2*b^3 + 2*a*b^4 + (8*a^3*b - 4*a^2*b^2 - 3*a*b^3 - b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)) - (8*a^9*b + 28*a^8*b^2 + 29*a^7*b^3 - 5*a^6*b^4 - 30*a^5*b^5 - 22*a^4*b^6 - 7*a^3*b^7 - a^2*b^8 - 2*(8*a^8*b + 36*a^7*b^2 + 65*a^6*b^3 + 60*a^5*b^4 + 30*a^4*b^5 + 8*a^3*b^6 + a^2*b^7)*sqrt(-a*b))*abs(-a^5*e^(2*c) - 3*a^4*b*e^(2*c) - 3*a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (16*a^13*b^2 + 88*a^12*b^3 + 186*a^11*b^4 + 162*a^10*b^5 - 22*a^9*b^6 - 174*a^8*b^7 - 162*a^7*b^8 - 74*a^6*b^9 - 18*a^5*b^10 - 2*a^4*b^11 + (8*a^13*b + 36*a^12*b^2 + 49*a^11*b^3 - 12*a^10*b^4 - 92*a^9*b^5 - 76*a^8*b^6 + 6*a^7*b^7 + 44*a^6*b^8 + 28*a^5*b^9 + 8*a^4*b^10 + a^3*b^11)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) + 2*a^5*b*e^(2*c) - 2*a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c) + sqrt((a^6*e^(2*c) + 2*a^5*b*e^(2*c) - 2*a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))^2 - (a^6*e^(4*c) + 4*a^5*b*e^(4*c) + 6*a^4*b^2*e^(4*c) + 4*a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)))/(a^6*e^(4*c) + 4*a^5*b*e^(4*c) + 6*a^4*b^2*e^(4*c) + 4*a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))))*e^(-4*c)/((a^13 + 9*a^12*b + 36*a^11*b^2 + 84*a^10*b^3 + 126*a^9*b^4 + 126*a^8*b^5 + 84*a^7*b^6 + 36*a^6*b^7 + 9*a^5*b^8 + a^4*b^9)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^5*e^(2*c) - 3*a^4*b*e^(2*c) - 3*a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))) + 3*(2*(a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 3*a^3*b^2*e^(2*c) + a^2*b^3*e^(2*c))^2*(16*a^3*b^2 + 8*a^2*b^3 + 2*a*b^4 - (8*a^3*b - 4*a^2*b^2 - 3*a*b^3 - b^4)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c)) - (8*a^9*b + 28*a^8*b^2 + 29*a^7*b^3 - 5*a^6*b^4 - 30*a^5*b^5 - 22*a^4*b^6 - 7*a^3*b^7 - a^2*b^8 + 2*(8*a^8*b + 36*a^7*b^2 + 65*a^6*b^3 + 60*a^5*b^4 + 30*a^4*b^5 + 8*a^3*b^6 + a^2*b^7)*sqrt(-a*b))*abs(-a^5*e^(2*c) - 3*a^4*b*e^(2*c) - 3*a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (16*a^13*b^2 + 88*a^12*b^3 + 186*a^11*b^4 + 162*a^10*b^5 - 22*a^9*b^6 - 174*a^8*b^7 - 162*a^7*b^8 - 74*a^6*b^9 - 18*a^5*b^10 - 2*a^4*b^11 - (8*a^13*b + 36*a^12*b^2 + 49*a^11*b^3 - 12*a^10*b^4 - 92*a^9*b^5 - 76*a^8*b^6 + 6*a^7*b^7 + 44*a^6*b^8 + 28*a^5*b^9 + 8*a^4*b^10 + a^3*b^11)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^6*e^(2*c) + 2*a^5*b*e^(2*c) - 2*a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c) - sqrt((a^6*e^(2*c) + 2*a^5*b*e^(2*c) - 2*a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))^2 - (a^6*e^(4*c) + 4*a^5*b*e^(4*c) + 6*a^4*b^2*e^(4*c) + 4*a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)))/(a^6*e^(4*c) + 4*a^5*b*e^(4*c) + 6*a^4*b^2*e^(4*c) + 4*a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))))*e^(-4*c)/((a^13 + 9*a^12*b + 36*a^11*b^2 + 84*a^10*b^3 + 126*a^9*b^4 + 126*a^8*b^5 + 84*a^7*b^6 + 36*a^6*b^7 + 9*a^5*b^8 + a^4*b^9)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^5*e^(2*c) - 3*a^4*b*e^(2*c) - 3*a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))) - 4*e^(d*x + 14*c)/(a^3*e^(13*c) + 3*a^2*b*e^(13*c) + 3*a*b^2*e^(13*c) + b^3*e^(13*c)) + 4*e^(-d*x)/(a^3*e^c + 3*a^2*b*e^c + 3*a*b^2*e^c + b^3*e^c) - 2*(12*a^2*b^2*e^(7*d*x + 7*c) + 15*a*b^3*e^(7*d*x + 7*c) + 3*b^4*e^(7*d*x + 7*c) + 12*a^2*b^2*e^(5*d*x + 5*c) - 25*a*b^3*e^(5*d*x + 5*c) - 9*b^4*e^(5*d*x + 5*c) - 12*a^2*b^2*e^(3*d*x + 3*c) + 25*a*b^3*e^(3*d*x + 3*c) + 9*b^4*e^(3*d*x + 3*c) - 12*a^2*b^2*e^(d*x + c) - 15*a*b^3*e^(d*x + c) - 3*b^4*e^(d*x + c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
127,1,1137,0,0.445177," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{{\left(8 \, a^{5} - 72 \, a^{4} b - 37 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 15 \, a b^{4} + {\left(40 \, a^{4} - 40 \, a^{3} b - 57 \, a^{2} b^{2} - 22 \, a b^{3} + 3 \, b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 3 \, a^{4} b e^{\left(4 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(4 \, c\right)} + a^{2} b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 3 \, a^{4} b e^{\left(4 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(4 \, c\right)} + a^{2} b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{10} - 11 \, a^{9} b - 39 \, a^{8} b^{2} - 27 \, a^{7} b^{3} + 27 \, a^{6} b^{4} + 39 \, a^{5} b^{5} + 11 \, a^{4} b^{6} - a^{3} b^{7} + 2 \, {\left(3 \, a^{9} + 2 \, a^{8} b - 19 \, a^{7} b^{2} - 36 \, a^{6} b^{3} - 19 \, a^{5} b^{4} + 2 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} \sqrt{-a b}} + \frac{{\left(8 \, a^{5} - 72 \, a^{4} b - 37 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 15 \, a b^{4} - {\left(40 \, a^{4} - 40 \, a^{3} b - 57 \, a^{2} b^{2} - 22 \, a b^{3} + 3 \, b^{4}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{5} e^{\left(4 \, c\right)} + 3 \, a^{4} b e^{\left(4 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(4 \, c\right)} + a^{2} b^{3} e^{\left(4 \, c\right)}\right)} {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)}}}{a^{5} e^{\left(4 \, c\right)} + 3 \, a^{4} b e^{\left(4 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(4 \, c\right)} + a^{2} b^{3} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{10} - 11 \, a^{9} b - 39 \, a^{8} b^{2} - 27 \, a^{7} b^{3} + 27 \, a^{6} b^{4} + 39 \, a^{5} b^{5} + 11 \, a^{4} b^{6} - a^{3} b^{7} - 2 \, {\left(3 \, a^{9} + 2 \, a^{8} b - 19 \, a^{7} b^{2} - 36 \, a^{6} b^{3} - 19 \, a^{5} b^{4} + 2 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} \sqrt{-a b}} + \frac{2 \, {\left(8 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} + 11 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 3 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 8 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 13 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 9 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 8 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 13 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} + 9 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 8 \, a^{2} b e^{\left(d x + c\right)} - 11 \, a b^{2} e^{\left(d x + c\right)} - 3 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"1/8*((8*a^5 - 72*a^4*b - 37*a^3*b^2 + 10*a^2*b^3 + 15*a*b^4 + (40*a^4 - 40*a^3*b - 57*a^2*b^2 - 22*a*b^3 + 3*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + a^4*b*e^(2*c) - a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c) + sqrt((a^5*e^(2*c) + a^4*b*e^(2*c) - a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))^2 - (a^5*e^(4*c) + 3*a^4*b*e^(4*c) + 3*a^3*b^2*e^(4*c) + a^2*b^3*e^(4*c))*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)))/(a^5*e^(4*c) + 3*a^4*b*e^(4*c) + 3*a^3*b^2*e^(4*c) + a^2*b^3*e^(4*c))))*e^(-2*c)/(a^10 - 11*a^9*b - 39*a^8*b^2 - 27*a^7*b^3 + 27*a^6*b^4 + 39*a^5*b^5 + 11*a^4*b^6 - a^3*b^7 + 2*(3*a^9 + 2*a^8*b - 19*a^7*b^2 - 36*a^6*b^3 - 19*a^5*b^4 + 2*a^4*b^5 + 3*a^3*b^6)*sqrt(-a*b)) + (8*a^5 - 72*a^4*b - 37*a^3*b^2 + 10*a^2*b^3 + 15*a*b^4 - (40*a^4 - 40*a^3*b - 57*a^2*b^2 - 22*a*b^3 + 3*b^4)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^5*e^(2*c) + a^4*b*e^(2*c) - a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c) - sqrt((a^5*e^(2*c) + a^4*b*e^(2*c) - a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))^2 - (a^5*e^(4*c) + 3*a^4*b*e^(4*c) + 3*a^3*b^2*e^(4*c) + a^2*b^3*e^(4*c))*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)))/(a^5*e^(4*c) + 3*a^4*b*e^(4*c) + 3*a^3*b^2*e^(4*c) + a^2*b^3*e^(4*c))))*e^(-2*c)/(a^10 - 11*a^9*b - 39*a^8*b^2 - 27*a^7*b^3 + 27*a^6*b^4 + 39*a^5*b^5 + 11*a^4*b^6 - a^3*b^7 - 2*(3*a^9 + 2*a^8*b - 19*a^7*b^2 - 36*a^6*b^3 - 19*a^5*b^4 + 2*a^4*b^5 + 3*a^3*b^6)*sqrt(-a*b)) + 2*(8*a^2*b*e^(7*d*x + 7*c) + 11*a*b^2*e^(7*d*x + 7*c) + 3*b^3*e^(7*d*x + 7*c) + 8*a^2*b*e^(5*d*x + 5*c) - 13*a*b^2*e^(5*d*x + 5*c) - 9*b^3*e^(5*d*x + 5*c) - 8*a^2*b*e^(3*d*x + 3*c) + 13*a*b^2*e^(3*d*x + 3*c) + 9*b^3*e^(3*d*x + 3*c) - 8*a^2*b*e^(d*x + c) - 11*a*b^2*e^(d*x + c) - 3*b^3*e^(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
128,1,320,0,0.750011," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{3 \, \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} a^{2}} - \frac{2 \, {\left(5 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} - a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 9 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 15 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 9 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 15 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 11 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 5 \, a^{3} + 13 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3}\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"1/8*(3*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2) - 2*(5*a^3*e^(6*d*x + 6*c) - a^2*b*e^(6*d*x + 6*c) - 9*a*b^2*e^(6*d*x + 6*c) - 3*b^3*e^(6*d*x + 6*c) + 15*a^3*e^(4*d*x + 4*c) - a^2*b*e^(4*d*x + 4*c) + 9*a*b^2*e^(4*d*x + 4*c) + 9*b^3*e^(4*d*x + 4*c) + 15*a^3*e^(2*d*x + 2*c) + 13*a^2*b*e^(2*d*x + 2*c) - 11*a*b^2*e^(2*d*x + 2*c) - 9*b^3*e^(2*d*x + 2*c) + 5*a^3 + 13*a^2*b + 11*a*b^2 + 3*b^3)/((a^4 + 2*a^3*b + a^2*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
129,1,1495,0,0.990542," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)}\right)}^{2} {\left(8 \, a^{2} b + 6 \, a b^{2} - {\left(4 \, a^{2} - a b - 3 \, b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(4 \, a^{6} + 7 \, a^{5} b - a^{4} b^{2} - 7 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 2 \, {\left(4 \, a^{5} + 11 \, a^{4} b + 10 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(8 \, a^{8} b + 14 \, a^{7} b^{2} - 2 \, a^{6} b^{3} - 14 \, a^{5} b^{4} - 6 \, a^{4} b^{5} - {\left(4 \, a^{8} + 3 \, a^{7} b - 8 \, a^{6} b^{2} - 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{11} + 5 \, a^{10} b + 9 \, a^{9} b^{2} + 5 \, a^{8} b^{3} - 5 \, a^{7} b^{4} - 9 \, a^{6} b^{5} - 5 \, a^{5} b^{6} - a^{4} b^{7} + 2 \, {\left(a^{10} + 6 \, a^{9} b + 15 \, a^{8} b^{2} + 20 \, a^{7} b^{3} + 15 \, a^{6} b^{4} + 6 \, a^{5} b^{5} + a^{4} b^{6}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|}} + \frac{{\left(2 \, {\left(16 \, a^{3} b - 4 \, a^{2} b^{2} - 12 \, a b^{3} + {\left(4 \, a^{3} - 21 \, a^{2} b - 14 \, a b^{2} + 3 \, b^{3}\right)} \sqrt{-a b}\right)} {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)}\right)}^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(4 \, a^{7} - 13 \, a^{6} b - 52 \, a^{5} b^{2} - 46 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5} - 4 \, {\left(4 \, a^{6} + 7 \, a^{5} b - a^{4} b^{2} - 7 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sqrt{-a b}\right)} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(2 \, c\right)} - {\left(16 \, a^{9} b + 12 \, a^{8} b^{2} - 32 \, a^{7} b^{3} - 24 \, a^{6} b^{4} + 16 \, a^{5} b^{5} + 12 \, a^{4} b^{6} + {\left(4 \, a^{9} - 17 \, a^{8} b - 39 \, a^{7} b^{2} + 6 \, a^{6} b^{3} + 38 \, a^{5} b^{4} + 11 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} \sqrt{-a b}\right)} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} e^{\left(4 \, c\right)}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)}}}{a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}}}}\right) e^{\left(-4 \, c\right)}}{{\left(a^{10} + 4 \, a^{9} b + 5 \, a^{8} b^{2} - 5 \, a^{6} b^{4} - 4 \, a^{5} b^{5} - a^{4} b^{6} - 2 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| -a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} \right|}} - \frac{2 \, {\left(4 \, a^{2} e^{\left(7 \, d x + 7 \, c\right)} + 7 \, a b e^{\left(7 \, d x + 7 \, c\right)} + 3 \, b^{2} e^{\left(7 \, d x + 7 \, c\right)} + 4 \, a^{2} e^{\left(5 \, d x + 5 \, c\right)} - a b e^{\left(5 \, d x + 5 \, c\right)} - 9 \, b^{2} e^{\left(5 \, d x + 5 \, c\right)} - 4 \, a^{2} e^{\left(3 \, d x + 3 \, c\right)} + a b e^{\left(3 \, d x + 3 \, c\right)} + 9 \, b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 4 \, a^{2} e^{\left(d x + c\right)} - 7 \, a b e^{\left(d x + c\right)} - 3 \, b^{2} e^{\left(d x + c\right)}\right)}}{{\left(a^{3} + a^{2} b\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((2*(a^3*e^(2*c) + a^2*b*e^(2*c))^2*(8*a^2*b + 6*a*b^2 - (4*a^2 - a*b - 3*b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)) - (4*a^6 + 7*a^5*b - a^4*b^2 - 7*a^3*b^3 - 3*a^2*b^4 + 2*(4*a^5 + 11*a^4*b + 10*a^3*b^2 + 3*a^2*b^3)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (8*a^8*b + 14*a^7*b^2 - 2*a^6*b^3 - 14*a^5*b^4 - 6*a^4*b^5 - (4*a^8 + 3*a^7*b - 8*a^6*b^2 - 6*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c) - sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c))^2 - (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*(a^4 + 2*a^3*b + a^2*b^2)))/(a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))))*e^(-4*c)/((a^11 + 5*a^10*b + 9*a^9*b^2 + 5*a^8*b^3 - 5*a^7*b^4 - 9*a^6*b^5 - 5*a^5*b^6 - a^4*b^7 + 2*(a^10 + 6*a^9*b + 15*a^8*b^2 + 20*a^7*b^3 + 15*a^6*b^4 + 6*a^5*b^5 + a^4*b^6)*sqrt(-a*b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))) + (2*(16*a^3*b - 4*a^2*b^2 - 12*a*b^3 + (4*a^3 - 21*a^2*b - 14*a*b^2 + 3*b^3)*sqrt(-a*b))*(a^3*e^(2*c) + a^2*b*e^(2*c))^2*abs(a*e^(2*c) + b*e^(2*c)) - (4*a^7 - 13*a^6*b - 52*a^5*b^2 - 46*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5 - 4*(4*a^6 + 7*a^5*b - a^4*b^2 - 7*a^3*b^3 - 3*a^2*b^4)*sqrt(-a*b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))*abs(a*e^(2*c) + b*e^(2*c))*e^(2*c) - (16*a^9*b + 12*a^8*b^2 - 32*a^7*b^3 - 24*a^6*b^4 + 16*a^5*b^5 + 12*a^4*b^6 + (4*a^9 - 17*a^8*b - 39*a^7*b^2 + 6*a^6*b^3 + 38*a^5*b^4 + 11*a^4*b^5 - 3*a^3*b^6)*sqrt(-a*b))*abs(a*e^(2*c) + b*e^(2*c))*e^(4*c))*arctan(e^(d*x)/sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c) + sqrt((a^4*e^(2*c) - a^2*b^2*e^(2*c))^2 - (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*(a^4 + 2*a^3*b + a^2*b^2)))/(a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))))*e^(-4*c)/((a^10 + 4*a^9*b + 5*a^8*b^2 - 5*a^6*b^4 - 4*a^5*b^5 - a^4*b^6 - 2*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(-a^3*e^(2*c) - a^2*b*e^(2*c))) - 2*(4*a^2*e^(7*d*x + 7*c) + 7*a*b*e^(7*d*x + 7*c) + 3*b^2*e^(7*d*x + 7*c) + 4*a^2*e^(5*d*x + 5*c) - a*b*e^(5*d*x + 5*c) - 9*b^2*e^(5*d*x + 5*c) - 4*a^2*e^(3*d*x + 3*c) + a*b*e^(3*d*x + 3*c) + 9*b^2*e^(3*d*x + 3*c) - 4*a^2*e^(d*x + c) - 7*a*b*e^(d*x + c) - 3*b^2*e^(d*x + c))/((a^3 + a^2*b)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
130,1,332,0,0.731247," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(a e^{\left(2 \, c\right)} - 3 \, b e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a^{2} b} + \frac{2 \, {\left(a^{3} e^{\left(6 \, d x + 6 \, c\right)} - a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 5 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 7 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 3 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} + 5 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3}\right)}}{{\left(a^{3} b + a^{2} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((a*e^(2*c) - 3*b*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a^2*b) + 2*(a^3*e^(6*d*x + 6*c) - a^2*b*e^(6*d*x + 6*c) - 5*a*b^2*e^(6*d*x + 6*c) - 3*b^3*e^(6*d*x + 6*c) + 3*a^3*e^(4*d*x + 4*c) + 7*a^2*b*e^(4*d*x + 4*c) - 3*a*b^2*e^(4*d*x + 4*c) + 9*b^3*e^(4*d*x + 4*c) + 3*a^3*e^(2*d*x + 2*c) + 13*a^2*b*e^(2*d*x + 2*c) + a*b^2*e^(2*d*x + 2*c) - 9*b^3*e^(2*d*x + 2*c) + a^3 + 5*a^2*b + 7*a*b^2 + 3*b^3)/((a^3*b + a^2*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
131,1,690,0,0.823302," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{3} - 10 \, a^{2} b + 5 \, a b^{2} + {\left(5 \, a^{2} - 10 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} {\left(a^{3} + a^{2} b\right)}}}{a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{8} - 13 \, a^{7} b - 14 \, a^{6} b^{2} + 14 \, a^{5} b^{3} + 13 \, a^{4} b^{4} - a^{3} b^{5} + 2 \, {\left(3 \, a^{7} - 4 \, a^{6} b - 14 \, a^{5} b^{2} - 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} \sqrt{-a b}} + \frac{3 \, {\left(a^{3} - 10 \, a^{2} b + 5 \, a b^{2} - {\left(5 \, a^{2} - 10 \, a b + b^{2}\right)} \sqrt{-a b}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} {\left(a^{3} + a^{2} b\right)}}}{a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{a^{8} - 13 \, a^{7} b - 14 \, a^{6} b^{2} + 14 \, a^{5} b^{3} + 13 \, a^{4} b^{4} - a^{3} b^{5} - 2 \, {\left(3 \, a^{7} - 4 \, a^{6} b - 14 \, a^{5} b^{2} - 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} \sqrt{-a b}} + \frac{2 \, {\left(3 \, a e^{\left(7 \, d x + 7 \, c\right)} + 3 \, b e^{\left(7 \, d x + 7 \, c\right)} + 11 \, a e^{\left(5 \, d x + 5 \, c\right)} - 9 \, b e^{\left(5 \, d x + 5 \, c\right)} - 11 \, a e^{\left(3 \, d x + 3 \, c\right)} + 9 \, b e^{\left(3 \, d x + 3 \, c\right)} - 3 \, a e^{\left(d x + c\right)} - 3 \, b e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2} a^{2}}}{8 \, d}"," ",0,"1/8*(3*(a^3 - 10*a^2*b + 5*a*b^2 + (5*a^2 - 10*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a^2*b*e^(2*c) + sqrt((a^3*e^(2*c) - a^2*b*e^(2*c))^2 - (a^3*e^(4*c) + a^2*b*e^(4*c))*(a^3 + a^2*b)))/(a^3*e^(4*c) + a^2*b*e^(4*c))))*e^(-2*c)/(a^8 - 13*a^7*b - 14*a^6*b^2 + 14*a^5*b^3 + 13*a^4*b^4 - a^3*b^5 + 2*(3*a^7 - 4*a^6*b - 14*a^5*b^2 - 4*a^4*b^3 + 3*a^3*b^4)*sqrt(-a*b)) + 3*(a^3 - 10*a^2*b + 5*a*b^2 - (5*a^2 - 10*a*b + b^2)*sqrt(-a*b))*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c))*arctan(e^(d*x)/sqrt((a^3*e^(2*c) - a^2*b*e^(2*c) - sqrt((a^3*e^(2*c) - a^2*b*e^(2*c))^2 - (a^3*e^(4*c) + a^2*b*e^(4*c))*(a^3 + a^2*b)))/(a^3*e^(4*c) + a^2*b*e^(4*c))))*e^(-2*c)/(a^8 - 13*a^7*b - 14*a^6*b^2 + 14*a^5*b^3 + 13*a^4*b^4 - a^3*b^5 - 2*(3*a^7 - 4*a^6*b - 14*a^5*b^2 - 4*a^4*b^3 + 3*a^3*b^4)*sqrt(-a*b)) + 2*(3*a*e^(7*d*x + 7*c) + 3*b*e^(7*d*x + 7*c) + 11*a*e^(5*d*x + 5*c) - 9*b*e^(5*d*x + 5*c) - 11*a*e^(3*d*x + 3*c) + 9*b*e^(3*d*x + 3*c) - 3*a*e^(d*x + c) - 3*b*e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2*a^2))/d","B",0
132,1,338,0,0.752107," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, a^{2} e^{\left(2 \, c\right)} - 2 \, a b e^{\left(2 \, c\right)} + 3 \, b^{2} e^{\left(2 \, c\right)}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right) e^{\left(-2 \, c\right)}}{\sqrt{a b} a^{2} b^{2}} + \frac{2 \, {\left(3 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 9 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - 15 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 15 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 9 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 13 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 13 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 3 \, b^{3}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2} a^{2} b^{2}}}{8 \, d}"," ",0,"1/8*((3*a^2*e^(2*c) - 2*a*b*e^(2*c) + 3*b^2*e^(2*c))*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))*e^(-2*c)/(sqrt(a*b)*a^2*b^2) + 2*(3*a^3*e^(6*d*x + 6*c) + a^2*b*e^(6*d*x + 6*c) + a*b^2*e^(6*d*x + 6*c) + 3*b^3*e^(6*d*x + 6*c) + 9*a^3*e^(4*d*x + 4*c) - 15*a^2*b*e^(4*d*x + 4*c) + 15*a*b^2*e^(4*d*x + 4*c) - 9*b^3*e^(4*d*x + 4*c) + 9*a^3*e^(2*d*x + 2*c) - 13*a^2*b*e^(2*d*x + 2*c) - 13*a*b^2*e^(2*d*x + 2*c) + 9*b^3*e^(2*d*x + 2*c) + 3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3)/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2*a^2*b^2))/d","B",0
133,1,1040,0,0.929173," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, {\left(8 \, a^{3} - 4 \, a^{2} b + 3 \, a b^{2}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} + {\left(8 \, a^{3} + 4 \, a^{2} b - a b^{2} + 3 \, b^{3}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| b \right|} - {\left(8 \, a^{3} b^{2} - 12 \, a^{2} b^{3} + 7 \, a b^{4} - 3 \, b^{5}\right)} \sqrt{a^{2} - b^{2} + 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)} + \sqrt{{\left(a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{3} b^{3} + a^{2} b^{4}\right)}}}{a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} \sqrt{-a b} {\left| b \right|}} - \frac{{\left(2 \, {\left(8 \, a^{3} - 4 \, a^{2} b + 3 \, a b^{2}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} b^{2} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} - {\left(8 \, a^{3} + 4 \, a^{2} b - a b^{2} + 3 \, b^{3}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} \sqrt{-a b} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|} {\left| b \right|} - {\left(8 \, a^{3} b^{2} - 12 \, a^{2} b^{3} + 7 \, a b^{4} - 3 \, b^{5}\right)} \sqrt{a^{2} - b^{2} - 2 \, \sqrt{-a b} {\left(a + b\right)}} {\left| a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)} \right|}\right)} \arctan\left(\frac{e^{\left(d x\right)}}{\sqrt{\frac{a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)} - \sqrt{{\left(a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)}^{2} - {\left(a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} {\left(a^{3} b^{3} + a^{2} b^{4}\right)}}}{a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}}}}\right) e^{\left(-2 \, c\right)}}{{\left(a^{5} b^{3} + 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} + a^{2} b^{6}\right)} \sqrt{-a b} {\left| b \right|}} - \frac{16 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b^{3}} - \frac{2 \, {\left(4 \, a^{3} e^{\left(7 \, d x + 7 \, c\right)} + 5 \, a^{2} b e^{\left(7 \, d x + 7 \, c\right)} - 2 \, a b^{2} e^{\left(7 \, d x + 7 \, c\right)} - 3 \, b^{3} e^{\left(7 \, d x + 7 \, c\right)} + 4 \, a^{3} e^{\left(5 \, d x + 5 \, c\right)} - 19 \, a^{2} b e^{\left(5 \, d x + 5 \, c\right)} - 14 \, a b^{2} e^{\left(5 \, d x + 5 \, c\right)} + 9 \, b^{3} e^{\left(5 \, d x + 5 \, c\right)} - 4 \, a^{3} e^{\left(3 \, d x + 3 \, c\right)} + 19 \, a^{2} b e^{\left(3 \, d x + 3 \, c\right)} + 14 \, a b^{2} e^{\left(3 \, d x + 3 \, c\right)} - 9 \, b^{3} e^{\left(3 \, d x + 3 \, c\right)} - 4 \, a^{3} e^{\left(d x + c\right)} - 5 \, a^{2} b e^{\left(d x + c\right)} + 2 \, a b^{2} e^{\left(d x + c\right)} + 3 \, b^{3} e^{\left(d x + c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2} a^{2} b^{2}}}{8 \, d}"," ",0,"1/8*((2*(8*a^3 - 4*a^2*b + 3*a*b^2)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*b^2*abs(a*e^(2*c) + b*e^(2*c)) + (8*a^3 + 4*a^2*b - a*b^2 + 3*b^3)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*abs(a*e^(2*c) + b*e^(2*c))*abs(b) - (8*a^3*b^2 - 12*a^2*b^3 + 7*a*b^4 - 3*b^5)*sqrt(a^2 - b^2 + 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c) + sqrt((a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))^2 - (a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*(a^3*b^3 + a^2*b^4)))/(a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))))*e^(-2*c)/((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*sqrt(-a*b)*abs(b)) - (2*(8*a^3 - 4*a^2*b + 3*a*b^2)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*b^2*abs(a*e^(2*c) + b*e^(2*c)) - (8*a^3 + 4*a^2*b - a*b^2 + 3*b^3)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*sqrt(-a*b)*abs(a*e^(2*c) + b*e^(2*c))*abs(b) - (8*a^3*b^2 - 12*a^2*b^3 + 7*a*b^4 - 3*b^5)*sqrt(a^2 - b^2 - 2*sqrt(-a*b)*(a + b))*abs(a*e^(2*c) + b*e^(2*c)))*arctan(e^(d*x)/sqrt((a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c) - sqrt((a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))^2 - (a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*(a^3*b^3 + a^2*b^4)))/(a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))))*e^(-2*c)/((a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 + a^2*b^6)*sqrt(-a*b)*abs(b)) - 16*arctan(e^(d*x + c))/b^3 - 2*(4*a^3*e^(7*d*x + 7*c) + 5*a^2*b*e^(7*d*x + 7*c) - 2*a*b^2*e^(7*d*x + 7*c) - 3*b^3*e^(7*d*x + 7*c) + 4*a^3*e^(5*d*x + 5*c) - 19*a^2*b*e^(5*d*x + 5*c) - 14*a*b^2*e^(5*d*x + 5*c) + 9*b^3*e^(5*d*x + 5*c) - 4*a^3*e^(3*d*x + 3*c) + 19*a^2*b*e^(3*d*x + 3*c) + 14*a*b^2*e^(3*d*x + 3*c) - 9*b^3*e^(3*d*x + 3*c) - 4*a^3*e^(d*x + c) - 5*a^2*b*e^(d*x + c) + 2*a*b^2*e^(d*x + c) + 3*b^3*e^(d*x + c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2*a^2*b^2))/d","B",0
134,1,134,0,0.210334," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} {\left(a + b\right)} + \frac{2 \, {\left(30 \, a e^{\left(8 \, d x + 8 \, c\right)} + 45 \, b e^{\left(8 \, d x + 8 \, c\right)} + 90 \, a e^{\left(6 \, d x + 6 \, c\right)} + 90 \, b e^{\left(6 \, d x + 6 \, c\right)} + 110 \, a e^{\left(4 \, d x + 4 \, c\right)} + 140 \, b e^{\left(4 \, d x + 4 \, c\right)} + 70 \, a e^{\left(2 \, d x + 2 \, c\right)} + 70 \, b e^{\left(2 \, d x + 2 \, c\right)} + 20 \, a + 23 \, b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*(d*x + c)*(a + b) + 2*(30*a*e^(8*d*x + 8*c) + 45*b*e^(8*d*x + 8*c) + 90*a*e^(6*d*x + 6*c) + 90*b*e^(6*d*x + 6*c) + 110*a*e^(4*d*x + 4*c) + 140*b*e^(4*d*x + 4*c) + 70*a*e^(2*d*x + 2*c) + 70*b*e^(2*d*x + 2*c) + 20*a + 23*b)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
135,1,92,0,0.181999," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} {\left(a + b\right)} - {\left(a + b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{2 \, {\left({\left(a + 2 \, b\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{4}}}{d}"," ",0,"-((d*x + c)*(a + b) - (a + b)*log(e^(2*d*x + 2*c) + 1) - 2*((a + 2*b)*e^(6*d*x + 6*c) + 2*(a + b)*e^(4*d*x + 4*c) + (a + 2*b)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^4)/d","B",0
136,1,86,0,0.174722," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} {\left(a + b\right)} + \frac{2 \, {\left(3 \, a e^{\left(4 \, d x + 4 \, c\right)} + 6 \, b e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a + 4 \, b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*(a + b) + 2*(3*a*e^(4*d*x + 4*c) + 6*b*e^(4*d*x + 4*c) + 6*a*e^(2*d*x + 2*c) + 6*b*e^(2*d*x + 2*c) + 3*a + 4*b)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
137,1,57,0,0.162226," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} {\left(a + b\right)} - {\left(a + b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{2 \, b e^{\left(2 \, d x + 2 \, c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{d}"," ",0,"-((d*x + c)*(a + b) - (a + b)*log(e^(2*d*x + 2*c) + 1) - 2*b*e^(2*d*x + 2*c)/(e^(2*d*x + 2*c) + 1)^2)/d","A",0
138,1,29,0,0.134005," ","integrate(a+b*tanh(d*x+c)^2,x, algorithm=""giac"")","a x + \frac{{\left(d x + c + \frac{2}{e^{\left(2 \, d x + 2 \, c\right)} + 1}\right)} b}{d}"," ",0,"a*x + (d*x + c + 2/(e^(2*d*x + 2*c) + 1))*b/d","A",0
139,1,46,0,0.158583," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} {\left(a + b\right)} - b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - a \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{d}"," ",0,"-((d*x + c)*(a + b) - b*log(e^(2*d*x + 2*c) + 1) - a*log(abs(e^(2*d*x + 2*c) - 1)))/d","A",0
140,1,30,0,0.169879," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} {\left(a + b\right)} - \frac{2 \, a}{e^{\left(2 \, d x + 2 \, c\right)} - 1}}{d}"," ",0,"((d*x + c)*(a + b) - 2*a/(e^(2*d*x + 2*c) - 1))/d","A",0
141,1,58,0,0.195565," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} {\left(a + b\right)} - {\left(a + b\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{2 \, a e^{\left(2 \, d x + 2 \, c\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{d}"," ",0,"-((d*x + c)*(a + b) - (a + b)*log(abs(e^(2*d*x + 2*c) - 1)) + 2*a*e^(2*d*x + 2*c)/(e^(2*d*x + 2*c) - 1)^2)/d","A",0
142,1,86,0,0.188474," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} {\left(a + b\right)} - \frac{2 \, {\left(6 \, a e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a + 3 \, b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*(a + b) - 2*(6*a*e^(4*d*x + 4*c) + 3*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) - 6*b*e^(2*d*x + 2*c) + 4*a + 3*b)/(e^(2*d*x + 2*c) - 1)^3)/d","B",0
143,1,93,0,0.236191," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} {\left(a + b\right)} - {\left(a + b\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{2 \, {\left({\left(2 \, a + b\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(2 \, a + b\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{4}}}{d}"," ",0,"-((d*x + c)*(a + b) - (a + b)*log(abs(e^(2*d*x + 2*c) - 1)) + 2*((2*a + b)*e^(6*d*x + 6*c) - 2*(a + b)*e^(4*d*x + 4*c) + (2*a + b)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) - 1)^4)/d","B",0
144,1,300,0,0.318441," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} + \frac{4 \, {\left(105 \, a^{2} e^{\left(12 \, d x + 12 \, c\right)} + 315 \, a b e^{\left(12 \, d x + 12 \, c\right)} + 210 \, b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 525 \, a^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1260 \, a b e^{\left(10 \, d x + 10 \, c\right)} + 630 \, b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1120 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 2555 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 1540 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 1330 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} + 3080 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 1540 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 945 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2121 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 1218 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 385 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 812 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 406 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 70 \, a^{2} + 161 \, a b + 88 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*(a^2 + 2*a*b + b^2)*(d*x + c) + 4*(105*a^2*e^(12*d*x + 12*c) + 315*a*b*e^(12*d*x + 12*c) + 210*b^2*e^(12*d*x + 12*c) + 525*a^2*e^(10*d*x + 10*c) + 1260*a*b*e^(10*d*x + 10*c) + 630*b^2*e^(10*d*x + 10*c) + 1120*a^2*e^(8*d*x + 8*c) + 2555*a*b*e^(8*d*x + 8*c) + 1540*b^2*e^(8*d*x + 8*c) + 1330*a^2*e^(6*d*x + 6*c) + 3080*a*b*e^(6*d*x + 6*c) + 1540*b^2*e^(6*d*x + 6*c) + 945*a^2*e^(4*d*x + 4*c) + 2121*a*b*e^(4*d*x + 4*c) + 1218*b^2*e^(4*d*x + 4*c) + 385*a^2*e^(2*d*x + 2*c) + 812*a*b*e^(2*d*x + 2*c) + 406*b^2*e^(2*d*x + 2*c) + 70*a^2 + 161*a*b + 88*b^2)/(e^(2*d*x + 2*c) + 1)^7)/d","B",0
145,1,191,0,0.287490," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{2 \, {\left(3 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} e^{\left(10 \, d x + 10 \, c\right)} + 6 \, {\left(2 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(9 \, a^{2} + 24 \, a b + 17 \, b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, {\left(2 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{6}}}{3 \, d}"," ",0,"-1/3*(3*(a^2 + 2*a*b + b^2)*(d*x + c) - 3*(a^2 + 2*a*b + b^2)*log(e^(2*d*x + 2*c) + 1) - 2*(3*(a^2 + 4*a*b + 3*b^2)*e^(10*d*x + 10*c) + 6*(2*a^2 + 6*a*b + 3*b^2)*e^(8*d*x + 8*c) + 2*(9*a^2 + 24*a*b + 17*b^2)*e^(6*d*x + 6*c) + 6*(2*a^2 + 6*a*b + 3*b^2)*e^(4*d*x + 4*c) + 3*(a^2 + 4*a*b + 3*b^2)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^6)/d","B",0
146,1,218,0,0.255687," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(15 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 45 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} + 180 \, a b e^{\left(6 \, d x + 6 \, c\right)} + 90 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 90 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 220 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 140 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 60 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} + 140 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 70 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*(a^2 + 2*a*b + b^2)*(d*x + c) + 2*(15*a^2*e^(8*d*x + 8*c) + 60*a*b*e^(8*d*x + 8*c) + 45*b^2*e^(8*d*x + 8*c) + 60*a^2*e^(6*d*x + 6*c) + 180*a*b*e^(6*d*x + 6*c) + 90*b^2*e^(6*d*x + 6*c) + 90*a^2*e^(4*d*x + 4*c) + 220*a*b*e^(4*d*x + 4*c) + 140*b^2*e^(4*d*x + 4*c) + 60*a^2*e^(2*d*x + 2*c) + 140*a*b*e^(2*d*x + 2*c) + 70*b^2*e^(2*d*x + 2*c) + 15*a^2 + 40*a*b + 23*b^2)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
147,1,116,0,0.222289," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{4 \, {\left({\left(a b + b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(2 \, a b + b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{4}}}{d}"," ",0,"-((a^2 + 2*a*b + b^2)*(d*x + c) - (a^2 + 2*a*b + b^2)*log(e^(2*d*x + 2*c) + 1) - 4*((a*b + b^2)*e^(6*d*x + 6*c) + (2*a*b + b^2)*e^(4*d*x + 4*c) + (a*b + b^2)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^4)/d","B",0
148,1,103,0,0.143507," ","integrate((a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} + \frac{4 \, {\left(3 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a b + 2 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^2 + 2*a*b + b^2)*(d*x + c) + 4*(3*a*b*e^(4*d*x + 4*c) + 3*b^2*e^(4*d*x + 4*c) + 6*a*b*e^(2*d*x + 2*c) + 3*b^2*e^(2*d*x + 2*c) + 3*a*b + 2*b^2)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
149,1,141,0,0.208070," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{a^{2} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right) + {\left(2 \, a b + b^{2}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right) - \frac{2 \, a b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 4 \, a b - 2 \, b^{2}}{e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2}}{2 \, d}"," ",0,"1/2*(a^2*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2) + (2*a*b + b^2)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2) - (2*a*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 4*a*b - 2*b^2)/(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2))/d","B",0
150,1,71,0,0.253345," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(a^{2} e^{\left(2 \, d x + 2 \, c\right)} - b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + b^{2}\right)}}{e^{\left(4 \, d x + 4 \, c\right)} - 1}}{d}"," ",0,"((a^2 + 2*a*b + b^2)*(d*x + c) - 2*(a^2*e^(2*d*x + 2*c) - b^2*e^(2*d*x + 2*c) + a^2 + b^2)/(e^(4*d*x + 4*c) - 1))/d","A",0
151,1,141,0,0.270089," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{b^{2} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right) + {\left(a^{2} + 2 \, a b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right) - \frac{a^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a^{2} - 4 \, a b}{e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2}}{2 \, d}"," ",0,"1/2*(b^2*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2) + (a^2 + 2*a*b)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2) - (a^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a^2 - 4*a*b)/(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2))/d","B",0
152,1,103,0,0.279495," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - \frac{4 \, {\left(3 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a b e^{\left(4 \, d x + 4 \, c\right)} - 3 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, a b e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{2} + 3 \, a b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^2 + 2*a*b + b^2)*(d*x + c) - 4*(3*a^2*e^(4*d*x + 4*c) + 3*a*b*e^(4*d*x + 4*c) - 3*a^2*e^(2*d*x + 2*c) - 6*a*b*e^(2*d*x + 2*c) + 2*a^2 + 3*a*b)/(e^(2*d*x + 2*c) - 1)^3)/d","B",0
153,1,118,0,0.335361," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{4 \, {\left({\left(a^{2} + a b\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(a^{2} + 2 \, a b\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{2} + a b\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{4}}}{d}"," ",0,"-((a^2 + 2*a*b + b^2)*(d*x + c) - (a^2 + 2*a*b + b^2)*log(abs(e^(2*d*x + 2*c) - 1)) + 4*((a^2 + a*b)*e^(6*d*x + 6*c) - (a^2 + 2*a*b)*e^(4*d*x + 4*c) + (a^2 + a*b)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) - 1)^4)/d","A",0
154,1,218,0,0.359794," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(45 \, a^{2} e^{\left(8 \, d x + 8 \, c\right)} + 60 \, a b e^{\left(8 \, d x + 8 \, c\right)} + 15 \, b^{2} e^{\left(8 \, d x + 8 \, c\right)} - 90 \, a^{2} e^{\left(6 \, d x + 6 \, c\right)} - 180 \, a b e^{\left(6 \, d x + 6 \, c\right)} - 60 \, b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 140 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 220 \, a b e^{\left(4 \, d x + 4 \, c\right)} + 90 \, b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 70 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - 140 \, a b e^{\left(2 \, d x + 2 \, c\right)} - 60 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*(a^2 + 2*a*b + b^2)*(d*x + c) - 2*(45*a^2*e^(8*d*x + 8*c) + 60*a*b*e^(8*d*x + 8*c) + 15*b^2*e^(8*d*x + 8*c) - 90*a^2*e^(6*d*x + 6*c) - 180*a*b*e^(6*d*x + 6*c) - 60*b^2*e^(6*d*x + 6*c) + 140*a^2*e^(4*d*x + 4*c) + 220*a*b*e^(4*d*x + 4*c) + 90*b^2*e^(4*d*x + 4*c) - 70*a^2*e^(2*d*x + 2*c) - 140*a*b*e^(2*d*x + 2*c) - 60*b^2*e^(2*d*x + 2*c) + 23*a^2 + 40*a*b + 15*b^2)/(e^(2*d*x + 2*c) - 1)^5)/d","B",0
155,1,192,0,0.431086," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} e^{\left(10 \, d x + 10 \, c\right)} - 6 \, {\left(3 \, a^{2} + 6 \, a b + 2 \, b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(17 \, a^{2} + 24 \, a b + 9 \, b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 6 \, {\left(3 \, a^{2} + 6 \, a b + 2 \, b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{6}}}{3 \, d}"," ",0,"-1/3*(3*(a^2 + 2*a*b + b^2)*(d*x + c) - 3*(a^2 + 2*a*b + b^2)*log(abs(e^(2*d*x + 2*c) - 1)) + 2*(3*(3*a^2 + 4*a*b + b^2)*e^(10*d*x + 10*c) - 6*(3*a^2 + 6*a*b + 2*b^2)*e^(8*d*x + 8*c) + 2*(17*a^2 + 24*a*b + 9*b^2)*e^(6*d*x + 6*c) - 6*(3*a^2 + 6*a*b + 2*b^2)*e^(4*d*x + 4*c) + 3*(3*a^2 + 4*a*b + b^2)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) - 1)^6)/d","B",0
156,1,534,0,0.538898," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(630 \, a^{3} e^{\left(16 \, d x + 16 \, c\right)} + 2835 \, a^{2} b e^{\left(16 \, d x + 16 \, c\right)} + 3780 \, a b^{2} e^{\left(16 \, d x + 16 \, c\right)} + 1575 \, b^{3} e^{\left(16 \, d x + 16 \, c\right)} + 4410 \, a^{3} e^{\left(14 \, d x + 14 \, c\right)} + 17010 \, a^{2} b e^{\left(14 \, d x + 14 \, c\right)} + 18900 \, a b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 6300 \, b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 13650 \, a^{3} e^{\left(12 \, d x + 12 \, c\right)} + 48510 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} + 54180 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 21000 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 24570 \, a^{3} e^{\left(10 \, d x + 10 \, c\right)} + 85050 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} + 94500 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 31500 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 28350 \, a^{3} e^{\left(8 \, d x + 8 \, c\right)} + 97524 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 105084 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 39438 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 21630 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + 73206 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 78876 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 26292 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 10710 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 35154 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 38124 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 13968 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 3150 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 10206 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 10476 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 3492 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{9}}}{315 \, d}"," ",0,"1/315*(315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) + 2*(630*a^3*e^(16*d*x + 16*c) + 2835*a^2*b*e^(16*d*x + 16*c) + 3780*a*b^2*e^(16*d*x + 16*c) + 1575*b^3*e^(16*d*x + 16*c) + 4410*a^3*e^(14*d*x + 14*c) + 17010*a^2*b*e^(14*d*x + 14*c) + 18900*a*b^2*e^(14*d*x + 14*c) + 6300*b^3*e^(14*d*x + 14*c) + 13650*a^3*e^(12*d*x + 12*c) + 48510*a^2*b*e^(12*d*x + 12*c) + 54180*a*b^2*e^(12*d*x + 12*c) + 21000*b^3*e^(12*d*x + 12*c) + 24570*a^3*e^(10*d*x + 10*c) + 85050*a^2*b*e^(10*d*x + 10*c) + 94500*a*b^2*e^(10*d*x + 10*c) + 31500*b^3*e^(10*d*x + 10*c) + 28350*a^3*e^(8*d*x + 8*c) + 97524*a^2*b*e^(8*d*x + 8*c) + 105084*a*b^2*e^(8*d*x + 8*c) + 39438*b^3*e^(8*d*x + 8*c) + 21630*a^3*e^(6*d*x + 6*c) + 73206*a^2*b*e^(6*d*x + 6*c) + 78876*a*b^2*e^(6*d*x + 6*c) + 26292*b^3*e^(6*d*x + 6*c) + 10710*a^3*e^(4*d*x + 4*c) + 35154*a^2*b*e^(4*d*x + 4*c) + 38124*a*b^2*e^(4*d*x + 4*c) + 13968*b^3*e^(4*d*x + 4*c) + 3150*a^3*e^(2*d*x + 2*c) + 10206*a^2*b*e^(2*d*x + 2*c) + 10476*a*b^2*e^(2*d*x + 2*c) + 3492*b^3*e^(2*d*x + 2*c) + 420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)/(e^(2*d*x + 2*c) + 1)^9)/d","B",0
157,1,309,0,0.466063," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{2 \, {\left(3 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} e^{\left(14 \, d x + 14 \, c\right)} + 18 \, {\left(a^{3} + 5 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} e^{\left(12 \, d x + 12 \, c\right)} + {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3}\right)} e^{\left(10 \, d x + 10 \, c\right)} + 4 \, {\left(15 \, a^{3} + 63 \, a^{2} b + 78 \, a b^{2} + 26 \, b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 18 \, {\left(a^{3} + 5 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{8}}}{3 \, d}"," ",0,"-1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(e^(2*d*x + 2*c) + 1) - 2*(3*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*e^(14*d*x + 14*c) + 18*(a^3 + 5*a^2*b + 6*a*b^2 + 2*b^3)*e^(12*d*x + 12*c) + (45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3)*e^(10*d*x + 10*c) + 4*(15*a^3 + 63*a^2*b + 78*a*b^2 + 26*b^3)*e^(8*d*x + 8*c) + (45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3)*e^(6*d*x + 6*c) + 18*(a^3 + 5*a^2*b + 6*a*b^2 + 2*b^3)*e^(4*d*x + 4*c) + 3*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^8)/d","B",0
158,1,418,0,0.394030," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(105 \, a^{3} e^{\left(12 \, d x + 12 \, c\right)} + 630 \, a^{2} b e^{\left(12 \, d x + 12 \, c\right)} + 945 \, a b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 420 \, b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 630 \, a^{3} e^{\left(10 \, d x + 10 \, c\right)} + 3150 \, a^{2} b e^{\left(10 \, d x + 10 \, c\right)} + 3780 \, a b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1260 \, b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 1575 \, a^{3} e^{\left(8 \, d x + 8 \, c\right)} + 6720 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 7665 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 3080 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 2100 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} + 7980 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 9240 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 3080 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 1575 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 5670 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 6363 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2436 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 630 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 2310 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 2436 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 812 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) + 2*(105*a^3*e^(12*d*x + 12*c) + 630*a^2*b*e^(12*d*x + 12*c) + 945*a*b^2*e^(12*d*x + 12*c) + 420*b^3*e^(12*d*x + 12*c) + 630*a^3*e^(10*d*x + 10*c) + 3150*a^2*b*e^(10*d*x + 10*c) + 3780*a*b^2*e^(10*d*x + 10*c) + 1260*b^3*e^(10*d*x + 10*c) + 1575*a^3*e^(8*d*x + 8*c) + 6720*a^2*b*e^(8*d*x + 8*c) + 7665*a*b^2*e^(8*d*x + 8*c) + 3080*b^3*e^(8*d*x + 8*c) + 2100*a^3*e^(6*d*x + 6*c) + 7980*a^2*b*e^(6*d*x + 6*c) + 9240*a*b^2*e^(6*d*x + 6*c) + 3080*b^3*e^(6*d*x + 6*c) + 1575*a^3*e^(4*d*x + 4*c) + 5670*a^2*b*e^(4*d*x + 4*c) + 6363*a*b^2*e^(4*d*x + 4*c) + 2436*b^3*e^(4*d*x + 4*c) + 630*a^3*e^(2*d*x + 2*c) + 2310*a^2*b*e^(2*d*x + 2*c) + 2436*a*b^2*e^(2*d*x + 2*c) + 812*b^3*e^(2*d*x + 2*c) + 105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3)/(e^(2*d*x + 2*c) + 1)^7)/d","B",0
159,1,216,0,0.352424," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) - \frac{2 \, {\left(9 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} e^{\left(10 \, d x + 10 \, c\right)} + 18 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 18 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{6}}}{3 \, d}"," ",0,"-1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(e^(2*d*x + 2*c) + 1) - 2*(9*(a^2*b + 2*a*b^2 + b^3)*e^(10*d*x + 10*c) + 18*(2*a^2*b + 3*a*b^2 + b^3)*e^(8*d*x + 8*c) + 2*(27*a^2*b + 36*a*b^2 + 17*b^3)*e^(6*d*x + 6*c) + 18*(2*a^2*b + 3*a*b^2 + b^3)*e^(4*d*x + 4*c) + 9*(a^2*b + 2*a*b^2 + b^3)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^6)/d","B",0
160,1,241,0,0.177461," ","integrate((a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(45 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 90 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 45 \, b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 180 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} + 270 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 90 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 270 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 330 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 140 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 180 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 210 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 70 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) + 2*(45*a^2*b*e^(8*d*x + 8*c) + 90*a*b^2*e^(8*d*x + 8*c) + 45*b^3*e^(8*d*x + 8*c) + 180*a^2*b*e^(6*d*x + 6*c) + 270*a*b^2*e^(6*d*x + 6*c) + 90*b^3*e^(6*d*x + 6*c) + 270*a^2*b*e^(4*d*x + 4*c) + 330*a*b^2*e^(4*d*x + 4*c) + 140*b^3*e^(4*d*x + 4*c) + 180*a^2*b*e^(2*d*x + 2*c) + 210*a*b^2*e^(2*d*x + 2*c) + 70*b^3*e^(2*d*x + 2*c) + 45*a^2*b + 60*a*b^2 + 23*b^3)/(e^(2*d*x + 2*c) + 1)^5)/d","B",0
161,1,267,0,0.331082," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right) + 2 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right) - \frac{9 \, a^{2} b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 9 \, a b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, b^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 36 \, a^{2} b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 12 \, a b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 4 \, b^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 36 \, a^{2} b - 12 \, a b^{2} - 4 \, b^{3}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right)}^{2}}}{4 \, d}"," ",0,"1/4*(2*a^3*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2) + 2*(3*a^2*b + 3*a*b^2 + b^3)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2) - (9*a^2*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 9*a*b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*b^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 36*a^2*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 12*a*b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 4*b^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 36*a^2*b - 12*a*b^2 - 4*b^3)/(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2)^2)/d","B",0
162,1,135,0,0.412745," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} - \frac{6 \, a^{3}}{e^{\left(2 \, d x + 2 \, c\right)} - 1} + \frac{2 \, {\left(9 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 18 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a b^{2} + 4 \, b^{3}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) - 6*a^3/(e^(2*d*x + 2*c) - 1) + 2*(9*a*b^2*e^(4*d*x + 4*c) + 6*b^3*e^(4*d*x + 4*c) + 18*a*b^2*e^(2*d*x + 2*c) + 6*b^3*e^(2*d*x + 2*c) + 9*a*b^2 + 4*b^3)/(e^(2*d*x + 2*c) + 1)^3)/d","B",0
163,1,274,0,0.443449," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, a b^{2} + b^{3}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right) + 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right) - \frac{a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, a^{2} b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, a b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + b^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 8 \, a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 8 \, b^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 12 \, a^{3} - 12 \, a^{2} b - 12 \, a b^{2} + 12 \, b^{3}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} - 4}}{4 \, d}"," ",0,"1/4*(2*(3*a*b^2 + b^3)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2) + 2*(a^3 + 3*a^2*b)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2) - (a^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*a^2*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*a*b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + b^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 8*a^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 8*b^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 12*a^3 - 12*a^2*b - 12*a*b^2 + 12*b^3)/((e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 - 4))/d","B",0
164,1,135,0,0.522727," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} + \frac{6 \, b^{3}}{e^{\left(2 \, d x + 2 \, c\right)} + 1} - \frac{2 \, {\left(6 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 18 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a^{3} + 9 \, a^{2} b\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) + 6*b^3/(e^(2*d*x + 2*c) + 1) - 2*(6*a^3*e^(4*d*x + 4*c) + 9*a^2*b*e^(4*d*x + 4*c) - 6*a^3*e^(2*d*x + 2*c) - 18*a^2*b*e^(2*d*x + 2*c) + 4*a^3 + 9*a^2*b)/(e^(2*d*x + 2*c) - 1)^3)/d","B",0
165,1,267,0,0.576701," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{2 \, b^{3} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2\right) + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right) - \frac{3 \, a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 9 \, a^{2} b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 9 \, a b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 4 \, a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 12 \, a^{2} b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 36 \, a b^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 4 \, a^{3} - 12 \, a^{2} b + 36 \, a b^{2}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2\right)}^{2}}}{4 \, d}"," ",0,"1/4*(2*b^3*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2) + 2*(a^3 + 3*a^2*b + 3*a*b^2)*log(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2) - (3*a^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 9*a^2*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 9*a*b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 4*a^3*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 12*a^2*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 36*a*b^2*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 4*a^3 - 12*a^2*b + 36*a*b^2)/(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2)^2)/d","B",0
166,1,241,0,0.556700," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(45 \, a^{3} e^{\left(8 \, d x + 8 \, c\right)} + 90 \, a^{2} b e^{\left(8 \, d x + 8 \, c\right)} + 45 \, a b^{2} e^{\left(8 \, d x + 8 \, c\right)} - 90 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} - 270 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 180 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 140 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 330 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 270 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 70 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 210 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 180 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) - 2*(45*a^3*e^(8*d*x + 8*c) + 90*a^2*b*e^(8*d*x + 8*c) + 45*a*b^2*e^(8*d*x + 8*c) - 90*a^3*e^(6*d*x + 6*c) - 270*a^2*b*e^(6*d*x + 6*c) - 180*a*b^2*e^(6*d*x + 6*c) + 140*a^3*e^(4*d*x + 4*c) + 330*a^2*b*e^(4*d*x + 4*c) + 270*a*b^2*e^(4*d*x + 4*c) - 70*a^3*e^(2*d*x + 2*c) - 210*a^2*b*e^(2*d*x + 2*c) - 180*a*b^2*e^(2*d*x + 2*c) + 23*a^3 + 60*a^2*b + 45*a*b^2)/(e^(2*d*x + 2*c) - 1)^5)/d","B",0
167,1,217,0,0.781648," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(d x + c\right)} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right) + \frac{2 \, {\left(9 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} e^{\left(10 \, d x + 10 \, c\right)} - 18 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 18 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{6}}}{3 \, d}"," ",0,"-1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(d*x + c) - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(abs(e^(2*d*x + 2*c) - 1)) + 2*(9*(a^3 + 2*a^2*b + a*b^2)*e^(10*d*x + 10*c) - 18*(a^3 + 3*a^2*b + 2*a*b^2)*e^(8*d*x + 8*c) + 2*(17*a^3 + 36*a^2*b + 27*a*b^2)*e^(6*d*x + 6*c) - 18*(a^3 + 3*a^2*b + 2*a*b^2)*e^(4*d*x + 4*c) + 9*(a^3 + 2*a^2*b + a*b^2)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) - 1)^6)/d","B",0
168,1,447,0,0.215916," ","integrate((a+b*tanh(d*x+c)^2)^4,x, algorithm=""giac"")","\frac{105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(d x + c\right)} + \frac{8 \, {\left(105 \, a^{3} b e^{\left(12 \, d x + 12 \, c\right)} + 315 \, a^{2} b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 315 \, a b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 105 \, b^{4} e^{\left(12 \, d x + 12 \, c\right)} + 630 \, a^{3} b e^{\left(10 \, d x + 10 \, c\right)} + 1575 \, a^{2} b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1260 \, a b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 315 \, b^{4} e^{\left(10 \, d x + 10 \, c\right)} + 1575 \, a^{3} b e^{\left(8 \, d x + 8 \, c\right)} + 3360 \, a^{2} b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 2555 \, a b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 770 \, b^{4} e^{\left(8 \, d x + 8 \, c\right)} + 2100 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} + 3990 \, a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 3080 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 770 \, b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 1575 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} + 2835 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 2121 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 609 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 630 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} + 1155 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 812 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 203 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(d*x + c) + 8*(105*a^3*b*e^(12*d*x + 12*c) + 315*a^2*b^2*e^(12*d*x + 12*c) + 315*a*b^3*e^(12*d*x + 12*c) + 105*b^4*e^(12*d*x + 12*c) + 630*a^3*b*e^(10*d*x + 10*c) + 1575*a^2*b^2*e^(10*d*x + 10*c) + 1260*a*b^3*e^(10*d*x + 10*c) + 315*b^4*e^(10*d*x + 10*c) + 1575*a^3*b*e^(8*d*x + 8*c) + 3360*a^2*b^2*e^(8*d*x + 8*c) + 2555*a*b^3*e^(8*d*x + 8*c) + 770*b^4*e^(8*d*x + 8*c) + 2100*a^3*b*e^(6*d*x + 6*c) + 3990*a^2*b^2*e^(6*d*x + 6*c) + 3080*a*b^3*e^(6*d*x + 6*c) + 770*b^4*e^(6*d*x + 6*c) + 1575*a^3*b*e^(4*d*x + 4*c) + 2835*a^2*b^2*e^(4*d*x + 4*c) + 2121*a*b^3*e^(4*d*x + 4*c) + 609*b^4*e^(4*d*x + 4*c) + 630*a^3*b*e^(2*d*x + 2*c) + 1155*a^2*b^2*e^(2*d*x + 2*c) + 812*a*b^3*e^(2*d*x + 2*c) + 203*b^4*e^(2*d*x + 2*c) + 105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)/(e^(2*d*x + 2*c) + 1)^7)/d","B",0
169,1,721,0,0.307703," ","integrate((a+b*tanh(d*x+c)^2)^5,x, algorithm=""giac"")","\frac{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)} {\left(d x + c\right)} + \frac{2 \, {\left(1575 \, a^{4} b e^{\left(16 \, d x + 16 \, c\right)} + 6300 \, a^{3} b^{2} e^{\left(16 \, d x + 16 \, c\right)} + 9450 \, a^{2} b^{3} e^{\left(16 \, d x + 16 \, c\right)} + 6300 \, a b^{4} e^{\left(16 \, d x + 16 \, c\right)} + 1575 \, b^{5} e^{\left(16 \, d x + 16 \, c\right)} + 12600 \, a^{4} b e^{\left(14 \, d x + 14 \, c\right)} + 44100 \, a^{3} b^{2} e^{\left(14 \, d x + 14 \, c\right)} + 56700 \, a^{2} b^{3} e^{\left(14 \, d x + 14 \, c\right)} + 31500 \, a b^{4} e^{\left(14 \, d x + 14 \, c\right)} + 6300 \, b^{5} e^{\left(14 \, d x + 14 \, c\right)} + 44100 \, a^{4} b e^{\left(12 \, d x + 12 \, c\right)} + 136500 \, a^{3} b^{2} e^{\left(12 \, d x + 12 \, c\right)} + 161700 \, a^{2} b^{3} e^{\left(12 \, d x + 12 \, c\right)} + 90300 \, a b^{4} e^{\left(12 \, d x + 12 \, c\right)} + 21000 \, b^{5} e^{\left(12 \, d x + 12 \, c\right)} + 88200 \, a^{4} b e^{\left(10 \, d x + 10 \, c\right)} + 245700 \, a^{3} b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 283500 \, a^{2} b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 157500 \, a b^{4} e^{\left(10 \, d x + 10 \, c\right)} + 31500 \, b^{5} e^{\left(10 \, d x + 10 \, c\right)} + 110250 \, a^{4} b e^{\left(8 \, d x + 8 \, c\right)} + 283500 \, a^{3} b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 325080 \, a^{2} b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 175140 \, a b^{4} e^{\left(8 \, d x + 8 \, c\right)} + 39438 \, b^{5} e^{\left(8 \, d x + 8 \, c\right)} + 88200 \, a^{4} b e^{\left(6 \, d x + 6 \, c\right)} + 216300 \, a^{3} b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 244020 \, a^{2} b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 131460 \, a b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 26292 \, b^{5} e^{\left(6 \, d x + 6 \, c\right)} + 44100 \, a^{4} b e^{\left(4 \, d x + 4 \, c\right)} + 107100 \, a^{3} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 117180 \, a^{2} b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 63540 \, a b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 13968 \, b^{5} e^{\left(4 \, d x + 4 \, c\right)} + 12600 \, a^{4} b e^{\left(2 \, d x + 2 \, c\right)} + 31500 \, a^{3} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 34020 \, a^{2} b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 17460 \, a b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 3492 \, b^{5} e^{\left(2 \, d x + 2 \, c\right)} + 1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{9}}}{315 \, d}"," ",0,"1/315*(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 + c) + 2*(1575*a^4*b*e^(16*d*x + 16*c) + 6300*a^3*b^2*e^(16*d*x + 16*c) + 9450*a^2*b^3*e^(16*d*x + 16*c) + 6300*a*b^4*e^(16*d*x + 16*c) + 1575*b^5*e^(16*d*x + 16*c) + 12600*a^4*b*e^(14*d*x + 14*c) + 44100*a^3*b^2*e^(14*d*x + 14*c) + 56700*a^2*b^3*e^(14*d*x + 14*c) + 31500*a*b^4*e^(14*d*x + 14*c) + 6300*b^5*e^(14*d*x + 14*c) + 44100*a^4*b*e^(12*d*x + 12*c) + 136500*a^3*b^2*e^(12*d*x + 12*c) + 161700*a^2*b^3*e^(12*d*x + 12*c) + 90300*a*b^4*e^(12*d*x + 12*c) + 21000*b^5*e^(12*d*x + 12*c) + 88200*a^4*b*e^(10*d*x + 10*c) + 245700*a^3*b^2*e^(10*d*x + 10*c) + 283500*a^2*b^3*e^(10*d*x + 10*c) + 157500*a*b^4*e^(10*d*x + 10*c) + 31500*b^5*e^(10*d*x + 10*c) + 110250*a^4*b*e^(8*d*x + 8*c) + 283500*a^3*b^2*e^(8*d*x + 8*c) + 325080*a^2*b^3*e^(8*d*x + 8*c) + 175140*a*b^4*e^(8*d*x + 8*c) + 39438*b^5*e^(8*d*x + 8*c) + 88200*a^4*b*e^(6*d*x + 6*c) + 216300*a^3*b^2*e^(6*d*x + 6*c) + 244020*a^2*b^3*e^(6*d*x + 6*c) + 131460*a*b^4*e^(6*d*x + 6*c) + 26292*b^5*e^(6*d*x + 6*c) + 44100*a^4*b*e^(4*d*x + 4*c) + 107100*a^3*b^2*e^(4*d*x + 4*c) + 117180*a^2*b^3*e^(4*d*x + 4*c) + 63540*a*b^4*e^(4*d*x + 4*c) + 13968*b^5*e^(4*d*x + 4*c) + 12600*a^4*b*e^(2*d*x + 2*c) + 31500*a^3*b^2*e^(2*d*x + 2*c) + 34020*a^2*b^3*e^(2*d*x + 2*c) + 17460*a*b^4*e^(2*d*x + 2*c) + 3492*b^5*e^(2*d*x + 2*c) + 1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)/(e^(2*d*x + 2*c) + 1)^9)/d","B",0
170,1,132,0,0.260478," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{a^{2} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a b^{2} + b^{3}} - \frac{2 \, {\left(d x + c\right)}}{a + b} - \frac{2 \, {\left(a - b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}{b^{2}} + \frac{4 \, e^{\left(2 \, d x + 2 \, c\right)}}{b {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(a^2*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a*b^2 + b^3) - 2*(d*x + c)/(a + b) - 2*(a - b)*log(e^(2*d*x + 2*c) + 1)/b^2 + 4*e^(2*d*x + 2*c)/(b*(e^(2*d*x + 2*c) + 1)^2))/d","B",0
171,1,87,0,0.225964," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{a^{2} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a b + b^{2}\right)} \sqrt{a b}} + \frac{d x + c}{a + b} + \frac{2}{b {\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}}}{d}"," ",0,"(a^2*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a*b + b^2)*sqrt(a*b)) + (d*x + c)/(a + b) + 2/(b*(e^(2*d*x + 2*c) + 1)))/d","A",0
172,1,96,0,0.228697," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{a \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a b + b^{2}} + \frac{2 \, {\left(d x + c\right)}}{a + b} - \frac{2 \, \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}{b}}{2 \, d}"," ",0,"-1/2*(a*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a*b + b^2) + 2*(d*x + c)/(a + b) - 2*log(e^(2*d*x + 2*c) + 1)/b)/d","B",0
173,1,65,0,0.184145," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{a \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)}} - \frac{d x + c}{a + b}}{d}"," ",0,"-(a*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)) - (d*x + c)/(a + b))/d","A",0
174,1,61,0,0.173676," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{2 \, {\left(a + b\right)} d}"," ",0,"1/2*log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/((a + b)*d)","A",0
175,1,63,0,0.148884," ","integrate(1/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{b \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)}} + \frac{d x + c}{a + b}}{d}"," ",0,"(b*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)) + (d*x + c)/(a + b))/d","A",0
176,1,97,0,0.175209," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{2} + a b} + \frac{2 \, {\left(d x + c\right)}}{a + b} - \frac{2 \, \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a}}{2 \, d}"," ",0,"-1/2*(b*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^2 + a*b) + 2*(d*x + c)/(a + b) - 2*log(abs(e^(2*d*x + 2*c) - 1))/a)/d","A",0
177,1,89,0,0.205149," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{b^{2} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{2} + a b\right)} \sqrt{a b}} - \frac{d x + c}{a + b} + \frac{2}{a {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}}}{d}"," ",0,"-(b^2*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + a*b)*sqrt(a*b)) - (d*x + c)/(a + b) + 2/(a*(e^(2*d*x + 2*c) - 1)))/d","A",0
178,1,133,0,0.250515," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{b^{2} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{3} + a^{2} b} - \frac{2 \, {\left(d x + c\right)}}{a + b} + \frac{2 \, {\left(a - b\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{2}} - \frac{4 \, e^{\left(2 \, d x + 2 \, c\right)}}{a {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(b^2*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^3 + a^2*b) - 2*(d*x + c)/(a + b) + 2*(a - b)*log(abs(e^(2*d*x + 2*c) - 1))/a^2 - 4*e^(2*d*x + 2*c)/(a*(e^(2*d*x + 2*c) - 1)^2))/d","A",0
179,1,147,0,0.251558," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{a b}} + \frac{3 \, {\left(d x + c\right)}}{a + b} - \frac{2 \, {\left(6 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a - 3 \, b\right)}}{a^{2} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*b^3*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3 + a^2*b)*sqrt(a*b)) + 3*(d*x + c)/(a + b) - 2*(6*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) + 6*b*e^(2*d*x + 2*c) + 4*a - 3*b)/(a^2*(e^(2*d*x + 2*c) - 1)^3))/d","B",0
180,1,194,0,0.446149," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} + 2 \, a b\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{2} b^{2} + 2 \, a b^{3} + b^{4}} + \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} + \frac{4 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} {\left(a + b\right)}^{2} b} - \frac{2 \, \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}{b^{2}}}{2 \, d}"," ",0,"-1/2*((a^2 + 2*a*b)*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^2*b^2 + 2*a*b^3 + b^4) + 2*(d*x + c)/(a^2 + 2*a*b + b^2) + 4*a^2*e^(2*d*x + 2*c)/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*(a + b)^2*b) - 2*log(e^(2*d*x + 2*c) + 1)/b^2)/d","B",0
181,1,195,0,0.335626," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} + 3 \, a b\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a^{2} e^{\left(2 \, d x + 2 \, c\right)} - a b e^{\left(2 \, d x + 2 \, c\right)} + a^{2} + a b\right)}}{{\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{2 \, d}"," ",0,"-1/2*((a^2 + 3*a*b)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2*b + 2*a*b^2 + b^3)*sqrt(a*b)) - 2*(d*x + c)/(a^2 + 2*a*b + b^2) + 2*(a^2*e^(2*d*x + 2*c) - a*b*e^(2*d*x + 2*c) + a^2 + a*b)/((a^2*b + 2*a*b^2 + b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
182,1,149,0,0.317648," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{\log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} - 2}{{\left(a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b\right)} {\left(a + b\right)}}}{2 \, d}"," ",0,"1/2*(log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/(a^2 + 2*a*b + b^2) - (e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) - 2)/((a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b)*(a + b)))/d","B",0
183,1,177,0,0.306773," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a - b\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(a e^{\left(2 \, d x + 2 \, c\right)} - b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{2 \, d}"," ",0,"-1/2*((a - b)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) - 2*(d*x + c)/(a^2 + 2*a*b + b^2) - 2*(a*e^(2*d*x + 2*c) - b*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
184,1,149,0,0.265526," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{\log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)} + 2}{{\left(a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b\right)} {\left(a + b\right)}}}{2 \, d}"," ",0,"1/2*(log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/(a^2 + 2*a*b + b^2) - (e^(2*d*x + 2*c) + e^(-2*d*x - 2*c) + 2)/((a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b)*(a + b)))/d","B",0
185,1,195,0,0.183660," ","integrate(1/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, a b + b^{2}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} + \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(a b e^{\left(2 \, d x + 2 \, c\right)} - b^{2} e^{\left(2 \, d x + 2 \, c\right)} + a b + b^{2}\right)}}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}}}{2 \, d}"," ",0,"1/2*((3*a*b + b^2)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3 + 2*a^2*b + a*b^2)*sqrt(a*b)) + 2*(d*x + c)/(a^2 + 2*a*b + b^2) - 2*(a*b*e^(2*d*x + 2*c) - b^2*e^(2*d*x + 2*c) + a*b + b^2)/((a^3 + 2*a^2*b + a*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)))/d","B",0
186,1,195,0,0.313740," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a b + b^{2}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{4} + 2 \, a^{3} b + a^{2} b^{2}} + \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} - \frac{4 \, b^{2} e^{\left(2 \, d x + 2 \, c\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} {\left(a + b\right)}^{2} a} - \frac{2 \, \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*((2*a*b + b^2)*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^4 + 2*a^3*b + a^2*b^2) + 2*(d*x + c)/(a^2 + 2*a*b + b^2) - 4*b^2*e^(2*d*x + 2*c)/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*(a + b)^2*a) - 2*log(abs(e^(2*d*x + 2*c) - 1))/a^2)/d","B",0
187,1,336,0,0.361045," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(5 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(2 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 5 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 4 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{3} + 6 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3}\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a e^{\left(6 \, d x + 6 \, c\right)} + b e^{\left(6 \, d x + 6 \, c\right)} + a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - a e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)}}}{2 \, d}"," ",0,"-1/2*((5*a*b^2 + 3*b^3)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt(a*b)) - 2*(d*x + c)/(a^2 + 2*a*b + b^2) + 2*(2*a^3*e^(4*d*x + 4*c) + 6*a^2*b*e^(4*d*x + 4*c) + 5*a*b^2*e^(4*d*x + 4*c) + 3*b^3*e^(4*d*x + 4*c) + 4*a^3*e^(2*d*x + 2*c) + 4*a^2*b*e^(2*d*x + 2*c) - 4*a*b^2*e^(2*d*x + 2*c) - 6*b^3*e^(2*d*x + 2*c) + 2*a^3 + 6*a^2*b + 7*a*b^2 + 3*b^3)/((a^4 + 2*a^3*b + a^2*b^2)*(a*e^(6*d*x + 6*c) + b*e^(6*d*x + 6*c) + a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) - a*e^(2*d*x + 2*c) + 3*b*e^(2*d*x + 2*c) - a - b)))/d","B",0
188,1,323,0,0.378025," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{{\left(3 \, a b^{2} + 2 \, b^{3}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{5} + 2 \, a^{4} b + a^{3} b^{2}} - \frac{2 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a - 2 \, b\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(\frac{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)}}{a + b} + \frac{2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - 2 \, a b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)}}{a + b} + \frac{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{a + b}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)} {\left(a + b\right)} a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((3*a*b^2 + 2*b^3)*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^5 + 2*a^4*b + a^3*b^2) - 2*(d*x + c)/(a^2 + 2*a*b + b^2) + 2*(a - 2*b)*log(abs(e^(2*d*x + 2*c) - 1))/a^3 - 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + 2*a*b^3)*e^(6*d*x + 6*c)/(a + b) + 2*(a^4 + a^3*b - a^2*b^2 - 2*a*b^3)*e^(4*d*x + 4*c)/(a + b) + (a^4 + 3*a^3*b + 3*a^2*b^2 + 2*a*b^3)*e^(2*d*x + 2*c)/(a + b))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)*(a + b)*a^3*(e^(2*d*x + 2*c) - 1)^2))/d","B",0
189,1,281,0,0.442369," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(7 \, a b^{3} + 5 \, b^{4}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{a b}} + \frac{6 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}} - \frac{6 \, {\left(a b^{3} e^{\left(2 \, d x + 2 \, c\right)} - b^{4} e^{\left(2 \, d x + 2 \, c\right)} + a b^{3} + b^{4}\right)}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}} - \frac{8 \, {\left(3 \, a e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} - 3 \, a e^{\left(2 \, d x + 2 \, c\right)} + 6 \, b e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a - 3 \, b\right)}}{a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(7*a*b^3 + 5*b^4)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt(a*b)) + 6*(d*x + c)/(a^2 + 2*a*b + b^2) - 6*(a*b^3*e^(2*d*x + 2*c) - b^4*e^(2*d*x + 2*c) + a*b^3 + b^4)/((a^5 + 2*a^4*b + a^3*b^2)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)) - 8*(3*a*e^(4*d*x + 4*c) - 3*b*e^(4*d*x + 4*c) - 3*a*e^(2*d*x + 2*c) + 6*b*e^(2*d*x + 2*c) + 2*a - 3*b)/(a^3*(e^(2*d*x + 2*c) - 1)^3))/d","A",0
190,1,408,0,0.601856," ","integrate(tanh(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{3} + 10 \, a^{2} b + 15 \, a b^{2}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sqrt{a b}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(3 \, a^{4} e^{\left(6 \, d x + 6 \, c\right)} + 13 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} + a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 9 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 9 \, a^{4} e^{\left(4 \, d x + 4 \, c\right)} + 21 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} - 9 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, a^{4} e^{\left(2 \, d x + 2 \, c\right)} + 23 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} - 13 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 27 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{4} + 15 \, a^{3} b + 21 \, a^{2} b^{2} + 9 \, a b^{3}\right)}}{{\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*a^3 + 10*a^2*b + 15*a*b^2)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sqrt(a*b)) - 8*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(3*a^4*e^(6*d*x + 6*c) + 13*a^3*b*e^(6*d*x + 6*c) + a^2*b^2*e^(6*d*x + 6*c) - 9*a*b^3*e^(6*d*x + 6*c) + 9*a^4*e^(4*d*x + 4*c) + 21*a^3*b*e^(4*d*x + 4*c) - 9*a^2*b^2*e^(4*d*x + 4*c) + 27*a*b^3*e^(4*d*x + 4*c) + 9*a^4*e^(2*d*x + 2*c) + 23*a^3*b*e^(2*d*x + 2*c) - 13*a^2*b^2*e^(2*d*x + 2*c) - 27*a*b^3*e^(2*d*x + 2*c) + 3*a^4 + 15*a^3*b + 21*a^2*b^2 + 9*a*b^3)/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
191,1,245,0,0.513864," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{3 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} - 4 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 12 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 4 \, a + 12 \, b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b\right)}^{2}}}{4 \, d}"," ",0,"1/4*(2*log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (3*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 - 4*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 12*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 4*a + 12*b)/((a^2 + 2*a*b + b^2)*(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b)^2))/d","B",0
192,1,384,0,0.488305," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} + 6 \, a b - 3 \, b^{2}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(a^{3} e^{\left(6 \, d x + 6 \, c\right)} - 9 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 5 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 5 \, b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - 17 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 13 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 15 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} - 11 \, a^{2} b e^{\left(2 \, d x + 2 \, c\right)} + a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 15 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{3} - 3 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)}}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((a^2 + 6*a*b - 3*b^2)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sqrt(a*b)) - 8*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(a^3*e^(6*d*x + 6*c) - 9*a^2*b*e^(6*d*x + 6*c) - 5*a*b^2*e^(6*d*x + 6*c) + 5*b^3*e^(6*d*x + 6*c) + 3*a^3*e^(4*d*x + 4*c) - 17*a^2*b*e^(4*d*x + 4*c) + 13*a*b^2*e^(4*d*x + 4*c) - 15*b^3*e^(4*d*x + 4*c) + 3*a^3*e^(2*d*x + 2*c) - 11*a^2*b*e^(2*d*x + 2*c) + a*b^2*e^(2*d*x + 2*c) + 15*b^3*e^(2*d*x + 2*c) + a^3 - 3*a^2*b - 9*a*b^2 - 5*b^3)/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
193,1,245,0,0.476905," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{3 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 4 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 4 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} - 4 \, a - 4 \, b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b\right)}^{2}}}{4 \, d}"," ",0,"1/4*(2*log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (3*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 4*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 4*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) - 4*a - 4*b)/((a^2 + 2*a*b + b^2)*(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b)^2))/d","B",0
194,1,388,0,0.440557," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(5 \, a^{3} e^{\left(6 \, d x + 6 \, c\right)} - 5 \, a^{2} b e^{\left(6 \, d x + 6 \, c\right)} - 9 \, a b^{2} e^{\left(6 \, d x + 6 \, c\right)} + b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 15 \, a^{3} e^{\left(4 \, d x + 4 \, c\right)} - 13 \, a^{2} b e^{\left(4 \, d x + 4 \, c\right)} + 17 \, a b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 15 \, a^{3} e^{\left(2 \, d x + 2 \, c\right)} + a^{2} b e^{\left(2 \, d x + 2 \, c\right)} - 11 \, a b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 5 \, a^{3} + 9 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)}}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((3*a^2 - 6*a*b - b^2)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)) - 8*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(5*a^3*e^(6*d*x + 6*c) - 5*a^2*b*e^(6*d*x + 6*c) - 9*a*b^2*e^(6*d*x + 6*c) + b^3*e^(6*d*x + 6*c) + 15*a^3*e^(4*d*x + 4*c) - 13*a^2*b*e^(4*d*x + 4*c) + 17*a*b^2*e^(4*d*x + 4*c) - 3*b^3*e^(4*d*x + 4*c) + 15*a^3*e^(2*d*x + 2*c) + a^2*b*e^(2*d*x + 2*c) - 11*a*b^2*e^(2*d*x + 2*c) + 3*b^3*e^(2*d*x + 2*c) + 5*a^3 + 9*a^2*b + 3*a*b^2 - b^3)/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
195,1,245,0,0.393569," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{3 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 3 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)}^{2} + 12 \, a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 4 \, b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 12 \, a - 4 \, b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + b {\left(e^{\left(2 \, d x + 2 \, c\right)} + e^{\left(-2 \, d x - 2 \, c\right)}\right)} + 2 \, a - 2 \, b\right)}^{2}}}{4 \, d}"," ",0,"1/4*(2*log(abs(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - (3*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 3*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c))^2 + 12*a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 4*b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 12*a - 4*b)/((a^2 + 2*a*b + b^2)*(a*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + b*(e^(2*d*x + 2*c) + e^(-2*d*x - 2*c)) + 2*a - 2*b)^2))/d","B",0
196,1,409,0,0.211120," ","integrate(1/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{{\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b}} + \frac{8 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(9 \, a^{3} b e^{\left(6 \, d x + 6 \, c\right)} - a^{2} b^{2} e^{\left(6 \, d x + 6 \, c\right)} - 13 \, a b^{3} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 27 \, a^{3} b e^{\left(4 \, d x + 4 \, c\right)} - 9 \, a^{2} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 21 \, a b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 9 \, b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 27 \, a^{3} b e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{2} b^{2} e^{\left(2 \, d x + 2 \, c\right)} - 23 \, a b^{3} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 15 \, a b^{3} + 3 \, b^{4}\right)}}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}}}{8 \, d}"," ",0,"1/8*((15*a^2*b + 10*a*b^2 + 3*b^3)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt(a*b)) + 8*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(9*a^3*b*e^(6*d*x + 6*c) - a^2*b^2*e^(6*d*x + 6*c) - 13*a*b^3*e^(6*d*x + 6*c) - 3*b^4*e^(6*d*x + 6*c) + 27*a^3*b*e^(4*d*x + 4*c) - 9*a^2*b^2*e^(4*d*x + 4*c) + 21*a*b^3*e^(4*d*x + 4*c) + 9*b^4*e^(4*d*x + 4*c) + 27*a^3*b*e^(2*d*x + 2*c) + 13*a^2*b^2*e^(2*d*x + 2*c) - 23*a*b^3*e^(2*d*x + 2*c) - 9*b^4*e^(2*d*x + 2*c) + 9*a^3*b + 21*a^2*b^2 + 15*a*b^3 + 3*b^4)/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2))/d","B",0
197,1,295,0,0.490548," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}} + \frac{2 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left({\left(3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + \frac{2 \, {\left(3 \, a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)}}{a + b}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2} {\left(a + b\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*((3*a^2*b + 3*a*b^2 + b^3)*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3) + 2*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*log(abs(e^(2*d*x + 2*c) - 1))/a^3 - 4*((3*a^2*b^2 + a*b^3)*e^(6*d*x + 6*c) + (3*a^2*b^2 + a*b^3)*e^(2*d*x + 2*c) + 2*(3*a^3*b^2 - a^2*b^3 - a*b^4)*e^(4*d*x + 4*c)/(a + b))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2*(a + b)^2*a^3))/d","B",0
198,1,437,0,0.549012," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(35 \, a^{2} b^{2} + 42 \, a b^{3} + 15 \, b^{4}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{a b}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(13 \, a^{3} b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, a^{2} b^{3} e^{\left(6 \, d x + 6 \, c\right)} - 17 \, a b^{4} e^{\left(6 \, d x + 6 \, c\right)} - 7 \, b^{5} e^{\left(6 \, d x + 6 \, c\right)} + 39 \, a^{3} b^{2} e^{\left(4 \, d x + 4 \, c\right)} - 5 \, a^{2} b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 25 \, a b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 21 \, b^{5} e^{\left(4 \, d x + 4 \, c\right)} + 39 \, a^{3} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 25 \, a^{2} b^{3} e^{\left(2 \, d x + 2 \, c\right)} - 35 \, a b^{4} e^{\left(2 \, d x + 2 \, c\right)} - 21 \, b^{5} e^{\left(2 \, d x + 2 \, c\right)} + 13 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 27 \, a b^{4} + 7 \, b^{5}\right)}}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}} + \frac{16}{a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}}}{8 \, d}"," ",0,"-1/8*((35*a^2*b^2 + 42*a*b^3 + 15*b^4)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt(a*b)) - 8*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(13*a^3*b^2*e^(6*d*x + 6*c) + 3*a^2*b^3*e^(6*d*x + 6*c) - 17*a*b^4*e^(6*d*x + 6*c) - 7*b^5*e^(6*d*x + 6*c) + 39*a^3*b^2*e^(4*d*x + 4*c) - 5*a^2*b^3*e^(4*d*x + 4*c) + 25*a*b^4*e^(4*d*x + 4*c) + 21*b^5*e^(4*d*x + 4*c) + 39*a^3*b^2*e^(2*d*x + 2*c) + 25*a^2*b^3*e^(2*d*x + 2*c) - 35*a*b^4*e^(2*d*x + 2*c) - 21*b^5*e^(2*d*x + 2*c) + 13*a^3*b^2 + 33*a^2*b^3 + 27*a*b^4 + 7*b^5)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2) + 16/(a^3*(e^(2*d*x + 2*c) - 1)))/d","B",0
199,1,474,0,1.062228," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{{\left(6 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}} - \frac{2 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(a - 3 \, b\right)} \log\left({\left| e^{\left(2 \, d x + 2 \, c\right)} - 1 \right|}\right)}{a^{4}} - \frac{4 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 11 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(10 \, d x + 10 \, c\right)} + 2 \, {\left(2 \, a^{5} + 6 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 13 \, a b^{4} - 6 \, b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 15 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(2 \, a^{5} + 6 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 13 \, a b^{4} - 6 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 11 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2} {\left(a + b\right)}^{3} a^{3} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((6*a^2*b^2 + 8*a*b^3 + 3*b^4)*log(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)/(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3) - 2*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(a - 3*b)*log(abs(e^(2*d*x + 2*c) - 1))/a^4 - 4*((a^5 + 5*a^4*b + 10*a^3*b^2 + 14*a^2*b^3 + 11*a*b^4 + 3*b^5)*e^(10*d*x + 10*c) + 2*(2*a^5 + 6*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 - 13*a*b^4 - 6*b^5)*e^(8*d*x + 8*c) + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 2*a^2*b^3 + 15*a*b^4 + 9*b^5)*e^(6*d*x + 6*c) + 2*(2*a^5 + 6*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 - 13*a*b^4 - 6*b^5)*e^(4*d*x + 4*c) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 14*a^2*b^3 + 11*a*b^4 + 3*b^5)*e^(2*d*x + 2*c))/((a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2*(a + b)^3*a^3*(e^(2*d*x + 2*c) - 1)^2))/d","B",0
200,1,493,0,1.017014," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(63 \, a^{2} b^{3} + 90 \, a b^{4} + 35 \, b^{5}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{a b}} + \frac{24 \, {\left(d x + c\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{6 \, {\left(17 \, a^{3} b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 7 \, a^{2} b^{4} e^{\left(6 \, d x + 6 \, c\right)} - 21 \, a b^{5} e^{\left(6 \, d x + 6 \, c\right)} - 11 \, b^{6} e^{\left(6 \, d x + 6 \, c\right)} + 51 \, a^{3} b^{3} e^{\left(4 \, d x + 4 \, c\right)} - a^{2} b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 29 \, a b^{5} e^{\left(4 \, d x + 4 \, c\right)} + 33 \, b^{6} e^{\left(4 \, d x + 4 \, c\right)} + 51 \, a^{3} b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 37 \, a^{2} b^{4} e^{\left(2 \, d x + 2 \, c\right)} - 47 \, a b^{5} e^{\left(2 \, d x + 2 \, c\right)} - 33 \, b^{6} e^{\left(2 \, d x + 2 \, c\right)} + 17 \, a^{3} b^{3} + 45 \, a^{2} b^{4} + 39 \, a b^{5} + 11 \, b^{6}\right)}}{{\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{2}} - \frac{16 \, {\left(6 \, a e^{\left(4 \, d x + 4 \, c\right)} - 9 \, b e^{\left(4 \, d x + 4 \, c\right)} - 6 \, a e^{\left(2 \, d x + 2 \, c\right)} + 18 \, b e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a - 9 \, b\right)}}{a^{4} {\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*(63*a^2*b^3 + 90*a*b^4 + 35*b^5)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(a*b)) + 24*(d*x + c)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 6*(17*a^3*b^3*e^(6*d*x + 6*c) + 7*a^2*b^4*e^(6*d*x + 6*c) - 21*a*b^5*e^(6*d*x + 6*c) - 11*b^6*e^(6*d*x + 6*c) + 51*a^3*b^3*e^(4*d*x + 4*c) - a^2*b^4*e^(4*d*x + 4*c) + 29*a*b^5*e^(4*d*x + 4*c) + 33*b^6*e^(4*d*x + 4*c) + 51*a^3*b^3*e^(2*d*x + 2*c) + 37*a^2*b^4*e^(2*d*x + 2*c) - 47*a*b^5*e^(2*d*x + 2*c) - 33*b^6*e^(2*d*x + 2*c) + 17*a^3*b^3 + 45*a^2*b^4 + 39*a*b^5 + 11*b^6)/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^2) - 16*(6*a*e^(4*d*x + 4*c) - 9*b*e^(4*d*x + 4*c) - 6*a*e^(2*d*x + 2*c) + 18*b*e^(2*d*x + 2*c) + 4*a - 9*b)/(a^4*(e^(2*d*x + 2*c) - 1)^3))/d","B",0
201,1,1356,0,0.530311," ","integrate(1/(a+b*tanh(d*x+c)^2)^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(35 \, a^{3} b + 35 \, a^{2} b^{2} + 21 \, a b^{3} + 5 \, b^{4}\right)} \arctan\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + b e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{{\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{a b}} + \frac{48 \, {\left(d x + c\right)}}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{2 \, {\left(87 \, a^{11} b e^{\left(10 \, d x + 10 \, c\right)} + 591 \, a^{10} b^{2} e^{\left(10 \, d x + 10 \, c\right)} + 1533 \, a^{9} b^{3} e^{\left(10 \, d x + 10 \, c\right)} + 1413 \, a^{8} b^{4} e^{\left(10 \, d x + 10 \, c\right)} - 1674 \, a^{7} b^{5} e^{\left(10 \, d x + 10 \, c\right)} - 6426 \, a^{6} b^{6} e^{\left(10 \, d x + 10 \, c\right)} - 8694 \, a^{5} b^{7} e^{\left(10 \, d x + 10 \, c\right)} - 6822 \, a^{4} b^{8} e^{\left(10 \, d x + 10 \, c\right)} - 3357 \, a^{3} b^{9} e^{\left(10 \, d x + 10 \, c\right)} - 1029 \, a^{2} b^{10} e^{\left(10 \, d x + 10 \, c\right)} - 183 \, a b^{11} e^{\left(10 \, d x + 10 \, c\right)} - 15 \, b^{12} e^{\left(10 \, d x + 10 \, c\right)} + 435 \, a^{11} b e^{\left(8 \, d x + 8 \, c\right)} + 2661 \, a^{10} b^{2} e^{\left(8 \, d x + 8 \, c\right)} + 6657 \, a^{9} b^{3} e^{\left(8 \, d x + 8 \, c\right)} + 8871 \, a^{8} b^{4} e^{\left(8 \, d x + 8 \, c\right)} + 7950 \, a^{7} b^{5} e^{\left(8 \, d x + 8 \, c\right)} + 8610 \, a^{6} b^{6} e^{\left(8 \, d x + 8 \, c\right)} + 12306 \, a^{5} b^{7} e^{\left(8 \, d x + 8 \, c\right)} + 13182 \, a^{4} b^{8} e^{\left(8 \, d x + 8 \, c\right)} + 8751 \, a^{3} b^{9} e^{\left(8 \, d x + 8 \, c\right)} + 3465 \, a^{2} b^{10} e^{\left(8 \, d x + 8 \, c\right)} + 765 \, a b^{11} e^{\left(8 \, d x + 8 \, c\right)} + 75 \, b^{12} e^{\left(8 \, d x + 8 \, c\right)} + 870 \, a^{11} b e^{\left(6 \, d x + 6 \, c\right)} + 5278 \, a^{10} b^{2} e^{\left(6 \, d x + 6 \, c\right)} + 13722 \, a^{9} b^{3} e^{\left(6 \, d x + 6 \, c\right)} + 19602 \, a^{8} b^{4} e^{\left(6 \, d x + 6 \, c\right)} + 14908 \, a^{7} b^{5} e^{\left(6 \, d x + 6 \, c\right)} + 300 \, a^{6} b^{6} e^{\left(6 \, d x + 6 \, c\right)} - 14412 \, a^{5} b^{7} e^{\left(6 \, d x + 6 \, c\right)} - 19228 \, a^{4} b^{8} e^{\left(6 \, d x + 6 \, c\right)} - 13698 \, a^{3} b^{9} e^{\left(6 \, d x + 6 \, c\right)} - 5802 \, a^{2} b^{10} e^{\left(6 \, d x + 6 \, c\right)} - 1390 \, a b^{11} e^{\left(6 \, d x + 6 \, c\right)} - 150 \, b^{12} e^{\left(6 \, d x + 6 \, c\right)} + 870 \, a^{11} b e^{\left(4 \, d x + 4 \, c\right)} + 5778 \, a^{10} b^{2} e^{\left(4 \, d x + 4 \, c\right)} + 16362 \, a^{9} b^{3} e^{\left(4 \, d x + 4 \, c\right)} + 26190 \, a^{8} b^{4} e^{\left(4 \, d x + 4 \, c\right)} + 27996 \, a^{7} b^{5} e^{\left(4 \, d x + 4 \, c\right)} + 25620 \, a^{6} b^{6} e^{\left(4 \, d x + 4 \, c\right)} + 24948 \, a^{5} b^{7} e^{\left(4 \, d x + 4 \, c\right)} + 22332 \, a^{4} b^{8} e^{\left(4 \, d x + 4 \, c\right)} + 14430 \, a^{3} b^{9} e^{\left(4 \, d x + 4 \, c\right)} + 5946 \, a^{2} b^{10} e^{\left(4 \, d x + 4 \, c\right)} + 1410 \, a b^{11} e^{\left(4 \, d x + 4 \, c\right)} + 150 \, b^{12} e^{\left(4 \, d x + 4 \, c\right)} + 435 \, a^{11} b e^{\left(2 \, d x + 2 \, c\right)} + 3411 \, a^{10} b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 11433 \, a^{9} b^{3} e^{\left(2 \, d x + 2 \, c\right)} + 20793 \, a^{8} b^{4} e^{\left(2 \, d x + 2 \, c\right)} + 20526 \, a^{7} b^{5} e^{\left(2 \, d x + 2 \, c\right)} + 6510 \, a^{6} b^{6} e^{\left(2 \, d x + 2 \, c\right)} - 9534 \, a^{5} b^{7} e^{\left(2 \, d x + 2 \, c\right)} - 14622 \, a^{4} b^{8} e^{\left(2 \, d x + 2 \, c\right)} - 9777 \, a^{3} b^{9} e^{\left(2 \, d x + 2 \, c\right)} - 3729 \, a^{2} b^{10} e^{\left(2 \, d x + 2 \, c\right)} - 795 \, a b^{11} e^{\left(2 \, d x + 2 \, c\right)} - 75 \, b^{12} e^{\left(2 \, d x + 2 \, c\right)} - 549755813673 \, a^{11} b + 841 \, a^{10} b^{2} + 3669 \, a^{9} b^{3} + 9531 \, a^{8} b^{4} + 16374 \, a^{7} b^{5} + 19530 \, a^{6} b^{6} + 16506 \, a^{5} b^{7} + 9894 \, a^{4} b^{8} + 4131 \, a^{3} b^{9} + 1149 \, a^{2} b^{10} + 193 \, a b^{11} + 15 \, b^{12}\right)}}{{\left(a^{13} + 10 \, a^{12} b + 45 \, a^{11} b^{2} + 120 \, a^{10} b^{3} + 210 \, a^{9} b^{4} + 252 \, a^{8} b^{5} + 210 \, a^{7} b^{6} + 120 \, a^{6} b^{7} + 45 \, a^{5} b^{8} + 10 \, a^{4} b^{9} + a^{3} b^{10}\right)} {\left(a e^{\left(4 \, d x + 4 \, c\right)} + b e^{\left(4 \, d x + 4 \, c\right)} + 2 \, a e^{\left(2 \, d x + 2 \, c\right)} - 2 \, b e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}^{3}}}{48 \, d}"," ",0,"1/48*(3*(35*a^3*b + 35*a^2*b^2 + 21*a*b^3 + 5*b^4)*arctan(1/2*(a*e^(2*d*x + 2*c) + b*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*sqrt(a*b)) + 48*(d*x + c)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 2*(87*a^11*b*e^(10*d*x + 10*c) + 591*a^10*b^2*e^(10*d*x + 10*c) + 1533*a^9*b^3*e^(10*d*x + 10*c) + 1413*a^8*b^4*e^(10*d*x + 10*c) - 1674*a^7*b^5*e^(10*d*x + 10*c) - 6426*a^6*b^6*e^(10*d*x + 10*c) - 8694*a^5*b^7*e^(10*d*x + 10*c) - 6822*a^4*b^8*e^(10*d*x + 10*c) - 3357*a^3*b^9*e^(10*d*x + 10*c) - 1029*a^2*b^10*e^(10*d*x + 10*c) - 183*a*b^11*e^(10*d*x + 10*c) - 15*b^12*e^(10*d*x + 10*c) + 435*a^11*b*e^(8*d*x + 8*c) + 2661*a^10*b^2*e^(8*d*x + 8*c) + 6657*a^9*b^3*e^(8*d*x + 8*c) + 8871*a^8*b^4*e^(8*d*x + 8*c) + 7950*a^7*b^5*e^(8*d*x + 8*c) + 8610*a^6*b^6*e^(8*d*x + 8*c) + 12306*a^5*b^7*e^(8*d*x + 8*c) + 13182*a^4*b^8*e^(8*d*x + 8*c) + 8751*a^3*b^9*e^(8*d*x + 8*c) + 3465*a^2*b^10*e^(8*d*x + 8*c) + 765*a*b^11*e^(8*d*x + 8*c) + 75*b^12*e^(8*d*x + 8*c) + 870*a^11*b*e^(6*d*x + 6*c) + 5278*a^10*b^2*e^(6*d*x + 6*c) + 13722*a^9*b^3*e^(6*d*x + 6*c) + 19602*a^8*b^4*e^(6*d*x + 6*c) + 14908*a^7*b^5*e^(6*d*x + 6*c) + 300*a^6*b^6*e^(6*d*x + 6*c) - 14412*a^5*b^7*e^(6*d*x + 6*c) - 19228*a^4*b^8*e^(6*d*x + 6*c) - 13698*a^3*b^9*e^(6*d*x + 6*c) - 5802*a^2*b^10*e^(6*d*x + 6*c) - 1390*a*b^11*e^(6*d*x + 6*c) - 150*b^12*e^(6*d*x + 6*c) + 870*a^11*b*e^(4*d*x + 4*c) + 5778*a^10*b^2*e^(4*d*x + 4*c) + 16362*a^9*b^3*e^(4*d*x + 4*c) + 26190*a^8*b^4*e^(4*d*x + 4*c) + 27996*a^7*b^5*e^(4*d*x + 4*c) + 25620*a^6*b^6*e^(4*d*x + 4*c) + 24948*a^5*b^7*e^(4*d*x + 4*c) + 22332*a^4*b^8*e^(4*d*x + 4*c) + 14430*a^3*b^9*e^(4*d*x + 4*c) + 5946*a^2*b^10*e^(4*d*x + 4*c) + 1410*a*b^11*e^(4*d*x + 4*c) + 150*b^12*e^(4*d*x + 4*c) + 435*a^11*b*e^(2*d*x + 2*c) + 3411*a^10*b^2*e^(2*d*x + 2*c) + 11433*a^9*b^3*e^(2*d*x + 2*c) + 20793*a^8*b^4*e^(2*d*x + 2*c) + 20526*a^7*b^5*e^(2*d*x + 2*c) + 6510*a^6*b^6*e^(2*d*x + 2*c) - 9534*a^5*b^7*e^(2*d*x + 2*c) - 14622*a^4*b^8*e^(2*d*x + 2*c) - 9777*a^3*b^9*e^(2*d*x + 2*c) - 3729*a^2*b^10*e^(2*d*x + 2*c) - 795*a*b^11*e^(2*d*x + 2*c) - 75*b^12*e^(2*d*x + 2*c) - 549755813673*a^11*b + 841*a^10*b^2 + 3669*a^9*b^3 + 9531*a^8*b^4 + 16374*a^7*b^5 + 19530*a^6*b^6 + 16506*a^5*b^7 + 9894*a^4*b^8 + 4131*a^3*b^9 + 1149*a^2*b^10 + 193*a*b^11 + 15*b^12)/((a^13 + 10*a^12*b + 45*a^11*b^2 + 120*a^10*b^3 + 210*a^9*b^4 + 252*a^8*b^5 + 210*a^7*b^6 + 120*a^6*b^7 + 45*a^5*b^8 + 10*a^4*b^9 + a^3*b^10)*(a*e^(4*d*x + 4*c) + b*e^(4*d*x + 4*c) + 2*a*e^(2*d*x + 2*c) - 2*b*e^(2*d*x + 2*c) + a + b)^3))/d","B",0
202,1,5,0,0.132807," ","integrate((1-tanh(x)^2)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(e^{x}\right)"," ",0,"2*arctan(e^x)","A",0
203,1,1,0,0.125834," ","integrate((-1+tanh(x)^2)^(1/2),x, algorithm=""giac"")","0"," ",0,"0","A",0
204,1,45,0,0.124790," ","integrate((1-tanh(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, \pi - \frac{e^{\left(-x\right)} - e^{x}}{{\left(e^{\left(-x\right)} - e^{x}\right)}^{2} + 4} + \frac{1}{2} \, \arctan\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right)"," ",0,"1/4*pi - (e^(-x) - e^x)/((e^(-x) - e^x)^2 + 4) + 1/2*arctan(1/2*(e^(2*x) - 1)*e^(-x))","B",0
205,1,41,0,0.117579," ","integrate((-1+tanh(x)^2)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{-e^{\left(2 \, x\right)}} + \frac{1}{\sqrt{-e^{\left(2 \, x\right)}}}}{{\left(\sqrt{-e^{\left(2 \, x\right)}} + \frac{1}{\sqrt{-e^{\left(2 \, x\right)}}}\right)}^{2} - 4}"," ",0,"(sqrt(-e^(2*x)) + 1/sqrt(-e^(2*x)))/((sqrt(-e^(2*x)) + 1/sqrt(-e^(2*x)))^2 - 4)","A",0
206,1,11,0,0.141220," ","integrate(1/(1-tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, e^{\left(-x\right)} + \frac{1}{2} \, e^{x}"," ",0,"-1/2*e^(-x) + 1/2*e^x","A",0
207,1,21,0,0.130420," ","integrate(1/(-1+tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-e^{\left(2 \, x\right)}} - \frac{1}{2 \, \sqrt{-e^{\left(2 \, x\right)}}}"," ",0,"-1/2*sqrt(-e^(2*x)) - 1/2/sqrt(-e^(2*x))","A",0
208,1,980,0,2.949520," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^5,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{4 \, {\left(15 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{9} {\left(2 \, a + 3 \, b\right)} + 15 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{8} {\left(10 \, a + 9 \, b\right)} \sqrt{a + b} + 20 \, {\left(18 \, a^{2} + 23 \, a b + b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{7} + 20 \, {\left(30 \, a^{2} - 7 \, a b - 65 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{6} \sqrt{a + b} + 2 \, {\left(330 \, a^{3} - 705 \, a^{2} b - 1480 \, a b^{2} + 19 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} + 10 \, {\left(18 \, a^{3} - 279 \, a^{2} b + 68 \, a b^{2} + 349 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} - 20 \, {\left(30 \, a^{4} + 81 \, a^{3} b - 149 \, a^{2} b^{2} - 245 \, a b^{3} + 19 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} - 20 \, {\left(42 \, a^{4} - 33 \, a^{3} b - 139 \, a^{2} b^{2} + 69 \, a b^{3} + 325 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} - 5 \, {\left(90 \, a^{5} - 121 \, a^{4} b - 184 \, a^{3} b^{2} + 658 \, a^{2} b^{3} + 166 \, a b^{4} - 1233 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(90 \, a^{5} - 215 \, a^{4} b + 240 \, a^{3} b^{2} + 638 \, a^{2} b^{3} - 2034 \, a b^{4} + 1713 \, b^{5}\right)} \sqrt{a + b}\right)}}{15 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{5}}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 4/15*(15*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^9*(2*a + 3*b) + 15*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^8*(10*a + 9*b)*sqrt(a + b) + 20*(18*a^2 + 23*a*b + b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^7 + 20*(30*a^2 - 7*a*b - 65*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^6*sqrt(a + b) + 2*(330*a^3 - 705*a^2*b - 1480*a*b^2 + 19*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 + 10*(18*a^3 - 279*a^2*b + 68*a*b^2 + 349*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) - 20*(30*a^4 + 81*a^3*b - 149*a^2*b^2 - 245*a*b^3 + 19*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 - 20*(42*a^4 - 33*a^3*b - 139*a^2*b^2 + 69*a*b^3 + 325*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) - 5*(90*a^5 - 121*a^4*b - 184*a^3*b^2 + 658*a^2*b^3 + 166*a*b^4 - 1233*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (90*a^5 - 215*a^4*b + 240*a^3*b^2 + 638*a^2*b^3 - 2034*a*b^4 + 1713*b^5)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^5","B",0
209,1,938,0,3.036269," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^4,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) + \frac{{\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{4 \, \sqrt{-b} b} - \frac{{\left(a^{2} + 12 \, a b + 16 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{7} + {\left(7 \, a^{2} + 52 \, a b + 16 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{6} \sqrt{a + b} + {\left(21 \, a^{3} + 109 \, a^{2} b + 28 \, a b^{2} - 48 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} + {\left(35 \, a^{3} + 115 \, a^{2} b - 156 \, a b^{2} - 176 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} + {\left(35 \, a^{4} + 130 \, a^{3} b - 317 \, a^{2} b^{2} - 156 \, a b^{3} + 304 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} + {\left(21 \, a^{4} + 94 \, a^{3} b - 379 \, a^{2} b^{2} + 476 \, a b^{3} + 48 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} + {\left(7 \, a^{5} + 53 \, a^{4} b - 135 \, a^{3} b^{2} + 271 \, a^{2} b^{3} - 140 \, a b^{4} - 272 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} + {\left(a^{5} + 11 \, a^{4} b - 17 \, a^{3} b^{2} + 65 \, a^{2} b^{3} - 116 \, a b^{4} + 112 \, b^{5}\right)} \sqrt{a + b}}{2 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{4} b}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) + 1/4*(a^2 - 4*a*b - 8*b^2)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/(sqrt(-b)*b) - 1/2*((a^2 + 12*a*b + 16*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^7 + (7*a^2 + 52*a*b + 16*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^6*sqrt(a + b) + (21*a^3 + 109*a^2*b + 28*a*b^2 - 48*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 + (35*a^3 + 115*a^2*b - 156*a*b^2 - 176*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) + (35*a^4 + 130*a^3*b - 317*a^2*b^2 - 156*a*b^3 + 304*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 + (21*a^4 + 94*a^3*b - 379*a^2*b^2 + 476*a*b^3 + 48*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) + (7*a^5 + 53*a^4*b - 135*a^3*b^2 + 271*a^2*b^3 - 140*a*b^4 - 272*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) + (a^5 + 11*a^4*b - 17*a^3*b^2 + 65*a^2*b^3 - 116*a*b^4 + 112*b^5)*sqrt(a + b))/(((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^4*b)","B",0
210,1,630,0,2.177413," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^3,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{4 \, {\left(3 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} {\left(a + 2 \, b\right)} + 3 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} {\left(3 \, a + 2 \, b\right)} \sqrt{a + b} + 2 \, {\left(3 \, a^{2} - 3 \, a b - 10 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} - 6 \, {\left(a^{2} + 3 \, a b + 6 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} - 3 \, {\left(3 \, a^{3} + 4 \, a^{2} b - 9 \, a b^{2} - 26 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(3 \, a^{3} - 17 \, a b^{2} + 34 \, b^{3}\right)} \sqrt{a + b}\right)}}{3 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{3}}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 4/3*(3*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5*(a + 2*b) + 3*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*(3*a + 2*b)*sqrt(a + b) + 2*(3*a^2 - 3*a*b - 10*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 - 6*(a^2 + 3*a*b + 6*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) - 3*(3*a^3 + 4*a^2*b - 9*a*b^2 - 26*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (3*a^3 - 17*a*b^2 + 34*b^3)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^3","B",0
211,1,554,0,1.743713," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""giac"")","-\frac{{\left(a + 2 \, b\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{\sqrt{-b}} - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{2 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} {\left(a + 2 \, b\right)} + {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} {\left(3 \, a - 2 \, b\right)} \sqrt{a + b} + {\left(3 \, a^{2} - 3 \, a b - 2 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} + {\left(a^{2} - a b + 2 \, b^{2}\right)} \sqrt{a + b}\right)}}{{\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{2}}"," ",0,"-(a + 2*b)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/sqrt(-b) - 1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 2*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3*(a + 2*b) + (sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*(3*a - 2*b)*sqrt(a + b) + (3*a^2 - 3*a*b - 2*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) + (a^2 - a*b + 2*b^2)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^2","B",0
212,1,349,0,0.989314," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{4 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} b - \sqrt{a + b} b\right)}}{{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 4*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*b - sqrt(a + b)*b)/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)","B",0
213,1,253,0,0.690002," ","integrate((a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, b \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{\sqrt{-b}} - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right)"," ",0,"-2*b*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/sqrt(-b) - 1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b)))","B",0
214,1,255,0,0.764763," ","integrate(coth(x)*(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, a \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right)"," ",0,"2*a*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))/sqrt(-a))/sqrt(-a) - 1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b)))","B",0
215,1,348,0,1.071677," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) + \frac{4 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} a + \sqrt{a + b} a\right)}}{{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} - 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} - 3 \, a + b}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) + 4*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*a + sqrt(a + b)*a)/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 - 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) - 3*a + b)","B",0
216,1,557,0,1.757097," ","integrate(coth(x)^3*(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, a + b\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) + \frac{2 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} {\left(2 \, a + b\right)} + {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} {\left(2 \, a - 3 \, b\right)} \sqrt{a + b} - {\left(2 \, a^{2} + 3 \, a b - 3 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(2 \, a^{2} - a b + b^{2}\right)} \sqrt{a + b}\right)}}{{\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} - 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} - 3 \, a + b\right)}^{2}}"," ",0,"(2*a + b)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))/sqrt(-a))/sqrt(-a) - 1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) + 2*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3*(2*a + b) + (sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*(2*a - 3*b)*sqrt(a + b) - (2*a^2 + 3*a*b - 3*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (2*a^2 - a*b + b^2)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 - 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) - 3*a + b)^2","B",0
217,1,629,0,2.215493," ","integrate(coth(x)^4*(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) + \frac{4 \, {\left(3 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} {\left(2 \, a + b\right)} - 3 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} {\left(2 \, a + 3 \, b\right)} \sqrt{a + b} - 2 \, {\left(10 \, a^{2} + 3 \, a b - 3 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} + 6 \, {\left(6 \, a^{2} + 3 \, a b + b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} + 3 \, {\left(26 \, a^{3} + 9 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} + {\left(34 \, a^{3} - 17 \, a^{2} b + 3 \, b^{3}\right)} \sqrt{a + b}\right)}}{3 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} - 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} - 3 \, a + b\right)}^{3}}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) + 4/3*(3*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5*(2*a + b) - 3*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*(2*a + 3*b)*sqrt(a + b) - 2*(10*a^2 + 3*a*b - 3*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 + 6*(6*a^2 + 3*a*b + b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) + 3*(26*a^3 + 9*a^2*b - 4*a*b^2 - 3*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) + (34*a^3 - 17*a^2*b + 3*b^3)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 - 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) - 3*a + b)^3","B",0
218,1,947,0,3.117516," ","integrate(coth(x)^5*(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right) + \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) + \frac{{\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b}}{2 \, \sqrt{-a}}\right)}{4 \, \sqrt{-a} a} + \frac{{\left(16 \, a^{2} + 12 \, a b + b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{7} - {\left(16 \, a^{2} + 52 \, a b + 7 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{6} \sqrt{a + b} - {\left(48 \, a^{3} - 28 \, a^{2} b - 109 \, a b^{2} - 21 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} + {\left(176 \, a^{3} + 156 \, a^{2} b - 115 \, a b^{2} - 35 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} + {\left(304 \, a^{4} - 156 \, a^{3} b - 317 \, a^{2} b^{2} + 130 \, a b^{3} + 35 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} - {\left(48 \, a^{4} + 476 \, a^{3} b - 379 \, a^{2} b^{2} + 94 \, a b^{3} + 21 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} - {\left(272 \, a^{5} + 140 \, a^{4} b - 271 \, a^{3} b^{2} + 135 \, a^{2} b^{3} - 53 \, a b^{4} - 7 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(112 \, a^{5} - 116 \, a^{4} b + 65 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 11 \, a b^{4} + b^{5}\right)} \sqrt{a + b}}{2 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} - 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} - 3 \, a + b\right)}^{4} a}"," ",0,"-1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b))) + 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*sqrt(a + b)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) + 1/4*(8*a^2 + 4*a*b - b^2)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))/sqrt(-a))/(sqrt(-a)*a) + 1/2*((16*a^2 + 12*a*b + b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^7 - (16*a^2 + 52*a*b + 7*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^6*sqrt(a + b) - (48*a^3 - 28*a^2*b - 109*a*b^2 - 21*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 + (176*a^3 + 156*a^2*b - 115*a*b^2 - 35*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) + (304*a^4 - 156*a^3*b - 317*a^2*b^2 + 130*a*b^3 + 35*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 - (48*a^4 + 476*a^3*b - 379*a^2*b^2 + 94*a*b^3 + 21*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) - (272*a^5 + 140*a^4*b - 271*a^3*b^2 + 135*a^2*b^3 - 53*a*b^4 - 7*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (112*a^5 - 116*a^4*b + 65*a^3*b^2 - 17*a^2*b^3 + 11*a*b^4 + b^5)*sqrt(a + b))/(((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 - 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) - 3*a + b)^4*a)","B",0
219,1,1063,0,4.081300," ","integrate(tanh(x)^3*(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{4 \, {\left(15 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{9} + 15 \, {\left(7 \, a^{2} + 20 \, a b + 9 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{8} \sqrt{a + b} + 20 \, {\left(15 \, a^{3} + 39 \, a^{2} b + 21 \, a b^{2} + b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{7} + 20 \, {\left(21 \, a^{3} + 21 \, a^{2} b - 57 \, a b^{2} - 65 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{6} \sqrt{a + b} + 2 \, {\left(105 \, a^{4} - 210 \, a^{3} b - 1860 \, a^{2} b^{2} - 1590 \, a b^{3} + 19 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} - 10 \, {\left(21 \, a^{4} + 126 \, a^{3} b + 288 \, a^{2} b^{2} - 390 \, a b^{3} - 349 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} - 20 \, {\left(21 \, a^{5} + 63 \, a^{4} b - 18 \, a^{3} b^{2} - 378 \, a^{2} b^{3} - 235 \, a b^{4} + 19 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} - 20 \, {\left(15 \, a^{5} + 21 \, a^{4} b - 126 \, a^{3} b^{2} - 90 \, a^{2} b^{3} + 367 \, a b^{4} + 325 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} - 5 \, {\left(21 \, a^{6} + 24 \, a^{5} b - 243 \, a^{4} b^{2} + 280 \, a^{3} b^{3} + 815 \, a^{2} b^{4} - 944 \, a b^{5} - 1233 \, b^{6}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(15 \, a^{6} - 165 \, a^{4} b^{2} + 920 \, a^{3} b^{3} - 1147 \, a^{2} b^{4} - 504 \, a b^{5} + 1713 \, b^{6}\right)} \sqrt{a + b}\right)}}{15 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{5}}"," ",0,"1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 4/15*(15*(a^2 + 4*a*b + 3*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^9 + 15*(7*a^2 + 20*a*b + 9*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^8*sqrt(a + b) + 20*(15*a^3 + 39*a^2*b + 21*a*b^2 + b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^7 + 20*(21*a^3 + 21*a^2*b - 57*a*b^2 - 65*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^6*sqrt(a + b) + 2*(105*a^4 - 210*a^3*b - 1860*a^2*b^2 - 1590*a*b^3 + 19*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 - 10*(21*a^4 + 126*a^3*b + 288*a^2*b^2 - 390*a*b^3 - 349*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) - 20*(21*a^5 + 63*a^4*b - 18*a^3*b^2 - 378*a^2*b^3 - 235*a*b^4 + 19*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 - 20*(15*a^5 + 21*a^4*b - 126*a^3*b^2 - 90*a^2*b^3 + 367*a*b^4 + 325*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) - 5*(21*a^6 + 24*a^5*b - 243*a^4*b^2 + 280*a^3*b^3 + 815*a^2*b^4 - 944*a*b^5 - 1233*b^6)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (15*a^6 - 165*a^4*b^2 + 920*a^3*b^3 - 1147*a^2*b^4 - 504*a*b^5 + 1713*b^6)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^5","B",0
220,1,949,0,3.671148," ","integrate(tanh(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(3 \, a^{2} + 12 \, a b + 8 \, b^{2}\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{4 \, \sqrt{-b}} - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{{\left(5 \, a^{2} + 20 \, a b + 16 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{7} + {\left(35 \, a^{2} + 76 \, a b + 16 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{6} \sqrt{a + b} + {\left(105 \, a^{3} + 153 \, a^{2} b - 28 \, a b^{2} - 48 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} + {\left(175 \, a^{3} - 25 \, a^{2} b - 260 \, a b^{2} - 176 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} + {\left(175 \, a^{4} - 110 \, a^{3} b - 417 \, a^{2} b^{2} + 60 \, a b^{3} + 304 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} + {\left(105 \, a^{4} - 210 \, a^{3} b - 55 \, a^{2} b^{2} + 484 \, a b^{3} + 48 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} + {\left(35 \, a^{5} - 79 \, a^{4} b + 53 \, a^{3} b^{2} + 195 \, a^{2} b^{3} - 308 \, a b^{4} - 272 \, b^{5}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} + {\left(5 \, a^{5} - 17 \, a^{4} b + 51 \, a^{3} b^{2} - 19 \, a^{2} b^{3} - 44 \, a b^{4} + 112 \, b^{5}\right)} \sqrt{a + b}}{2 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{4}}"," ",0,"-1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 1/4*(3*a^2 + 12*a*b + 8*b^2)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/sqrt(-b) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 1/2*((5*a^2 + 20*a*b + 16*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^7 + (35*a^2 + 76*a*b + 16*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^6*sqrt(a + b) + (105*a^3 + 153*a^2*b - 28*a*b^2 - 48*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 + (175*a^3 - 25*a^2*b - 260*a*b^2 - 176*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) + (175*a^4 - 110*a^3*b - 417*a^2*b^2 + 60*a*b^3 + 304*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 + (105*a^4 - 210*a^3*b - 55*a^2*b^2 + 484*a*b^3 + 48*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) + (35*a^5 - 79*a^4*b + 53*a^3*b^2 + 195*a^2*b^3 - 308*a*b^4 - 272*b^5)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) + (5*a^5 - 17*a^4*b + 51*a^3*b^2 - 19*a^2*b^3 - 44*a*b^4 + 112*b^5)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^4","B",0
221,1,662,0,2.591325," ","integrate(tanh(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{8 \, {\left(3 \, {\left(a b + b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{5} + 3 \, {\left(3 \, a b + b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{4} \sqrt{a + b} + 2 \, {\left(3 \, a^{2} b - 6 \, a b^{2} - 5 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} - 6 \, {\left(a^{2} b + 4 \, a b^{2} + 3 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} - 3 \, {\left(3 \, a^{3} b + a^{2} b^{2} - 15 \, a b^{3} - 13 \, b^{4}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} - {\left(3 \, a^{3} b - 9 \, a^{2} b^{2} + 5 \, a b^{3} + 17 \, b^{4}\right)} \sqrt{a + b}\right)}}{3 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{3}}"," ",0,"1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 8/3*(3*(a*b + b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^5 + 3*(3*a*b + b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^4*sqrt(a + b) + 2*(3*a^2*b - 6*a*b^2 - 5*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 - 6*(a^2*b + 4*a*b^2 + 3*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) - 3*(3*a^3*b + a^2*b^2 - 15*a*b^3 - 13*b^4)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) - (3*a^3*b - 9*a^2*b^2 + 5*a*b^3 + 17*b^4)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^3","B",0
222,1,584,0,1.996522," ","integrate((a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{\sqrt{-b}} - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{2 \, {\left({\left(a b + 2 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{3} + {\left(3 \, a b - 2 \, b^{2}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} \sqrt{a + b} + {\left(3 \, a^{2} b - 3 \, a b^{2} - 2 \, b^{3}\right)} {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} + {\left(a^{2} b - a b^{2} + 2 \, b^{3}\right)} \sqrt{a + b}\right)}}{{\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b\right)}^{2}}"," ",0,"-1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - (3*a*b + 2*b^2)*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/sqrt(-b) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 2*((a*b + 2*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^3 + (3*a*b - 2*b^2)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2*sqrt(a + b) + (3*a^2*b - 3*a*b^2 - 2*b^3)*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b)) + (a^2*b - a*b^2 + 2*b^3)*sqrt(a + b))/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)^2","B",0
223,1,433,0,2.776451," ","integrate(coth(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, a^{2} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a}} + \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) - \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{4 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} b^{2} - \sqrt{a + b} b^{2}\right)}}{{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} + 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} + a - 3 \, b}"," ",0,"2*a^2*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))/sqrt(-a))/sqrt(-a) + 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) - 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 4*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*b^2 - sqrt(a + b)*b^2)/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 + 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) + a - 3*b)","B",0
224,1,430,0,2.794699," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, b^{2} \arctan\left(-\frac{\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b}}{2 \, \sqrt{-b}}\right)}{\sqrt{-b}} - \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right) + \frac{1}{2} \, {\left(a + b\right)}^{\frac{3}{2}} \log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right) - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} + \frac{4 \, {\left({\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} a^{2} + \sqrt{a + b} a^{2}\right)}}{{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)}^{2} - 2 \, {\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} \sqrt{a + b} - 3 \, a + b}"," ",0,"-2*b^2*arctan(-1/2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))/sqrt(-b))/sqrt(-b) - 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b))) + 1/2*(a + b)^(3/2)*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b))) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) + 4*((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*a^2 + sqrt(a + b)*a^2)/((sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))^2 - 2*(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*sqrt(a + b) - 3*a + b)","B",0
225,1,104,0,0.154041," ","integrate((1+tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1}{\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} - 1}\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/2*sqrt(2)*(sqrt(2)*log((sqrt(2) - sqrt(e^(4*x) + 1) + e^(2*x) + 1)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) - 1)) + log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + log(sqrt(e^(4*x) + 1) - e^(2*x)) - log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","B",0
226,1,104,0,0.165724," ","integrate((-1-tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1}{\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} - 1}\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/2*I*sqrt(2)*(sqrt(2)*log((sqrt(2) - sqrt(e^(4*x) + 1) + e^(2*x) + 1)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) - 1)) + log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + log(sqrt(e^(4*x) + 1) - e^(2*x)) - log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","C",0
227,1,202,0,0.139318," ","integrate((1+tanh(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} {\left(5 \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1}{\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} - 1}\right) - \frac{4 \, {\left(3 \, {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{3} - {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} - \sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} - 1\right)}}{{\left({\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} - 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} + 2 \, e^{\left(2 \, x\right)} - 1\right)}^{2}} + 4 \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + 4 \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - 4 \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/4*sqrt(2)*(5*sqrt(2)*log((sqrt(2) - sqrt(e^(4*x) + 1) + e^(2*x) + 1)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) - 1)) - 4*(3*(sqrt(e^(4*x) + 1) - e^(2*x))^3 - (sqrt(e^(4*x) + 1) - e^(2*x))^2 - sqrt(e^(4*x) + 1) + e^(2*x) - 1)/((sqrt(e^(4*x) + 1) - e^(2*x))^2 - 2*sqrt(e^(4*x) + 1) + 2*e^(2*x) - 1)^2 + 4*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + 4*log(sqrt(e^(4*x) + 1) - e^(2*x)) - 4*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","B",0
228,1,204,0,0.171604," ","integrate((-1-tanh(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} {\left(-5 i \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1}{\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} - 1}\right) - \frac{4 \, {\left(-3 i \, {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{3} + i \, {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} + i \, \sqrt{e^{\left(4 \, x\right)} + 1} - i \, e^{\left(2 \, x\right)} + i\right)}}{{\left({\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} - 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} + 2 \, e^{\left(2 \, x\right)} - 1\right)}^{2}} - 4 i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) - 4 i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) + 4 i \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/4*sqrt(2)*(-5*I*sqrt(2)*log((sqrt(2) - sqrt(e^(4*x) + 1) + e^(2*x) + 1)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) - 1)) - 4*(-3*I*(sqrt(e^(4*x) + 1) - e^(2*x))^3 + I*(sqrt(e^(4*x) + 1) - e^(2*x))^2 + I*sqrt(e^(4*x) + 1) - I*e^(2*x) + I)/((sqrt(e^(4*x) + 1) - e^(2*x))^2 - 2*sqrt(e^(4*x) + 1) + 2*e^(2*x) - 1)^2 - 4*I*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) - 4*I*log(sqrt(e^(4*x) + 1) - e^(2*x)) + 4*I*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","C",0
229,-2,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.99Error: Bad Argument Type","F(-2)",0
230,-2,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.6Error: Bad Argument Type","F(-2)",0
231,-2,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
232,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
233,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
234,1,188,0,0.321889," ","integrate(1/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -{\left(\sqrt{a + b} e^{\left(2 \, x\right)} - \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b}\right)} {\left(a + b\right)} - \sqrt{a + b} {\left(a - b\right)} \right|}\right)}{2 \, \sqrt{a + b}} - \frac{\log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} + \sqrt{a + b} \right|}\right)}{2 \, \sqrt{a + b}} + \frac{\log\left({\left| -\sqrt{a + b} e^{\left(2 \, x\right)} + \sqrt{a e^{\left(4 \, x\right)} + b e^{\left(4 \, x\right)} + 2 \, a e^{\left(2 \, x\right)} - 2 \, b e^{\left(2 \, x\right)} + a + b} - \sqrt{a + b} \right|}\right)}{2 \, \sqrt{a + b}}"," ",0,"-1/2*log(abs(-(sqrt(a + b)*e^(2*x) - sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b))*(a + b) - sqrt(a + b)*(a - b)))/sqrt(a + b) - 1/2*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) + sqrt(a + b)))/sqrt(a + b) + 1/2*log(abs(-sqrt(a + b)*e^(2*x) + sqrt(a*e^(4*x) + b*e^(4*x) + 2*a*e^(2*x) - 2*b*e^(2*x) + a + b) - sqrt(a + b)))/sqrt(a + b)","B",0
235,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
236,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
237,-2,0,0,0.000000," ","integrate(coth(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.68Error: Bad Argument Type","F(-2)",0
238,-2,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 1.35Error: Bad Argument Type","F(-2)",0
239,-2,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
240,-2,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Error: Bad Argument Type","F(-2)",0
241,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Error: Bad Argument Type","F(-2)",0
242,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Error: Bad Argument Type","F(-2)",0
243,-2,0,0,0.000000," ","integrate(1/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Error: Bad Argument Type","F(-2)",0
244,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
245,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 1.12Error: Bad Argument Type","F(-2)",0
246,-2,0,0,0.000000," ","integrate(tanh(x)^6/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.73Error: Bad Argument Type","F(-2)",0
247,-2,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.79Error: Bad Argument Type","F(-2)",0
248,-2,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.54Error: Bad Argument Type","F(-2)",0
249,-2,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.56Error: Bad Argument Type","F(-2)",0
250,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.5Error: Bad Argument Type","F(-2)",0
251,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.56Error: Bad Argument Type","F(-2)",0
252,-2,0,0,0.000000," ","integrate(1/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.55Error: Bad Argument Type","F(-2)",0
253,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.74Error: Bad Argument Type","F(-2)",0
254,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 2.08Error: Bad Argument Type","F(-2)",0
255,1,58,0,0.119446," ","integrate(1/(1+tanh(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} {\left(\log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/4*sqrt(2)*(log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + log(sqrt(e^(4*x) + 1) - e^(2*x)) - log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","B",0
256,1,58,0,0.136637," ","integrate(1/(-1-tanh(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} i \, \sqrt{2} {\left(\log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"1/4*I*sqrt(2)*(log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + log(sqrt(e^(4*x) + 1) - e^(2*x)) - log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","C",0
257,1,142,0,0.158576," ","integrate((a+b*tanh(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{30 \, a b \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right) + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(23 \, b^{2} + 15 \, {\left(2 \, a b + 3 \, b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 90 \, {\left(a b + b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 10 \, {\left(9 \, a b + 14 \, b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 10 \, {\left(3 \, a b + 7 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}^{5}}}{15 \, d}"," ",0,"1/15*(30*a*b*log(e^(2*d*x + 2*c) + 1) + 15*(a^2 - 2*a*b + b^2)*(d*x + c) + 2*(23*b^2 + 15*(2*a*b + 3*b^2)*e^(8*d*x + 8*c) + 90*(a*b + b^2)*e^(6*d*x + 6*c) + 10*(9*a*b + 14*b^2)*e^(4*d*x + 4*c) + 10*(3*a*b + 7*b^2)*e^(2*d*x + 2*c))/(e^(2*d*x + 2*c) + 1)^5)/d","A",0
258,1,25,0,0.113920," ","integrate(1/(1+tanh(x)^3),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} e^{\left(2 \, x\right)}\right) + \frac{1}{2} \, x - \frac{1}{12} \, e^{\left(-2 \, x\right)}"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*e^(2*x)) + 1/2*x - 1/12*e^(-2*x)","A",0
259,0,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(3/2),x, algorithm=""giac"")","\int {\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)\,{d x}"," ",0,"integrate((b*tanh(x)^4 + a)^(3/2)*tanh(x), x)","F",0
260,0,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{b \tanh\left(x\right)^{4} + a} \tanh\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^4 + a)*tanh(x), x)","F",0
261,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{\tanh\left(x\right)}{\sqrt{b \tanh\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tanh(x)/sqrt(b*tanh(x)^4 + a), x)","F",0
262,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(3/2),x, algorithm=""giac"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^4 + a)^(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(5/2),x, algorithm=""giac"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^4 + a)^(5/2), x)","F",0
