1,1,721,0,0.308628," ","integrate((a+b*coth(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
2,1,447,0,0.231839," ","integrate((a+b*coth(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
3,1,241,0,0.194727," ","integrate((a+b*coth(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
4,1,103,0,0.158062," ","integrate((a+b*coth(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
5,1,65,0,0.134011," ","integrate(1/(a+b*coth(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
6,1,198,0,0.169315," ","integrate(1/(a+b*coth(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
7,1,409,0,0.217189," ","integrate(1/(a+b*coth(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
8,1,1356,0,0.499218," ","integrate(1/(a+b*coth(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
9,1,38,0,0.113420," ","integrate(1/(1-2*coth(x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(2 \, x\right)} - 3}{2 \, \sqrt{2} + e^{\left(2 \, x\right)} + 3}\right) - x"," ",0,"1/2*sqrt(2)*log(-(2*sqrt(2) - e^(2*x) - 3)/(2*sqrt(2) + e^(2*x) + 3)) - x","B",0
10,1,26,0,0.140091," ","integrate((1-coth(x)^2)^(1/2),x, algorithm=""giac"")","{\left(i \, \log\left(e^{x} + 1\right) - i \, \log\left({\left| e^{x} - 1 \right|}\right)\right)} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)"," ",0,"(I*log(e^x + 1) - I*log(abs(e^x - 1)))*sgn(-e^(2*x) + 1)","C",0
11,1,23,0,0.118250," ","integrate((-1+coth(x)^2)^(1/2),x, algorithm=""giac"")","-{\left(\log\left(e^{x} + 1\right) - \log\left({\left| e^{x} - 1 \right|}\right)\right)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"-(log(e^x + 1) - log(abs(e^x - 1)))*sgn(e^(2*x) - 1)","A",0
12,1,60,0,0.129662," ","integrate((1-coth(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{4 \, {\left(i \, e^{\left(-x\right)} + i \, e^{x}\right)}}{{\left(e^{\left(-x\right)} + e^{x}\right)}^{2} - 4} - i \, \log\left(e^{\left(-x\right)} + e^{x} + 2\right) + i \, \log\left(e^{\left(-x\right)} + e^{x} - 2\right)\right)} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)"," ",0,"-1/4*(4*(I*e^(-x) + I*e^x)/((e^(-x) + e^x)^2 - 4) - I*log(e^(-x) + e^x + 2) + I*log(e^(-x) + e^x - 2))*sgn(-e^(2*x) + 1)","C",0
13,1,52,0,0.121661," ","integrate((-1+coth(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{4 \, {\left(e^{\left(-x\right)} + e^{x}\right)}}{{\left(e^{\left(-x\right)} + e^{x}\right)}^{2} - 4} - \log\left(e^{\left(-x\right)} + e^{x} + 2\right) + \log\left(e^{\left(-x\right)} + e^{x} - 2\right)\right)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"-1/4*(4*(e^(-x) + e^x)/((e^(-x) + e^x)^2 - 4) - log(e^(-x) + e^x + 2) + log(e^(-x) + e^x - 2))*sgn(e^(2*x) - 1)","B",0
14,1,24,0,0.119779," ","integrate(1/(1-coth(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{-i \, e^{\left(-x\right)} - i \, e^{x}}{2 \, \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)}"," ",0,"-1/2*(-I*e^(-x) - I*e^x)/sgn(-e^(2*x) + 1)","C",0
15,1,18,0,0.115017," ","integrate(1/(-1+coth(x)^2)^(1/2),x, algorithm=""giac"")","\frac{e^{\left(-x\right)} + e^{x}}{2 \, \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)}"," ",0,"1/2*(e^(-x) + e^x)/sgn(e^(2*x) - 1)","A",0
16,-2,0,0,0.000000," ","integrate(coth(x)^3*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 2.04Error: Bad Argument Type","F(-2)",0
17,-2,0,0,0.000000," ","integrate(coth(x)^2*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 1.66Error: Bad Argument Type","F(-2)",0
18,-2,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 0.75Error: Bad Argument Type","F(-2)",0
19,1,262,0,0.742026," ","integrate((a+b*coth(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{4 \, 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}} - \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) + \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) - \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)\right)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"1/2*(4*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) - 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))) + 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))) - 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))))*sgn(e^(2*x) - 1)","B",0
20,1,259,0,0.762781," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{4 \, 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}} + \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) + \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) - \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)\right)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"-1/2*(4*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) + 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))) + 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))) - 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))))*sgn(e^(2*x) - 1)","B",0
21,-2,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x)^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(exp(2*x)-1)]Evaluation time: 0.86Error: Bad Argument Type","F(-2)",0
22,-2,0,0,0.000000," ","integrate(coth(x)^3*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 4.09Error: Bad Argument Type","F(-2)",0
23,-2,0,0,0.000000," ","integrate(coth(x)^2*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 3.31Error: Bad Argument Type","F(-2)",0
24,-2,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(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(exp(2*x)-1)]Evaluation time: 2.32Error: Bad Argument Type","F(-2)",0
25,-2,0,0,0.000000," ","integrate((a+b*coth(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(exp(2*x)-1)]Evaluation time: 1.85Error: Bad Argument Type","F(-2)",0
26,1,470,0,7.811506," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x),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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) + \sqrt{a + b} b^{2} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)\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))*sgn(e^(2*x) - 1)/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)))*sgn(e^(2*x) - 1) - 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)))*sgn(e^(2*x) - 1) - 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)))*sgn(e^(2*x) - 1)/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*sgn(e^(2*x) - 1) + sqrt(a + b)*b^2*sgn(e^(2*x) - 1))/((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
27,1,473,0,7.971909," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x)^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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) - \sqrt{a + b} a^{2} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)\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))*sgn(e^(2*x) - 1)/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)))*sgn(e^(2*x) - 1) + 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)))*sgn(e^(2*x) - 1) - 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)))*sgn(e^(2*x) - 1)/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*sgn(e^(2*x) - 1) - sqrt(a + b)*a^2*sgn(e^(2*x) - 1))/((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
28,1,119,0,0.147379," ","integrate((1+coth(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} - 2 \, e^{\left(2 \, x\right)} + 2 \right|}}{2 \, {\left(\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right)}}\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)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)"," ",0,"1/2*sqrt(2)*(sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(e^(4*x) + 1) - 2*e^(2*x) + 2)/(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))*sgn(e^(2*x) - 1)","B",0
29,1,124,0,0.195888," ","integrate((-1-coth(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(i \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} - 2 \, e^{\left(2 \, x\right)} + 2 \right|}}{2 \, {\left(\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right)}}\right) + i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) - i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - i \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)"," ",0,"-1/2*sqrt(2)*(I*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(e^(4*x) + 1) - 2*e^(2*x) + 2)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) + 1)) + I*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) - I*log(sqrt(e^(4*x) + 1) - e^(2*x)) - I*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))*sgn(-e^(2*x) + 1)","C",0
30,1,265,0,0.197252," ","integrate((1+coth(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left(5 \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} - 2 \, e^{\left(2 \, x\right)} + 2 \right|}}{2 \, {\left(\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right)}}\right) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) + 4 \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) - 4 \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) - 4 \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right) \mathrm{sgn}\left(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} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) + {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) - {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)} \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right) + \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)\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}}\right)}"," ",0,"1/4*sqrt(2)*(5*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(e^(4*x) + 1) - 2*e^(2*x) + 2)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) + 1))*sgn(e^(2*x) - 1) + 4*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1)*sgn(e^(2*x) - 1) - 4*log(sqrt(e^(4*x) + 1) - e^(2*x))*sgn(e^(2*x) - 1) - 4*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1)*sgn(e^(2*x) - 1) - 4*(3*(sqrt(e^(4*x) + 1) - e^(2*x))^3*sgn(e^(2*x) - 1) + (sqrt(e^(4*x) + 1) - e^(2*x))^2*sgn(e^(2*x) - 1) - (sqrt(e^(4*x) + 1) - e^(2*x))*sgn(e^(2*x) - 1) + sgn(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)","B",0
31,1,285,0,0.201976," ","integrate((-1-coth(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} {\left(-5 i \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(4 \, x\right)} + 1} - 2 \, e^{\left(2 \, x\right)} + 2 \right|}}{2 \, {\left(\sqrt{2} + \sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right)}}\right) \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) - 4 i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) + 4 i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) + 4 i \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right) \mathrm{sgn}\left(-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} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) + i \, {\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right)}^{2} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) + {\left(-i \, \sqrt{e^{\left(4 \, x\right)} + 1} + i \, e^{\left(2 \, x\right)}\right)} \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right) + i \, \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)\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}}\right)}"," ",0,"-1/4*sqrt(2)*(-5*I*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(e^(4*x) + 1) - 2*e^(2*x) + 2)/(sqrt(2) + sqrt(e^(4*x) + 1) - e^(2*x) + 1))*sgn(-e^(2*x) + 1) - 4*I*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1)*sgn(-e^(2*x) + 1) + 4*I*log(sqrt(e^(4*x) + 1) - e^(2*x))*sgn(-e^(2*x) + 1) + 4*I*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1)*sgn(-e^(2*x) + 1) + 4*(3*I*(sqrt(e^(4*x) + 1) - e^(2*x))^3*sgn(-e^(2*x) + 1) + I*(sqrt(e^(4*x) + 1) - e^(2*x))^2*sgn(-e^(2*x) + 1) + (-I*sqrt(e^(4*x) + 1) + I*e^(2*x))*sgn(-e^(2*x) + 1) + I*sgn(-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)","C",0
32,-2,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(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
33,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(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
34,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(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
35,1,196,0,0.345248," ","integrate(1/(a+b*coth(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\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)}{\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)}{\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)}{\sqrt{a + b}}}{2 \, \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\right)}"," ",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) - 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) + 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))/sgn(e^(2*x) - 1)","B",0
36,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(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
37,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(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
38,-2,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(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
39,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(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
40,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(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
41,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(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
42,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(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: 1.22Error: Bad Argument Type","F(-2)",0
43,-2,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(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: 0.57Error: Bad Argument Type","F(-2)",0
44,-2,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(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
45,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(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
46,-2,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(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: 0.72Error: Bad Argument Type","F(-2)",0
47,-2,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(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: 2.02Error: Bad Argument Type","F(-2)",0
48,1,69,0,0.126033," ","integrate(1/(1+coth(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\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)}}{4 \, \mathrm{sgn}\left(e^{\left(2 \, x\right)} - 1\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))/sgn(e^(2*x) - 1)","B",0
49,1,73,0,0.155247," ","integrate(1/(-1-coth(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + i \, \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) + i \, \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}}{4 \, \mathrm{sgn}\left(-e^{\left(2 \, x\right)} + 1\right)}"," ",0,"-1/4*sqrt(2)*(-I*log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + I*log(sqrt(e^(4*x) + 1) - e^(2*x)) + I*log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))/sgn(-e^(2*x) + 1)","C",0
50,1,25,0,0.131205," ","integrate(1/(1+coth(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
51,0,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(x)^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{b \coth\left(x\right)^{4} + a} \coth\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^4 + a)*coth(x), x)","F",0
52,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{\coth\left(x\right)}{\sqrt{b \coth\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(coth(x)/sqrt(b*coth(x)^4 + a), x)","F",0
53,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^4)^(3/2),x, algorithm=""giac"")","\int \frac{\coth\left(x\right)}{{\left(b \coth\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*coth(x)^4 + a)^(3/2), x)","F",0
