1,1,472,152,0.020000," ","int((a+b*coth(d*x+c)^2)^5,x)","-\frac{\left(\coth^{5}\left(d x +c \right)\right) a \,b^{4}}{d}-\frac{2 \left(\coth^{5}\left(d x +c \right)\right) a^{2} b^{3}}{d}-\frac{5 \left(\coth^{7}\left(d x +c \right)\right) a \,b^{4}}{7 d}-\frac{10 \left(\coth^{3}\left(d x +c \right)\right) a^{3} b^{2}}{3 d}-\frac{10 \left(\coth^{3}\left(d x +c \right)\right) a^{2} b^{3}}{3 d}+\frac{5 \ln \left(\coth \left(d x +c \right)+1\right) a^{3} b^{2}}{d}+\frac{5 \ln \left(\coth \left(d x +c \right)+1\right) a \,b^{4}}{2 d}-\frac{5 a^{4} b \coth \left(d x +c \right)}{d}-\frac{5 \ln \left(\coth \left(d x +c \right)-1\right) a \,b^{4}}{2 d}+\frac{5 \ln \left(\coth \left(d x +c \right)+1\right) a^{4} b}{2 d}-\frac{5 \ln \left(\coth \left(d x +c \right)-1\right) a^{3} b^{2}}{d}-\frac{5 \ln \left(\coth \left(d x +c \right)-1\right) a^{2} b^{3}}{d}-\frac{10 a^{2} b^{3} \coth \left(d x +c \right)}{d}-\frac{5 a \,b^{4} \coth \left(d x +c \right)}{d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) a^{5}}{2 d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) a^{5}}{2 d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) b^{5}}{2 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) b^{5}}{2 d}-\frac{b^{5} \coth \left(d x +c \right)}{d}-\frac{5 \left(\coth^{3}\left(d x +c \right)\right) a \,b^{4}}{3 d}-\frac{10 a^{3} b^{2} \coth \left(d x +c \right)}{d}-\frac{5 \ln \left(\coth \left(d x +c \right)-1\right) a^{4} b}{2 d}+\frac{5 \ln \left(\coth \left(d x +c \right)+1\right) a^{2} b^{3}}{d}-\frac{b^{5} \left(\coth^{9}\left(d x +c \right)\right)}{9 d}-\frac{\left(\coth^{5}\left(d x +c \right)\right) b^{5}}{5 d}-\frac{\left(\coth^{3}\left(d x +c \right)\right) b^{5}}{3 d}-\frac{\left(\coth^{7}\left(d x +c \right)\right) b^{5}}{7 d}"," ",0,"5/d*ln(coth(d*x+c)+1)*a^3*b^2+5/2/d*ln(coth(d*x+c)+1)*a*b^4-5/d*a^4*b*coth(d*x+c)-5/2/d*ln(coth(d*x+c)-1)*a*b^4+5/2/d*ln(coth(d*x+c)+1)*a^4*b-10/3/d*coth(d*x+c)^3*a^3*b^2-10/3/d*coth(d*x+c)^3*a^2*b^3-5/3/d*coth(d*x+c)^3*a*b^4-5/d*ln(coth(d*x+c)-1)*a^3*b^2-5/d*ln(coth(d*x+c)-1)*a^2*b^3-5/7/d*coth(d*x+c)^7*a*b^4-10/d*a^2*b^3*coth(d*x+c)-5/d*a*b^4*coth(d*x+c)-1/d*coth(d*x+c)^5*a*b^4+1/2/d*ln(coth(d*x+c)+1)*a^5-1/2/d*ln(coth(d*x+c)-1)*a^5-1/2/d*ln(coth(d*x+c)-1)*b^5+1/2/d*ln(coth(d*x+c)+1)*b^5-1/5/d*coth(d*x+c)^5*b^5-1/3/d*coth(d*x+c)^3*b^5-1/7/d*coth(d*x+c)^7*b^5-1/d*b^5*coth(d*x+c)-2/d*coth(d*x+c)^5*a^2*b^3-10/d*a^3*b^2*coth(d*x+c)-5/2/d*ln(coth(d*x+c)-1)*a^4*b+5/d*ln(coth(d*x+c)+1)*a^2*b^3-1/9*b^5*coth(d*x+c)^9/d","B"
2,1,344,104,0.026000," ","int((a+b*coth(d*x+c)^2)^4,x)","-\frac{\left(\coth^{5}\left(d x +c \right)\right) b^{4}}{5 d}-\frac{b^{4} \left(\coth^{3}\left(d x +c \right)\right)}{3 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) a^{4}}{2 d}+\frac{2 \ln \left(\coth \left(d x +c \right)+1\right) a^{3} b}{d}+\frac{3 \ln \left(\coth \left(d x +c \right)+1\right) a^{2} b^{2}}{d}+\frac{2 \ln \left(\coth \left(d x +c \right)+1\right) a \,b^{3}}{d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) b^{4}}{2 d}-\frac{\coth \left(d x +c \right) b^{4}}{d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) a^{4}}{2 d}-\frac{2 \ln \left(\coth \left(d x +c \right)-1\right) a^{3} b}{d}-\frac{3 \ln \left(\coth \left(d x +c \right)-1\right) a^{2} b^{2}}{d}-\frac{2 \ln \left(\coth \left(d x +c \right)-1\right) a \,b^{3}}{d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) b^{4}}{2 d}-\frac{b^{4} \left(\coth^{7}\left(d x +c \right)\right)}{7 d}-\frac{4 \left(\coth^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}-\frac{2 \left(\coth^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{4 \left(\coth^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}-\frac{4 a \,b^{3} \coth \left(d x +c \right)}{d}-\frac{4 a^{3} b \coth \left(d x +c \right)}{d}-\frac{6 a^{2} b^{2} \coth \left(d x +c \right)}{d}"," ",0,"-1/5/d*coth(d*x+c)^5*b^4-1/3/d*coth(d*x+c)^3*b^4+1/2/d*ln(coth(d*x+c)+1)*a^4+2/d*ln(coth(d*x+c)+1)*a^3*b+3/d*ln(coth(d*x+c)+1)*a^2*b^2+2/d*ln(coth(d*x+c)+1)*a*b^3+1/2/d*ln(coth(d*x+c)+1)*b^4-1/d*coth(d*x+c)*b^4-1/2/d*ln(coth(d*x+c)-1)*a^4-2/d*ln(coth(d*x+c)-1)*a^3*b-3/d*ln(coth(d*x+c)-1)*a^2*b^2-2/d*ln(coth(d*x+c)-1)*a*b^3-1/2/d*ln(coth(d*x+c)-1)*b^4-1/7*b^4*coth(d*x+c)^7/d-4/5/d*coth(d*x+c)^5*a*b^3-2/d*coth(d*x+c)^3*a^2*b^2-4/3/d*coth(d*x+c)^3*a*b^3-4/d*a*b^3*coth(d*x+c)-4/d*a^3*b*coth(d*x+c)-6/d*a^2*b^2*coth(d*x+c)","B"
3,1,235,70,0.020000," ","int((a+b*coth(d*x+c)^2)^3,x)","-\frac{\ln \left(\coth \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\coth \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\coth \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{\left(\coth^{3}\left(d x +c \right)\right) b^{3}}{3 d}-\frac{\coth \left(d x +c \right) b^{3}}{d}-\frac{b^{3} \left(\coth^{5}\left(d x +c \right)\right)}{5 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) a^{3}}{2 d}+\frac{3 \ln \left(\coth \left(d x +c \right)+1\right) a^{2} b}{2 d}+\frac{3 \ln \left(\coth \left(d x +c \right)+1\right) a \,b^{2}}{2 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) b^{3}}{2 d}-\frac{\left(\coth^{3}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{3 \coth \left(d x +c \right) a^{2} b}{d}-\frac{3 a \,b^{2} \coth \left(d x +c \right)}{d}"," ",0,"-1/2/d*ln(coth(d*x+c)-1)*a^3-3/2/d*ln(coth(d*x+c)-1)*a^2*b-3/2/d*ln(coth(d*x+c)-1)*a*b^2-1/2/d*ln(coth(d*x+c)-1)*b^3-1/3/d*coth(d*x+c)^3*b^3-1/d*coth(d*x+c)*b^3-1/5*b^3*coth(d*x+c)^5/d+1/2/d*ln(coth(d*x+c)+1)*a^3+3/2/d*ln(coth(d*x+c)+1)*a^2*b+3/2/d*ln(coth(d*x+c)+1)*a*b^2+1/2/d*ln(coth(d*x+c)+1)*b^3-1/d*coth(d*x+c)^3*a*b^2-3/d*coth(d*x+c)*a^2*b-3*a*b^2*coth(d*x+c)/d","B"
4,1,144,41,0.020000," ","int((a+b*coth(d*x+c)^2)^2,x)","-\frac{b^{2} \left(\coth^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \coth \left(d x +c \right)}{d}-\frac{b^{2} \coth \left(d x +c \right)}{d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\coth \left(d x +c \right)-1\right) b^{2}}{2 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) a^{2}}{2 d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) a b}{d}+\frac{\ln \left(\coth \left(d x +c \right)+1\right) b^{2}}{2 d}"," ",0,"-1/3*b^2*coth(d*x+c)^3/d-2/d*a*b*coth(d*x+c)-b^2*coth(d*x+c)/d-1/2/d*ln(coth(d*x+c)-1)*a^2-1/d*ln(coth(d*x+c)-1)*a*b-1/2/d*ln(coth(d*x+c)-1)*b^2+1/2/d*ln(coth(d*x+c)+1)*a^2+1/d*ln(coth(d*x+c)+1)*a*b+1/2/d*ln(coth(d*x+c)+1)*b^2","B"
5,1,76,38,0.115000," ","int(1/(a+b*coth(d*x+c)^2),x)","-\frac{\ln \left(\coth \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}+\frac{\ln \left(\coth \left(d x +c \right)+1\right)}{d \left(2 b +2 a \right)}+\frac{b \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a +b \right) \sqrt{a b}}"," ",0,"-1/d/(2*b+2*a)*ln(coth(d*x+c)-1)+1/d/(2*b+2*a)*ln(coth(d*x+c)+1)+1/d*b/(a+b)/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))","A"
6,1,172,77,0.130000," ","int(1/(a+b*coth(d*x+c)^2)^2,x)","-\frac{\ln \left(\coth \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(\coth \left(d x +c \right)+1\right)}{2 d \left(a +b \right)^{2}}+\frac{b \coth \left(d x +c \right)}{2 d \left(a +b \right)^{2} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)}+\frac{b^{2} \coth \left(d x +c \right)}{2 d \left(a +b \right)^{2} a \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)}+\frac{3 b \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^2*ln(coth(d*x+c)-1)+1/2/d/(a+b)^2*ln(coth(d*x+c)+1)+1/2/d*b/(a+b)^2*coth(d*x+c)/(a+b*coth(d*x+c)^2)+1/2/d*b^2/(a+b)^2/a*coth(d*x+c)/(a+b*coth(d*x+c)^2)+3/2/d*b/(a+b)^2/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+1/2/d*b^2/(a+b)^2/a/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))","B"
7,1,352,128,0.125000," ","int(1/(a+b*coth(d*x+c)^2)^3,x)","-\frac{\ln \left(\coth \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{\ln \left(\coth \left(d x +c \right)+1\right)}{2 d \left(a +b \right)^{3}}+\frac{7 b^{2} \left(\coth^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{5 b^{3} \left(\coth^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2} a}+\frac{3 b^{4} \left(\coth^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2} a^{2}}+\frac{9 b a \coth \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{7 b^{2} \coth \left(d x +c \right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{5 b^{3} \coth \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{2} a}+\frac{15 b \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} \sqrt{a b}}+\frac{5 b^{2} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{4 d \left(a +b \right)^{3} a \sqrt{a b}}+\frac{3 b^{3} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^3*ln(coth(d*x+c)-1)+1/2/d/(a+b)^3*ln(coth(d*x+c)+1)+7/8/d/(a+b)^3*b^2/(a+b*coth(d*x+c)^2)^2*coth(d*x+c)^3+5/4/d/(a+b)^3*b^3/(a+b*coth(d*x+c)^2)^2/a*coth(d*x+c)^3+3/8/d/(a+b)^3*b^4/(a+b*coth(d*x+c)^2)^2/a^2*coth(d*x+c)^3+9/8/d/(a+b)^3*b/(a+b*coth(d*x+c)^2)^2*a*coth(d*x+c)+7/4/d/(a+b)^3*b^2/(a+b*coth(d*x+c)^2)^2*coth(d*x+c)+5/8/d/(a+b)^3*b^3/(a+b*coth(d*x+c)^2)^2/a*coth(d*x+c)+15/8/d/(a+b)^3*b/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+5/4/d/(a+b)^3*b^2/a/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+3/8/d/(a+b)^3*b^3/a^2/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))","B"
8,1,608,185,0.129000," ","int(1/(a+b*coth(d*x+c)^2)^4,x)","-\frac{\ln \left(\coth \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{4}}+\frac{\ln \left(\coth \left(d x +c \right)+1\right)}{2 d \left(a +b \right)^{4}}+\frac{19 b^{3} \left(\coth^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{35 b^{4} \left(\coth^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{21 b^{5} \left(\coth^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a^{2}}+\frac{5 b^{6} \left(\coth^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a^{3}}+\frac{17 b^{2} a \left(\coth^{3}\left(d x +c \right)\right)}{6 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{11 b^{3} \left(\coth^{3}\left(d x +c \right)\right)}{2 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{7 b^{4} \left(\coth^{3}\left(d x +c \right)\right)}{2 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{5 b^{5} \left(\coth^{3}\left(d x +c \right)\right)}{6 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a^{2}}+\frac{29 b \,a^{2} \coth \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{61 b^{2} a \coth \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{43 b^{3} \coth \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{11 b^{4} \coth \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\coth^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{35 b \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a \sqrt{a b}}+\frac{21 b^{3} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a^{2} \sqrt{a b}}+\frac{5 b^{4} \arctan \left(\frac{\coth \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a^{3} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^4*ln(coth(d*x+c)-1)+1/2/d/(a+b)^4*ln(coth(d*x+c)+1)+19/16/d/(a+b)^4*b^3/(a+b*coth(d*x+c)^2)^3*coth(d*x+c)^5+35/16/d/(a+b)^4*b^4/(a+b*coth(d*x+c)^2)^3/a*coth(d*x+c)^5+21/16/d/(a+b)^4*b^5/(a+b*coth(d*x+c)^2)^3/a^2*coth(d*x+c)^5+5/16/d/(a+b)^4*b^6/(a+b*coth(d*x+c)^2)^3/a^3*coth(d*x+c)^5+17/6/d/(a+b)^4*b^2/(a+b*coth(d*x+c)^2)^3*a*coth(d*x+c)^3+11/2/d/(a+b)^4*b^3/(a+b*coth(d*x+c)^2)^3*coth(d*x+c)^3+7/2/d/(a+b)^4*b^4/(a+b*coth(d*x+c)^2)^3/a*coth(d*x+c)^3+5/6/d/(a+b)^4*b^5/(a+b*coth(d*x+c)^2)^3/a^2*coth(d*x+c)^3+29/16/d/(a+b)^4*b/(a+b*coth(d*x+c)^2)^3*a^2*coth(d*x+c)+61/16/d/(a+b)^4*b^2/(a+b*coth(d*x+c)^2)^3*a*coth(d*x+c)+43/16/d/(a+b)^4*b^3/(a+b*coth(d*x+c)^2)^3*coth(d*x+c)+11/16/d/(a+b)^4*b^4/(a+b*coth(d*x+c)^2)^3/a*coth(d*x+c)+35/16/d/(a+b)^4*b/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+35/16/d/(a+b)^4*b^2/a/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+21/16/d/(a+b)^4*b^3/a^2/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))+5/16/d/(a+b)^4*b^4/a^3/(a*b)^(1/2)*arctan(coth(d*x+c)*b/(a*b)^(1/2))","B"
9,1,27,16,0.080000," ","int(1/(1-2*coth(x)^2),x)","\frac{\ln \left(\coth \left(x \right)-1\right)}{2}-\frac{\ln \left(1+\coth \left(x \right)\right)}{2}+\sqrt{2}\, \arctanh \left(\sqrt{2}\, \coth \left(x \right)\right)"," ",0,"1/2*ln(coth(x)-1)-1/2*ln(1+coth(x))+2^(1/2)*arctanh(2^(1/2)*coth(x))","A"
10,1,4,3,0.078000," ","int((1-coth(x)^2)^(1/2),x)","\arcsin \left(\coth \left(x \right)\right)"," ",0,"arcsin(coth(x))","A"
11,1,15,12,0.139000," ","int((-1+coth(x)^2)^(1/2),x)","-\ln \left(\coth \left(x \right)+\sqrt{-1+\coth^{2}\left(x \right)}\right)"," ",0,"-ln(coth(x)+(-1+coth(x)^2)^(1/2))","A"
12,1,21,18,0.072000," ","int((1-coth(x)^2)^(3/2),x)","\frac{\coth \left(x \right) \sqrt{1-\left(\coth^{2}\left(x \right)\right)}}{2}+\frac{\arcsin \left(\coth \left(x \right)\right)}{2}"," ",0,"1/2*coth(x)*(1-coth(x)^2)^(1/2)+1/2*arcsin(coth(x))","A"
13,1,28,23,0.128000," ","int((-1+coth(x)^2)^(3/2),x)","-\frac{\coth \left(x \right) \sqrt{-1+\coth^{2}\left(x \right)}}{2}+\frac{\ln \left(\coth \left(x \right)+\sqrt{-1+\coth^{2}\left(x \right)}\right)}{2}"," ",0,"-1/2*coth(x)*(-1+coth(x)^2)^(1/2)+1/2*ln(coth(x)+(-1+coth(x)^2)^(1/2))","A"
14,1,14,11,0.060000," ","int(1/(1-coth(x)^2)^(1/2),x)","\frac{\coth \left(x \right)}{\sqrt{1-\left(\coth^{2}\left(x \right)\right)}}"," ",0,"1/(1-coth(x)^2)^(1/2)*coth(x)","A"
15,1,12,9,0.102000," ","int(1/(-1+coth(x)^2)^(1/2),x)","\frac{\coth \left(x \right)}{\sqrt{-1+\coth^{2}\left(x \right)}}"," ",0,"coth(x)/(-1+coth(x)^2)^(1/2)","A"
16,1,253,51,0.140000," ","int(coth(x)^3*(a+b*coth(x)^2)^(1/2),x)","-\frac{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3 b}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2}"," ",0,"-1/3*(a+b*coth(x)^2)^(3/2)/b-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
17,1,276,67,0.101000," ","int(coth(x)^2*(a+b*coth(x)^2)^(1/2),x)","-\frac{\coth \left(x \right) \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}{2}-\frac{a \ln \left(\sqrt{b}\, \coth \left(x \right)+\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}\right)}{2 \sqrt{b}}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2}"," ",0,"-1/2*coth(x)*(a+b*coth(x)^2)^(1/2)-1/2*a/b^(1/2)*ln(b^(1/2)*coth(x)+(a+b*coth(x)^2)^(1/2))-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
18,1,238,36,0.088000," ","int(coth(x)*(a+b*coth(x)^2)^(1/2),x)","-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2}"," ",0,"-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
19,1,238,48,0.121000," ","int((a+b*coth(x)^2)^(1/2),x)","-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2}"," ",0,"-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
20,0,0,44,0.545000," ","int((a+b*coth(x)^2)^(1/2)*tanh(x),x)","\int \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}\, \tanh \left(x \right)\, dx"," ",0,"int((a+b*coth(x)^2)^(1/2)*tanh(x),x)","F"
21,0,0,40,0.474000," ","int((a+b*coth(x)^2)^(1/2)*tanh(x)^2,x)","\int \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}\, \left(\tanh^{2}\left(x \right)\right)\, dx"," ",0,"int((a+b*coth(x)^2)^(1/2)*tanh(x)^2,x)","F"
22,1,593,66,0.084000," ","int(coth(x)^3*(a+b*coth(x)^2)^(3/2),x)","-\frac{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}{5 b}-\frac{\left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, b}{2}-\frac{\left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}+\frac{b \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, \coth \left(x \right)}{4}+\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) a}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, a}{2}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) b}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/5*(a+b*coth(x)^2)^(5/2)/b-1/6*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)-1/4*b*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*a-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*b-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b-1/6*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)+1/4*b*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)+3/4*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*a-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*a+1/2*b^(3/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*b-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b","B"
23,1,633,101,0.087000," ","int(coth(x)^2*(a+b*coth(x)^2)^(3/2),x)","-\frac{\coth \left(x \right) \left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{4}-\frac{3 a \coth \left(x \right) \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}{8}-\frac{3 a^{2} \ln \left(\sqrt{b}\, \coth \left(x \right)+\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}\right)}{8 \sqrt{b}}-\frac{\left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, b}{2}+\frac{\left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right) a}{4}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) a}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, a}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) b}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/4*coth(x)*(a+b*coth(x)^2)^(3/2)-3/8*a*coth(x)*(a+b*coth(x)^2)^(1/2)-3/8*a^2/b^(1/2)*ln(b^(1/2)*coth(x)+(a+b*coth(x)^2)^(1/2))-1/6*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)-1/4*b*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*a-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*b-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b+1/6*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)-1/4*b*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))*a-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*a+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*a-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*b-1/2*b^(3/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b","B"
24,1,578,51,0.069000," ","int(coth(x)*(a+b*coth(x)^2)^(3/2),x)","-\frac{\left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, a}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) b}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, b}{2}-\frac{\left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}+\frac{b \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, \coth \left(x \right)}{4}+\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) a}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, a}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) b}{2}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/6*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)-1/4*b*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*a-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*b-1/2*b^(3/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b-1/6*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)+1/4*b*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)+3/4*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*a-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*a+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*b+1/2*b^(3/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))-1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b","B"
25,1,578,70,0.112000," ","int((a+b*coth(x)^2)^(3/2),x)","-\frac{\left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\coth \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}\, b}{2}+\frac{\left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, \coth \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right) a}{4}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) a}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\coth \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right) b}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/6*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)-1/4*b*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*a-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((coth(x)-1)*b+b)/b^(1/2)+((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))*b-1/2*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b+1/6*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)-1/4*b*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)-3/4*b^(1/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))*a-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*a+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((1+coth(x))*b-b)/b^(1/2)+((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))*b+1/2*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b","B"
26,0,0,57,0.449000," ","int((a+b*coth(x)^2)^(3/2)*tanh(x),x)","\int \left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}} \tanh \left(x \right)\, dx"," ",0,"int((a+b*coth(x)^2)^(3/2)*tanh(x),x)","F"
27,0,0,63,0.454000," ","int((a+b*coth(x)^2)^(3/2)*tanh(x)^2,x)","\int \left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}} \left(\tanh^{2}\left(x \right)\right)\, dx"," ",0,"int((a+b*coth(x)^2)^(3/2)*tanh(x)^2,x)","F"
28,1,97,25,0.142000," ","int((1+coth(x)^2)^(1/2),x)","-\frac{\sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}}{2}-\arcsinh \left(\coth \left(x \right)\right)+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \coth \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}}\right)}{2}+\frac{\sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}}{2}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}}\right)}{2}"," ",0,"-1/2*((coth(x)-1)^2+2*coth(x))^(1/2)-arcsinh(coth(x))+1/2*2^(1/2)*arctanh(1/4*(2*coth(x)+2)*2^(1/2)/((coth(x)-1)^2+2*coth(x))^(1/2))+1/2*((1+coth(x))^2-2*coth(x))^(1/2)-1/2*2^(1/2)*arctanh(1/4*(2-2*coth(x))*2^(1/2)/((1+coth(x))^2-2*coth(x))^(1/2))","B"
29,1,142,37,0.149000," ","int((-1-coth(x)^2)^(1/2),x)","-\frac{\sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}{2}+\frac{\arctan \left(\frac{\coth \left(x \right)}{\sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}\right)}{2}+\frac{\sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}{2}+\frac{\arctan \left(\frac{\coth \left(x \right)}{\sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}\right)}{2}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}\right)}{2}"," ",0,"-1/2*(-(coth(x)-1)^2-2*coth(x))^(1/2)+1/2*arctan(coth(x)/(-(coth(x)-1)^2-2*coth(x))^(1/2))+1/2*2^(1/2)*arctan(1/4*(-2-2*coth(x))*2^(1/2)/(-(coth(x)-1)^2-2*coth(x))^(1/2))+1/2*(-(1+coth(x))^2+2*coth(x))^(1/2)+1/2*arctan(coth(x)/(-(1+coth(x))^2+2*coth(x))^(1/2))-1/2*2^(1/2)*arctan(1/4*(-2+2*coth(x))*2^(1/2)/(-(1+coth(x))^2+2*coth(x))^(1/2))","B"
30,1,158,38,0.115000," ","int((1+coth(x)^2)^(3/2),x)","-\frac{\left(\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)\right)^{\frac{3}{2}}}{6}-\frac{\coth \left(x \right) \sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}}{4}-\frac{5 \arcsinh \left(\coth \left(x \right)\right)}{2}-\sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}+\sqrt{2}\, \arctanh \left(\frac{\left(2 \coth \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}}\right)+\frac{\left(\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)\right)^{\frac{3}{2}}}{6}-\frac{\coth \left(x \right) \sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}}{4}+\sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}-\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}}\right)"," ",0,"-1/6*((coth(x)-1)^2+2*coth(x))^(3/2)-1/4*coth(x)*((coth(x)-1)^2+2*coth(x))^(1/2)-5/2*arcsinh(coth(x))-((coth(x)-1)^2+2*coth(x))^(1/2)+2^(1/2)*arctanh(1/4*(2*coth(x)+2)*2^(1/2)/((coth(x)-1)^2+2*coth(x))^(1/2))+1/6*((1+coth(x))^2-2*coth(x))^(3/2)-1/4*coth(x)*((1+coth(x))^2-2*coth(x))^(1/2)+((1+coth(x))^2-2*coth(x))^(1/2)-2^(1/2)*arctanh(1/4*(2-2*coth(x))*2^(1/2)/((1+coth(x))^2-2*coth(x))^(1/2))","B"
31,1,211,53,0.121000," ","int((-1-coth(x)^2)^(3/2),x)","-\frac{\left(-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)\right)^{\frac{3}{2}}}{6}+\frac{\coth \left(x \right) \sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}{4}-\frac{5 \arctan \left(\frac{\coth \left(x \right)}{\sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}\right)}{4}+\sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}-\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}\right)+\frac{\left(-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)\right)^{\frac{3}{2}}}{6}+\frac{\coth \left(x \right) \sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}{4}-\frac{5 \arctan \left(\frac{\coth \left(x \right)}{\sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}\right)}{4}-\sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}+\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}\right)"," ",0,"-1/6*(-(coth(x)-1)^2-2*coth(x))^(3/2)+1/4*coth(x)*(-(coth(x)-1)^2-2*coth(x))^(1/2)-5/4*arctan(coth(x)/(-(coth(x)-1)^2-2*coth(x))^(1/2))+(-(coth(x)-1)^2-2*coth(x))^(1/2)-2^(1/2)*arctan(1/4*(-2-2*coth(x))*2^(1/2)/(-(coth(x)-1)^2-2*coth(x))^(1/2))+1/6*(-(1+coth(x))^2+2*coth(x))^(3/2)+1/4*coth(x)*(-(1+coth(x))^2+2*coth(x))^(1/2)-5/4*arctan(coth(x)/(-(1+coth(x))^2+2*coth(x))^(1/2))-(-(1+coth(x))^2+2*coth(x))^(1/2)+2^(1/2)*arctan(1/4*(-2+2*coth(x))*2^(1/2)/(-(1+coth(x))^2+2*coth(x))^(1/2))","B"
32,1,129,39,0.118000," ","int(coth(x)^3/(a+b*coth(x)^2)^(1/2),x)","-\frac{\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}{b}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-(a+b*coth(x)^2)^(1/2)/b+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
33,1,137,48,0.116000," ","int(coth(x)^2/(a+b*coth(x)^2)^(1/2),x)","-\frac{\ln \left(\sqrt{b}\, \coth \left(x \right)+\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}\right)}{\sqrt{b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-ln(b^(1/2)*coth(x)+(a+b*coth(x)^2)^(1/2))/b^(1/2)+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
34,1,114,23,0.099000," ","int(coth(x)/(a+b*coth(x)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
35,1,114,25,0.125000," ","int(1/(a+b*coth(x)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
36,0,0,44,0.500000," ","int(tanh(x)/(a+b*coth(x)^2)^(1/2),x)","\int \frac{\tanh \left(x \right)}{\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}\, dx"," ",0,"int(tanh(x)/(a+b*coth(x)^2)^(1/2),x)","F"
37,0,0,43,0.511000," ","int(tanh(x)^2/(a+b*coth(x)^2)^(1/2),x)","\int \frac{\tanh^{2}\left(x \right)}{\sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}\, dx"," ",0,"int(tanh(x)^2/(a+b*coth(x)^2)^(1/2),x)","F"
38,1,287,44,0.093000," ","int(coth(x)^3/(a+b*coth(x)^2)^(3/2),x)","\frac{1}{b \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\coth \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{b \left(2 \left(1+\coth \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"1/b/(a+b*coth(x)^2)^(1/2)-1/2/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(coth(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-b/(a+b)*(2*(1+coth(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
39,1,289,45,0.098000," ","int(coth(x)^2/(a+b*coth(x)^2)^(3/2),x)","-\frac{\coth \left(x \right)}{a \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\coth \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}+\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{b \left(2 \left(1+\coth \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-coth(x)/a/(a+b*coth(x)^2)^(1/2)-1/2/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(coth(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/2/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+b/(a+b)*(2*(1+coth(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
40,1,273,41,0.081000," ","int(coth(x)/(a+b*coth(x)^2)^(3/2),x)","-\frac{1}{2 \left(a +b \right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\coth \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{b \left(2 \left(1+\coth \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-1/2/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(coth(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/2/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-b/(a+b)*(2*(1+coth(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
41,0,0,64,0.464000," ","int(tanh(x)/(a+b*coth(x)^2)^(3/2),x)","\int \frac{\tanh \left(x \right)}{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tanh(x)/(a+b*coth(x)^2)^(3/2),x)","F"
42,0,0,75,0.478000," ","int(tanh(x)^2/(a+b*coth(x)^2)^(3/2),x)","\int \frac{\tanh^{2}\left(x \right)}{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(tanh(x)^2/(a+b*coth(x)^2)^(3/2),x)","F"
43,1,435,62,0.098000," ","int(coth(x)^3/(a+b*coth(x)^2)^(5/2),x)","\frac{1}{3 b \left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"1/3/b/(a+b*coth(x)^2)^(3/2)-1/6/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)*coth(x)+1/3*b/(a+b)/a^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-1/2/(a+b)^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b*coth(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/6/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)-1/6*b/(a+b)/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)*coth(x)-1/3*b/(a+b)/a^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)-1/2/(a+b)^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-1/2/(a+b)^2/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b*coth(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
44,1,454,74,0.097000," ","int(coth(x)^2/(a+b*coth(x)^2)^(5/2),x)","-\frac{\coth \left(x \right)}{3 a \left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{2 \coth \left(x \right)}{3 a^{2} \sqrt{a +b \left(\coth^{2}\left(x \right)\right)}}-\frac{1}{6 \left(a +b \right) \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}+\frac{1}{6 \left(a +b \right) \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-1/3*coth(x)/a/(a+b*coth(x)^2)^(3/2)-2/3/a^2*coth(x)/(a+b*coth(x)^2)^(1/2)-1/6/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)*coth(x)+1/3*b/(a+b)/a^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-1/2/(a+b)^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b*coth(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))+1/6/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)+1/6*b/(a+b)/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)*coth(x)+1/3*b/(a+b)/a^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)+1/2/(a+b)^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)+1/2/(a+b)^2/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b*coth(x)-1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
45,1,420,58,0.083000," ","int(coth(x)/(a+b*coth(x)^2)^(5/2),x)","-\frac{1}{6 \left(a +b \right) \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\coth \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\coth \left(x \right)-1\right)^{2} b +2 \left(\coth \left(x \right)-1\right) b +a +b}}{\coth \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \coth \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \coth \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}-\frac{b \coth \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\coth \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\coth \left(x \right)\right)^{2} b -2 \left(1+\coth \left(x \right)\right) b +a +b}}{1+\coth \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-1/6/(a+b)/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(3/2)*coth(x)+1/3*b/(a+b)/a^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*coth(x)-1/2/(a+b)^2/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2)*b*coth(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(coth(x)-1)*b+2*(a+b)^(1/2)*((coth(x)-1)^2*b+2*(coth(x)-1)*b+a+b)^(1/2))/(coth(x)-1))-1/6/(a+b)/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)-1/6*b/(a+b)/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(3/2)*coth(x)-1/3*b/(a+b)/a^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*coth(x)-1/2/(a+b)^2/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)-1/2/(a+b)^2/a/((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2)*b*coth(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+coth(x))*b+2*(a+b)^(1/2)*((1+coth(x))^2*b-2*(1+coth(x))*b+a+b)^(1/2))/(1+coth(x)))","B"
46,0,0,90,0.462000," ","int(tanh(x)/(a+b*coth(x)^2)^(5/2),x)","\int \frac{\tanh \left(x \right)}{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(tanh(x)/(a+b*coth(x)^2)^(5/2),x)","F"
47,0,0,113,0.489000," ","int(tanh(x)^2/(a+b*coth(x)^2)^(5/2),x)","\int \frac{\tanh^{2}\left(x \right)}{\left(a +b \left(\coth^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(tanh(x)^2/(a+b*coth(x)^2)^(5/2),x)","F"
48,1,62,20,0.137000," ","int(1/(1+coth(x)^2)^(1/2),x)","\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \coth \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\coth \left(x \right)-1\right)^{2}+2 \coth \left(x \right)}}\right)}{4}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\coth \left(x \right)\right)^{2}-2 \coth \left(x \right)}}\right)}{4}"," ",0,"1/4*2^(1/2)*arctanh(1/4*(2*coth(x)+2)*2^(1/2)/((coth(x)-1)^2+2*coth(x))^(1/2))-1/4*2^(1/2)*arctanh(1/4*(2-2*coth(x))*2^(1/2)/((1+coth(x))^2-2*coth(x))^(1/2))","B"
49,1,66,22,0.135000," ","int(1/(-1-coth(x)^2)^(1/2),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\coth \left(x \right)-1\right)^{2}-2 \coth \left(x \right)}}\right)}{4}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \coth \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\coth \left(x \right)\right)^{2}+2 \coth \left(x \right)}}\right)}{4}"," ",0,"-1/4*2^(1/2)*arctan(1/4*(-2-2*coth(x))*2^(1/2)/(-(coth(x)-1)^2-2*coth(x))^(1/2))+1/4*2^(1/2)*arctan(1/4*(-2+2*coth(x))*2^(1/2)/(-(1+coth(x))^2+2*coth(x))^(1/2))","B"
50,1,41,29,0.079000," ","int(1/(1+coth(x)^3),x)","-\frac{\ln \left(\coth \left(x \right)-1\right)}{4}-\frac{1}{6 \left(1+\coth \left(x \right)\right)}+\frac{\ln \left(1+\coth \left(x \right)\right)}{4}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 \coth \left(x \right)-1\right) \sqrt{3}}{3}\right)}{9}"," ",0,"-1/4*ln(coth(x)-1)-1/6/(1+coth(x))+1/4*ln(1+coth(x))+2/9*3^(1/2)*arctan(1/3*(2*coth(x)-1)*3^(1/2))","A"
51,1,116,69,0.166000," ","int(coth(x)*(a+b*coth(x)^4)^(1/2),x)","-\frac{\sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}{2}-\frac{\sqrt{b}\, \ln \left(2 \sqrt{b}\, \left(\coth^{2}\left(x \right)\right)+2 \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}\right)}{2}+\frac{a \arctanh \left(\frac{2 b \left(\coth^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{b \arctanh \left(\frac{2 b \left(\coth^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}"," ",0,"-1/2*(a+b*coth(x)^4)^(1/2)-1/2*b^(1/2)*ln(2*b^(1/2)*coth(x)^2+2*(a+b*coth(x)^4)^(1/2))+1/2*a/(a+b)^(1/2)*arctanh(1/2*(2*b*coth(x)^2+2*a)/(a+b)^(1/2)/(a+b*coth(x)^4)^(1/2))+1/2*b/(a+b)^(1/2)*arctanh(1/2*(2*b*coth(x)^2+2*a)/(a+b)^(1/2)/(a+b*coth(x)^4)^(1/2))","A"
52,1,37,32,0.141000," ","int(coth(x)/(a+b*coth(x)^4)^(1/2),x)","\frac{\arctanh \left(\frac{2 b \left(\coth^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*coth(x)^2+2*a)/(a+b)^(1/2)/(a+b*coth(x)^4)^(1/2))","A"
53,1,431,63,0.124000," ","int(coth(x)/(a+b*coth(x)^4)^(3/2),x)","\frac{b \left(\frac{\coth^{3}\left(x \right)}{4 a \left(a +b \right)}+\frac{\coth^{2}\left(x \right)}{4 a \left(a +b \right)}+\frac{\coth \left(x \right)}{4 a \left(a +b \right)}-\frac{1}{4 \left(a +b \right) b}\right)}{\sqrt{\left(\coth^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\coth^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}-\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\coth^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\coth^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\coth \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}}{2 \left(a +b \right)}+\frac{b \left(-\frac{\coth^{3}\left(x \right)}{4 a \left(a +b \right)}+\frac{\coth^{2}\left(x \right)}{4 a \left(a +b \right)}-\frac{\coth \left(x \right)}{4 a \left(a +b \right)}-\frac{1}{4 \left(a +b \right) b}\right)}{\sqrt{\left(\coth^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\coth^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\coth^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\coth^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\coth \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\coth^{4}\left(x \right)\right)}}}{2 \left(a +b \right)}"," ",0,"b*(1/4/a/(a+b)*coth(x)^3+1/4/a/(a+b)*coth(x)^2+1/4/a/(a+b)*coth(x)-1/4/(a+b)/b)/((coth(x)^4+a/b)*b)^(1/2)-1/2/(a+b)*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*coth(x)^2+2*a)/(a+b)^(1/2)/(a+b*coth(x)^4)^(1/2))-1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*coth(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*coth(x)^2)^(1/2)/(a+b*coth(x)^4)^(1/2)*EllipticPi(coth(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))+b*(-1/4/a/(a+b)*coth(x)^3+1/4/a/(a+b)*coth(x)^2-1/4/a/(a+b)*coth(x)-1/4/(a+b)/b)/((coth(x)^4+a/b)*b)^(1/2)-1/2/(a+b)*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*coth(x)^2+2*a)/(a+b)^(1/2)/(a+b*coth(x)^4)^(1/2))+1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*coth(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*coth(x)^2)^(1/2)/(a+b*coth(x)^4)^(1/2)*EllipticPi(coth(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))","C"