lst:=[[(d*x^2+c)^4*arccoth(a*x),x,5,1/630*d*(420*a^6*c^3+378*a^4*c^2*d+180*a^2*c*d^2+35*d^3)*x^2/a^7+1/1260*d^2*(378*a^4*c^2+180*a^2*c*d+35*d^2)*x^4/a^5+1/378*d^3*(36*a^2*c+7*d)*x^6/a^3+1/72*d^4*x^8/a+c^4*x*arccoth(a*x)+4/3*c^3*d*x^3*arccoth(a*x)+6/5*c^2*d^2*x^5*arccoth(a*x)+4/7*c*d^3*x^7*arccoth(a*x)+1/9*d^4*x^9*arccoth(a*x)+1/630*(315*a^8*c^4+420*a^6*c^3*d+378*a^4*c^2*d^2+180*a^2*c*d^3+35*d^4)*ln(-a^2*x^2+1)/a^9,1],
[(d*x^2+c)^3*arccoth(a*x),x,5,1/70*d*(35*a^4*c^2+21*a^2*c*d+5*d^2)*x^2/a^5+1/140*d^2*(21*a^2*c+5*d)*x^4/a^3+1/42*d^3*x^6/a+c^3*x*arccoth(a*x)+c^2*d*x^3*arccoth(a*x)+3/5*c*d^2*x^5*arccoth(a*x)+1/7*d^3*x^7*arccoth(a*x)+1/70*(35*a^6*c^3+35*a^4*c^2*d+21*a^2*c*d^2+5*d^3)*ln(-a^2*x^2+1)/a^7,1],
[(d*x^2+c)^2*arccoth(a*x),x,5,1/30*d*(10*a^2*c+3*d)*x^2/a^3+1/20*d^2*x^4/a+c^2*x*arccoth(a*x)+2/3*c*d*x^3*arccoth(a*x)+1/5*d^2*x^5*arccoth(a*x)+1/30*(15*a^4*c^2+10*a^2*c*d+3*d^2)*ln(-a^2*x^2+1)/a^5,1],
[(d*x^2+c)*arccoth(a*x),x,4,1/6*d*x^2/a+c*x*arccoth(a*x)+1/3*d*x^3*arccoth(a*x)+1/6*(3*a^2*c+d)*ln(-a^2*x^2+1)/a^3,1],
[arccoth(a*x)/(d*x^2+c),x,25,-1/2*arctan(sqrt(d)*x/sqrt(c))*ln(1-1/a/x)/sqrt(c)/sqrt(d)+1/2*arctan(sqrt(d)*x/sqrt(c))*ln(1+1/a/x)/sqrt(c)/sqrt(d)+1/2*arctan(sqrt(d)*x/sqrt(c))*ln(-2*sqrt(c)*sqrt(d)*(-a*x+1)/(I*a*sqrt(c)-sqrt(d))/(sqrt(c)-I*sqrt(d)*x))/sqrt(c)/sqrt(d)-1/2*arctan(sqrt(d)*x/sqrt(c))*ln(2*sqrt(c)*sqrt(d)*(a*x+1)/(I*a*sqrt(c)+sqrt(d))/(sqrt(c)-I*sqrt(d)*x))/sqrt(c)/sqrt(d)-1/4*I*polylog(2,1+2*sqrt(c)*sqrt(d)*(-a*x+1)/(I*a*sqrt(c)-sqrt(d))/(sqrt(c)-I*sqrt(d)*x))/sqrt(c)/sqrt(d)+1/4*I*polylog(2,1-2*sqrt(c)*sqrt(d)*(a*x+1)/(I*a*sqrt(c)+sqrt(d))/(sqrt(c)-I*sqrt(d)*x))/sqrt(c)/sqrt(d),1],
[arccoth(a*x)/(d*x^2+c)^2,x,25,1/2*x*arccoth(a*x)/c/(d*x^2+c)+1/2*arccoth(a*x)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)+1/8*I*ln(sqrt(d)*(-a*x+1)/(I*a*sqrt(c)+sqrt(d)))*ln(1-I*sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)-1/8*I*ln(-sqrt(d)*(a*x+1)/(I*a*sqrt(c)-sqrt(d)))*ln(1-I*sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)-1/8*I*ln(-sqrt(d)*(-a*x+1)/(I*a*sqrt(c)-sqrt(d)))*ln(1+I*sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)+1/8*I*ln(sqrt(d)*(a*x+1)/(I*a*sqrt(c)+sqrt(d)))*ln(1+I*sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)+1/4*a*ln(-a^2*x^2+1)/c/(a^2*c+d)-1/4*a*ln(d*x^2+c)/c/(a^2*c+d)+1/8*I*polylog(2,a*(sqrt(c)-I*sqrt(d)*x)/(a*sqrt(c)-I*sqrt(d)))/c^(3/2)/sqrt(d)-1/8*I*polylog(2,a*(sqrt(c)-I*sqrt(d)*x)/(a*sqrt(c)+I*sqrt(d)))/c^(3/2)/sqrt(d)+1/8*I*polylog(2,a*(sqrt(c)+I*sqrt(d)*x)/(a*sqrt(c)-I*sqrt(d)))/c^(3/2)/sqrt(d)-1/8*I*polylog(2,a*(sqrt(c)+I*sqrt(d)*x)/(a*sqrt(c)+I*sqrt(d)))/c^(3/2)/sqrt(d),1],
[arccoth(a*x)/(d*x^2+c)^3,x,23,1/8*a/c/(a^2*c+d)/(d*x^2+c)+1/4*x*arccoth(a*x)/c/(d*x^2+c)^2+3/8*x*arccoth(a*x)/c^2/(d*x^2+c)+3/8*arccoth(a*x)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)+3/32*I*ln(sqrt(d)*(-a*x+1)/(I*a*sqrt(c)+sqrt(d)))*ln(1-I*sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)-3/32*I*ln(-sqrt(d)*(a*x+1)/(I*a*sqrt(c)-sqrt(d)))*ln(1-I*sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)-3/32*I*ln(-sqrt(d)*(-a*x+1)/(I*a*sqrt(c)-sqrt(d)))*ln(1+I*sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)+3/32*I*ln(sqrt(d)*(a*x+1)/(I*a*sqrt(c)+sqrt(d)))*ln(1+I*sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)+1/16*a*(5*a^2*c+3*d)*ln(-a^2*x^2+1)/c^2/(a^2*c+d)^2-1/16*a*(5*a^2*c+3*d)*ln(d*x^2+c)/c^2/(a^2*c+d)^2+3/32*I*polylog(2,a*(sqrt(c)-I*sqrt(d)*x)/(a*sqrt(c)-I*sqrt(d)))/c^(5/2)/sqrt(d)-3/32*I*polylog(2,a*(sqrt(c)-I*sqrt(d)*x)/(a*sqrt(c)+I*sqrt(d)))/c^(5/2)/sqrt(d)+3/32*I*polylog(2,a*(sqrt(c)+I*sqrt(d)*x)/(a*sqrt(c)-I*sqrt(d)))/c^(5/2)/sqrt(d)-3/32*I*polylog(2,a*(sqrt(c)+I*sqrt(d)*x)/(a*sqrt(c)+I*sqrt(d)))/c^(5/2)/sqrt(d),1],
[sqrt(-a*x^2+a)*arccoth(x),x,3,1/2*sqrt(-a*x^2+a)+1/2*x*sqrt(-a*x^2+a)*arccoth(x)-a*sqrt(-x^2+1)*arccoth(x)*arctan(sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a)-1/2*I*a*sqrt(-x^2+1)*polylog(2,-I*sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a)+1/2*I*a*sqrt(-x^2+1)*polylog(2,I*sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a),1],
[arccoth(x)/sqrt(-a*x^2+a),x,2,-2*sqrt(-x^2+1)*arccoth(x)*arctan(sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a)-I*sqrt(-x^2+1)*polylog(2,-I*sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a)+I*sqrt(-x^2+1)*polylog(2,I*sqrt(1-x)/sqrt(1+x))/sqrt(-a*x^2+a),1],
[arccoth(x)/(-a*x^2+a)^(3/2),x,1,-1/a/sqrt(-a*x^2+a)+x*arccoth(x)/a/sqrt(-a*x^2+a),1],
[arccoth(x)/(-a*x^2+a)^(5/2),x,2,-1/9/a/(-a*x^2+a)^(3/2)-2/3/a^2/sqrt(-a*x^2+a)+1/3*x*arccoth(x)/a/(-a*x^2+a)^(3/2)+2/3*x*arccoth(x)/a^2/sqrt(-a*x^2+a),1],
[arccoth(x)/(-a*x^2+a)^(7/2),x,3,-1/25/a/(-a*x^2+a)^(5/2)-4/45/a^2/(-a*x^2+a)^(3/2)-8/15/a^3/sqrt(-a*x^2+a)+1/5*x*arccoth(x)/a/(-a*x^2+a)^(5/2)+4/15*x*arccoth(x)/a^2/(-a*x^2+a)^(3/2)+8/15*x*arccoth(x)/a^3/sqrt(-a*x^2+a),1],
[sqrt(d*x^2+c)*arccoth(a*x),x,0,Defer(Int)(sqrt(d*x^2+c)*arccoth(a*x),x),0],
[arccoth(a*x)/sqrt(d*x^2+c),x,0,Defer(Int)(arccoth(a*x)/sqrt(d*x^2+c),x),0],
[arccoth(a*x)/(d*x^2+c)^(3/2),x,4,x*arccoth(a*x)/c/sqrt(d*x^2+c)-arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c+d))/c/sqrt(a^2*c+d),1],
[arccoth(a*x)/(d*x^2+c)^(5/2),x,6,1/3*a/c/(a^2*c+d)/sqrt(d*x^2+c)+1/3*x*arccoth(a*x)/c/(d*x^2+c)^(3/2)+2/3*x*arccoth(a*x)/c^2/sqrt(d*x^2+c)-1/3*(3*a^2*c+2*d)*arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c+d))/c^2/(a^2*c+d)^(3/2),1],
[arccoth(a*x)/(d*x^2+c)^(7/2),x,7,1/15*a/c/(a^2*c+d)/(d*x^2+c)^(3/2)+1/15*a*(7*a^2*c+4*d)/c^2/(a^2*c+d)^2/sqrt(d*x^2+c)+1/5*x*arccoth(a*x)/c/(d*x^2+c)^(5/2)+4/15*x*arccoth(a*x)/c^2/(d*x^2+c)^(3/2)+8/15*x*arccoth(a*x)/c^3/sqrt(d*x^2+c)-1/15*(15*a^4*c^2+20*a^2*c*d+8*d^2)*arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c+d))/c^3/(a^2*c+d)^(5/2),1],
[arccoth(a*x)/(d*x^2+c)^(9/2),x,7,1/35*a/c/(a^2*c+d)/(d*x^2+c)^(5/2)+1/105*a*(11*a^2*c+6*d)/c^2/(a^2*c+d)^2/(d*x^2+c)^(3/2)+1/35*a*(19*a^4*c^2+22*a^2*c*d+8*d^2)/c^3/(a^2*c+d)^3/sqrt(d*x^2+c)+1/7*x*arccoth(a*x)/c/(d*x^2+c)^(7/2)+6/35*x*arccoth(a*x)/c^2/(d*x^2+c)^(5/2)+8/35*x*arccoth(a*x)/c^3/(d*x^2+c)^(3/2)+16/35*x*arccoth(a*x)/c^4/sqrt(d*x^2+c)-1/35*(35*a^6*c^3+70*a^4*c^2*d+56*a^2*c*d^2+16*d^3)*arctanh(a*sqrt(d*x^2+c)/sqrt(a^2*c+d))/c^4/(a^2*c+d)^(7/2),1],
[1/(-x^2+1)/arccoth(x),x,1,ln(arccoth(x)),1],
[arccoth(x)^2/(-x^2+1)^2,x,4,x/(-4*x^2+4)-arccoth(x)/(-2*x^2+2)+x*arccoth(x)^2/(-2*x^2+2)+1/6*arccoth(x)^3+1/4*arctanh(x),1],
[arccoth(x)^n/(-x^2+1),x,1,arccoth(x)^(1+n)/(1+n),1],
[x*arccoth(x)/(-x^2+1),x,4,-1/2*arccoth(x)^2+arccoth(x)*ln(2/(1-x))+1/2*polylog(2,-(1+x)/(1-x)),1],
[arccoth(x)/(-x^2+1),x,1,1/2*arccoth(x)^2,1],
[x*arccoth(x)/(-x^2+1)^2,x,3,-1/4*x/(-x^2+1)+arccoth(x)/(-2*x^2+2)-1/4*arctanh(x),1],
[arccoth(x)/(-x^2+1)^2,x,2,-1/4/(-x^2+1)+x*arccoth(x)/(-2*x^2+2)+1/4*arccoth(x)^2,1],
[x*arccoth(x)/(-x^2+1)^3,x,4,-1/16*x/(-x^2+1)^2-3*x/(-32*x^2+32)+1/4*arccoth(x)/(-x^2+1)^2-3/32*arctanh(x),1],
[arccoth(x)/(-x^2+1)^3,x,3,-1/16/(-x^2+1)^2-3/(-16*x^2+16)+1/4*x*arccoth(x)/(-x^2+1)^2+3*x*arccoth(x)/(-8*x^2+8)+3/16*arccoth(x)^2,1]]: