lst:=[[x^5*arccot(a*x),x,4,1/6*x/a^5-1/18*x^3/a^3+1/30*x^5/a+1/6*x^6*arccot(a*x)-1/6*arctan(a*x)/a^6,1],
[x^4*arccot(a*x),x,4,-1/10*x^2/a^3+1/20*x^4/a+1/5*x^5*arccot(a*x)+1/10*ln(a^2*x^2+1)/a^5,1],
[x^3*arccot(a*x),x,4,-1/4*x/a^3+1/12*x^3/a+1/4*x^4*arccot(a*x)+1/4*arctan(a*x)/a^4,1],
[x^2*arccot(a*x),x,4,1/6*x^2/a+1/3*x^3*arccot(a*x)-1/6*ln(a^2*x^2+1)/a^3,1],
[x*arccot(a*x),x,3,1/2*x/a+1/2*x^2*arccot(a*x)-1/2*arctan(a*x)/a^2,1],
[arccot(a*x),x,2,x*arccot(a*x)+1/2*ln(a^2*x^2+1)/a,1],
[arccot(a*x)/x,x,3,-1/2*I*polylog(2,-I/a/x)+1/2*I*polylog(2,I/a/x),1],
[arccot(a*x)/x^2,x,5,-arccot(a*x)/x-a*ln(x)+1/2*a*ln(a^2*x^2+1),1],
[arccot(a*x)/x^3,x,3,1/2*a/x-1/2*arccot(a*x)/x^2+1/2*a^2*arctan(a*x),1],
[arccot(a*x)/x^4,x,4,1/6*a/x^2-1/3*arccot(a*x)/x^3+1/3*a^3*ln(x)-1/6*a^3*ln(a^2*x^2+1),1],
[arccot(a*x)/x^5,x,4,1/12*a/x^3-1/4*a^3/x-1/4*arccot(a*x)/x^4-1/4*a^4*arctan(a*x),1],
[x^5*arccot(a*x)^2,x,15,-4/45*x^2/a^4+1/60*x^4/a^2+1/3*x*arccot(a*x)/a^5-1/9*x^3*arccot(a*x)/a^3+1/15*x^5*arccot(a*x)/a+1/6*arccot(a*x)^2/a^6+1/6*x^6*arccot(a*x)^2+23/90*ln(a^2*x^2+1)/a^6,1],
[x^4*arccot(a*x)^2,x,14,-3/10*x/a^4+1/30*x^3/a^2-1/5*x^2*arccot(a*x)/a^3+1/10*x^4*arccot(a*x)/a+1/5*I*arccot(a*x)^2/a^5+1/5*x^5*arccot(a*x)^2+3/10*arctan(a*x)/a^5-2/5*arccot(a*x)*ln(2/(1+I*a*x))/a^5+1/5*I*polylog(2,1-2/(1+I*a*x))/a^5,1],
[x^3*arccot(a*x)^2,x,10,1/12*x^2/a^2-1/2*x*arccot(a*x)/a^3+1/6*x^3*arccot(a*x)/a-1/4*arccot(a*x)^2/a^4+1/4*x^4*arccot(a*x)^2-1/3*ln(a^2*x^2+1)/a^4,1],
[x^2*arccot(a*x)^2,x,9,1/3*x/a^2+1/3*x^2*arccot(a*x)/a-1/3*I*arccot(a*x)^2/a^3+1/3*x^3*arccot(a*x)^2-1/3*arctan(a*x)/a^3+2/3*arccot(a*x)*ln(2/(1+I*a*x))/a^3-1/3*I*polylog(2,1-2/(1+I*a*x))/a^3,1],
[x*arccot(a*x)^2,x,5,x*arccot(a*x)/a+1/2*arccot(a*x)^2/a^2+1/2*x^2*arccot(a*x)^2+1/2*ln(a^2*x^2+1)/a^2,1],
[arccot(a*x)^2,x,5,I*arccot(a*x)^2/a+x*arccot(a*x)^2-2*arccot(a*x)*ln(2/(1+I*a*x))/a+I*polylog(2,1-2/(1+I*a*x))/a,1],
[arccot(a*x)^2/x,x,6,2*arccot(a*x)^2*arccoth(1-2/(1+I*a*x))-I*arccot(a*x)*polylog(2,1-2*I/(I+a*x))+I*arccot(a*x)*polylog(2,1-2*a*x/(I+a*x))-1/2*polylog(3,1-2*I/(I+a*x))+1/2*polylog(3,1-2*a*x/(I+a*x)),1],
[arccot(a*x)^2/x^2,x,4,-I*a*arccot(a*x)^2-arccot(a*x)^2/x-2*a*arccot(a*x)*ln(2-2/(1-I*a*x))-I*a*polylog(2,-1+2/(1-I*a*x)),1],
[arccot(a*x)^2/x^3,x,8,a*arccot(a*x)/x-1/2*a^2*arccot(a*x)^2-1/2*arccot(a*x)^2/x^2+a^2*ln(x)-1/2*a^2*ln(a^2*x^2+1),1],
[arccot(a*x)^2/x^4,x,8,-1/3*a^2/x+1/3*a*arccot(a*x)/x^2+1/3*I*a^3*arccot(a*x)^2-1/3*arccot(a*x)^2/x^3-1/3*a^3*arctan(a*x)+2/3*a^3*arccot(a*x)*ln(2-2/(1-I*a*x))+1/3*I*a^3*polylog(2,-1+2/(1-I*a*x)),1],
[arccot(a*x)^2/x^5,x,13,-1/12*a^2/x^2+1/6*a*arccot(a*x)/x^3-1/2*a^3*arccot(a*x)/x+1/4*a^4*arccot(a*x)^2-1/4*arccot(a*x)^2/x^4-2/3*a^4*ln(x)+1/3*a^4*ln(a^2*x^2+1),1],
[x^5*arccot(a*x)^3,x,33,-19/60*x/a^5+1/60*x^3/a^3-4/15*x^2*arccot(a*x)/a^4+1/20*x^4*arccot(a*x)/a^2+23/30*I*arccot(a*x)^2/a^6+1/2*x*arccot(a*x)^2/a^5-1/6*x^3*arccot(a*x)^2/a^3+1/10*x^5*arccot(a*x)^2/a+1/6*arccot(a*x)^3/a^6+1/6*x^6*arccot(a*x)^3+19/60*arctan(a*x)/a^6-23/15*arccot(a*x)*ln(2/(1+I*a*x))/a^6+23/30*I*polylog(2,1-2/(1+I*a*x))/a^6,1],
[x^4*arccot(a*x)^3,x,22,1/20*x^2/a^3-9/10*x*arccot(a*x)/a^4+1/10*x^3*arccot(a*x)/a^2-9/20*arccot(a*x)^2/a^5-3/10*x^2*arccot(a*x)^2/a^3+3/20*x^4*arccot(a*x)^2/a+1/5*I*arccot(a*x)^3/a^5+1/5*x^5*arccot(a*x)^3-3/5*arccot(a*x)^2*ln(2/(1+I*a*x))/a^5-1/2*ln(a^2*x^2+1)/a^5+3/5*I*arccot(a*x)*polylog(2,1-2/(1+I*a*x))/a^5-3/10*polylog(3,1-2/(1+I*a*x))/a^5,1],
[x^3*arccot(a*x)^3,x,18,1/4*x/a^3+1/4*x^2*arccot(a*x)/a^2-I*arccot(a*x)^2/a^4-3/4*x*arccot(a*x)^2/a^3+1/4*x^3*arccot(a*x)^2/a-1/4*arccot(a*x)^3/a^4+1/4*x^4*arccot(a*x)^3-1/4*arctan(a*x)/a^4+2*arccot(a*x)*ln(2/(1+I*a*x))/a^4-I*polylog(2,1-2/(1+I*a*x))/a^4,1],
[x^2*arccot(a*x)^3,x,11,x*arccot(a*x)/a^2+1/2*arccot(a*x)^2/a^3+1/2*x^2*arccot(a*x)^2/a-1/3*I*arccot(a*x)^3/a^3+1/3*x^3*arccot(a*x)^3+arccot(a*x)^2*ln(2/(1+I*a*x))/a^3+1/2*ln(a^2*x^2+1)/a^3-I*arccot(a*x)*polylog(2,1-2/(1+I*a*x))/a^3+1/2*polylog(3,1-2/(1+I*a*x))/a^3,1],
[x*arccot(a*x)^3,x,8,3/2*I*arccot(a*x)^2/a^2+3/2*x*arccot(a*x)^2/a+1/2*arccot(a*x)^3/a^2+1/2*x^2*arccot(a*x)^3-3*arccot(a*x)*ln(2/(1+I*a*x))/a^2+3/2*I*polylog(2,1-2/(1+I*a*x))/a^2,1],
[arccot(a*x)^3,x,5,I*arccot(a*x)^3/a+x*arccot(a*x)^3-3*arccot(a*x)^2*ln(2/(1+I*a*x))/a+3*I*arccot(a*x)*polylog(2,1-2/(1+I*a*x))/a-3/2*polylog(3,1-2/(1+I*a*x))/a,1],
[arccot(a*x)^3/x,x,8,2*arccot(a*x)^3*arccoth(1-2/(1+I*a*x))-3/2*I*arccot(a*x)^2*polylog(2,1-2*I/(I+a*x))+3/2*I*arccot(a*x)^2*polylog(2,1-2*a*x/(I+a*x))-3/2*arccot(a*x)*polylog(3,1-2*I/(I+a*x))+3/2*arccot(a*x)*polylog(3,1-2*a*x/(I+a*x))+3/4*I*polylog(4,1-2*I/(I+a*x))-3/4*I*polylog(4,1-2*a*x/(I+a*x)),1],
[arccot(a*x)^3/x^2,x,5,-I*a*arccot(a*x)^3-arccot(a*x)^3/x-3*a*arccot(a*x)^2*ln(2-2/(1-I*a*x))-3*I*a*arccot(a*x)*polylog(2,-1+2/(1-I*a*x))-3/2*a*polylog(3,-1+2/(1-I*a*x)),1],
[arccot(a*x)^3/x^3,x,7,3/2*I*a^2*arccot(a*x)^2+3/2*a*arccot(a*x)^2/x-1/2*a^2*arccot(a*x)^3-1/2*arccot(a*x)^3/x^2+3*a^2*arccot(a*x)*ln(2-2/(1-I*a*x))+3/2*I*a^2*polylog(2,-1+2/(1-I*a*x)),1],
[arccot(a*x)^3/x^4,x,14,-a^2*arccot(a*x)/x+1/2*a^3*arccot(a*x)^2+1/2*a*arccot(a*x)^2/x^2+1/3*I*a^3*arccot(a*x)^3-1/3*arccot(a*x)^3/x^3-a^3*ln(x)+1/2*a^3*ln(a^2*x^2+1)+a^3*arccot(a*x)^2*ln(2-2/(1-I*a*x))+I*a^3*arccot(a*x)*polylog(2,-1+2/(1-I*a*x))+1/2*a^3*polylog(3,-1+2/(1-I*a*x)),1],
[arccot(a*x)^3/x^5,x,16,1/4*a^3/x-1/4*a^2*arccot(a*x)/x^2-I*a^4*arccot(a*x)^2+1/4*a*arccot(a*x)^2/x^3-3/4*a^3*arccot(a*x)^2/x+1/4*a^4*arccot(a*x)^3-1/4*arccot(a*x)^3/x^4+1/4*a^4*arctan(a*x)-2*a^4*arccot(a*x)*ln(2-2/(1-I*a*x))-I*a^4*polylog(2,-1+2/(1-I*a*x)),1],
[x^m*arccot(a*x)^3,x,0,Defer(Int)(x^m*arccot(a*x)^3,x),0],
[x^m*arccot(a*x)^2,x,0,Defer(Int)(x^m*arccot(a*x)^2,x),0],
[x^m*arccot(a*x),x,2,x^(1+m)*arccot(a*x)/(1+m)+a*x^(2+m)*hypergeom([1, 1+1/2*m],[2+1/2*m],-a^2*x^2)/(m^2+3*m+2),1],
[x^5*arccot(a*x^2),x,4,1/12*x^4/a+1/6*x^6*arccot(a*x^2)-1/12*ln(a^2*x^4+1)/a^3,1],
[x^3*arccot(a*x^2),x,4,1/4*x^2/a+1/4*x^4*arccot(a*x^2)-1/4*arctan(a*x^2)/a^2,1],
[x*arccot(a*x^2),x,3,1/2*x^2*arccot(a*x^2)+1/4*ln(a^2*x^4+1)/a,1],
[arccot(a*x^2)/x,x,4,-1/4*I*polylog(2,-I/a/x^2)+1/4*I*polylog(2,I/a/x^2),1],
[arccot(a*x^2)/x^3,x,5,-1/2*arccot(a*x^2)/x^2-a*ln(x)+1/4*a*ln(a^2*x^4+1),1],
[arccot(a*x^2)/x^5,x,4,1/4*a/x^2-1/4*arccot(a*x^2)/x^4+1/4*a^2*arctan(a*x^2),1],
[x^4*arccot(a*x^2),x,10,2/15*x^3/a+1/5*x^5*arccot(a*x^2)+1/5*arctan(1-sqrt(2)*sqrt(a)*x)/sqrt(2)/a^(5/2)-1/5*arctan(1+sqrt(2)*sqrt(a)*x)/sqrt(2)/a^(5/2)+1/5*arctanh(sqrt(2)*sqrt(a)*x/(a*x^2+1))/sqrt(2)/a^(5/2),1],
[x^2*arccot(a*x^2),x,10,2/3*x/a+1/3*x^3*arccot(a*x^2)+1/3*arctan(1-sqrt(2)*sqrt(a)*x)/sqrt(2)/a^(3/2)-1/3*arctan(1+sqrt(2)*sqrt(a)*x)/sqrt(2)/a^(3/2)-1/3*arctanh(sqrt(2)*sqrt(a)*x/(a*x^2+1))/sqrt(2)/a^(3/2),1],
[arccot(a*x^2),x,9,x*arccot(a*x^2)-arctan(1-sqrt(2)*sqrt(a)*x)/sqrt(2)/sqrt(a)+arctan(1+sqrt(2)*sqrt(a)*x)/sqrt(2)/sqrt(a)-arctanh(sqrt(2)*sqrt(a)*x/(a*x^2+1))/sqrt(2)/sqrt(a),1],
[arccot(a*x^2)/x^2,x,9,-arccot(a*x^2)/x+sqrt(a)*arctan(1-sqrt(2)*sqrt(a)*x)/sqrt(2)-sqrt(a)*arctan(1+sqrt(2)*sqrt(a)*x)/sqrt(2)-sqrt(a)*arctanh(sqrt(2)*sqrt(a)*x/(a*x^2+1))/sqrt(2),1],
[arccot(a*x^2)/x^4,x,10,2/3*a/x-1/3*arccot(a*x^2)/x^3-1/3*a^(3/2)*arctan(1-sqrt(2)*sqrt(a)*x)/sqrt(2)+1/3*a^(3/2)*arctan(1+sqrt(2)*sqrt(a)*x)/sqrt(2)-1/3*a^(3/2)*arctanh(sqrt(2)*sqrt(a)*x/(a*x^2+1))/sqrt(2),1],
[arccot(a*x^5)/x,x,4,-1/10*I*polylog(2,-I/a/x^5)+1/10*I*polylog(2,I/a/x^5),1],
[arccot(1/x),x,3,x*arccot(1/x)-1/2*ln(x^2+1),1],
[x^2*arccot(sqrt(x)),x,6,1/3*sqrt(x)-1/9*x^(3/2)+1/15*x^(5/2)+1/3*x^3*arccot(sqrt(x))-1/3*arctan(sqrt(x)),1],
[x*arccot(sqrt(x)),x,5,-1/2*sqrt(x)+1/6*x^(3/2)+1/2*x^2*arccot(sqrt(x))+1/2*arctan(sqrt(x)),1],
[arccot(sqrt(x)),x,4,sqrt(x)+x*arccot(sqrt(x))-arctan(sqrt(x)),1],
[arccot(sqrt(x))/x,x,4,-I*polylog(2,-I/sqrt(x))+I*polylog(2,I/sqrt(x)),1],
[arccot(sqrt(x))/x^2,x,4,1/sqrt(x)-arccot(sqrt(x))/x+arctan(sqrt(x)),1],
[arccot(sqrt(x))/x^3,x,5,1/6/x^(3/2)-1/2/sqrt(x)-1/2*arccot(sqrt(x))/x^2-1/2*arctan(sqrt(x)),1],
[x^(3/2)*arccot(sqrt(x)),x,3,-1/5*x+1/10*x^2+2/5*x^(5/2)*arccot(sqrt(x))+1/5*ln(1+x),1],
[sqrt(x)*arccot(sqrt(x)),x,3,1/3*x+2/3*x^(3/2)*arccot(sqrt(x))-1/3*ln(1+x),1],
[arccot(sqrt(x))/sqrt(x),x,2,2*sqrt(x)*arccot(sqrt(x))+ln(1+x),1],
[arccot(sqrt(x))/x^(3/2),x,4,-2*arccot(sqrt(x))/sqrt(x)-ln(x)+ln(1+x),1],
[arccot(sqrt(x))/x^(5/2),x,3,1/3/x-2/3*arccot(sqrt(x))/x^(3/2)+1/3*ln(x)-1/3*ln(1+x),1],
[arccot(a*x^n)/x,x,4,-1/2*I*polylog(2,-I/a/(x^n))/n+1/2*I*polylog(2,I/a/(x^n))/n,1]]: