lst:=[[x^7*sqrt(x^2+sqrt(x^4+1)),x,7,8/315*x^2/sqrt(x^2+sqrt(x^4+1))-1/63*x^6/sqrt(x^2+sqrt(x^4+1))-16/315*sqrt(x^2+sqrt(x^4+1))+2/105*x^4*sqrt(x^2+sqrt(x^4+1))+1/9*x^8*sqrt(x^2+sqrt(x^4+1)),1],
[x^5*sqrt(x^2+sqrt(x^4+1)),x,6,8/105/sqrt(x^2+sqrt(x^4+1))-1/35*x^4/sqrt(x^2+sqrt(x^4+1))+4/105*x^2*sqrt(x^2+sqrt(x^4+1))+1/7*x^6*sqrt(x^2+sqrt(x^4+1)),1],
[x^3*sqrt(x^2+sqrt(x^4+1)),x,5,-1/15*x^2/sqrt(x^2+sqrt(x^4+1))+2/15*sqrt(x^2+sqrt(x^4+1))+1/5*x^4*sqrt(x^2+sqrt(x^4+1)),1],
[x*sqrt(x^2+sqrt(x^4+1)),x,4,-1/2/sqrt(x^2+sqrt(x^4+1))+1/6*(x^2+sqrt(x^4+1))^(3/2),1],
[sqrt(x^2+sqrt(x^4+1))/x,x,5,sqrt(x^2+sqrt(x^4+1))-arctan(sqrt(x^2+sqrt(x^4+1)))-arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[sqrt(x^2+sqrt(x^4+1))/x^3,x,6,-1/2*sqrt(x^2+sqrt(x^4+1))/x^2+1/2*arctan(sqrt(x^2+sqrt(x^4+1)))-1/2*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[sqrt(x^2+sqrt(x^4+1))/x^5,x,7,-1/8/x^2/sqrt(x^2+sqrt(x^4+1))-1/4*sqrt(x^2+sqrt(x^4+1))/x^4-1/8*arctan(sqrt(x^2+sqrt(x^4+1)))-1/8*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[x^2*sqrt(x^2+sqrt(x^4+1)),x,4,-1/8*x/sqrt(x^2+sqrt(x^4+1))+1/4*x^3*sqrt(x^2+sqrt(x^4+1))+1/8*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1)),x,3,1/2*x*sqrt(x^2+sqrt(x^4+1))+1/2*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/x^2,x,3,-sqrt(x^2+sqrt(x^4+1))/x+arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/x^4,x,2,1/6/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/2*sqrt(x^2+sqrt(x^4+1))/x^3,1],
[sqrt(x^2+sqrt(x^4+1))/x^6,x,3,-1/5*sqrt(x^2+sqrt(x^4+1))/x^5-1/15*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[sqrt(x^2+sqrt(x^4+1))/x^8,x,4,-4/105/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/35/x^5/sqrt(x^2+sqrt(x^4+1))-1/7*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[sqrt(x^2+sqrt(x^4+1))/x^10,x,5,-1/63/x^7/sqrt(x^2+sqrt(x^4+1))-1/9*sqrt(x^2+sqrt(x^4+1))/x^9-2/105*sqrt(x^2+sqrt(x^4+1))/x^5+8/315*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[(x^2+sqrt(x^4+1))^(9/2),x,4,3/5*x*sqrt(x^2+sqrt(x^4+1))+3/10*x*(x^2+sqrt(x^4+1))^(5/2)+1/10*x*(x^2+sqrt(x^4+1))^(9/2),1],
[(x^2+sqrt(x^4+1))^(7/2),x,5,7/16*x*(x^2+sqrt(x^4+1))^(3/2)+1/8*x*(x^2+sqrt(x^4+1))^(7/2)+7/16*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[(x^2+sqrt(x^4+1))^(3/2),x,4,1/4*x*(x^2+sqrt(x^4+1))^(3/2)+3/4*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^7/sqrt(x^2+sqrt(x^4+1)),x,7,-16/315/sqrt(x^2+sqrt(x^4+1))+2/105*x^4/sqrt(x^2+sqrt(x^4+1))+1/9*x^8/sqrt(x^2+sqrt(x^4+1))-8/315*x^2*sqrt(x^2+sqrt(x^4+1))+1/63*x^6*sqrt(x^2+sqrt(x^4+1)),1],
[x^5/sqrt(x^2+sqrt(x^4+1)),x,6,4/105*x^2/sqrt(x^2+sqrt(x^4+1))+1/7*x^6/sqrt(x^2+sqrt(x^4+1))-8/105*sqrt(x^2+sqrt(x^4+1))+1/35*x^4*sqrt(x^2+sqrt(x^4+1)),1],
[x^3/sqrt(x^2+sqrt(x^4+1)),x,5,2/15/sqrt(x^2+sqrt(x^4+1))+1/5*x^4/sqrt(x^2+sqrt(x^4+1))+1/15*x^2*sqrt(x^2+sqrt(x^4+1)),1],
[x/sqrt(x^2+sqrt(x^4+1)),x,4,-1/6/(x^2+sqrt(x^4+1))^(3/2)+1/2*sqrt(x^2+sqrt(x^4+1)),1],
[1/x/sqrt(x^2+sqrt(x^4+1)),x,5,1/sqrt(x^2+sqrt(x^4+1))+arctan(sqrt(x^2+sqrt(x^4+1)))-arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[1/x^3/sqrt(x^2+sqrt(x^4+1)),x,5,-1/2/x^2/sqrt(x^2+sqrt(x^4+1))+1/2*arctan(sqrt(x^2+sqrt(x^4+1)))+1/2*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[1/x^5/sqrt(x^2+sqrt(x^4+1)),x,6,-1/4/x^4/sqrt(x^2+sqrt(x^4+1))+1/8*sqrt(x^2+sqrt(x^4+1))/x^2+1/8*arctan(sqrt(x^2+sqrt(x^4+1)))-1/8*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[x^6/sqrt(x^2+sqrt(x^4+1)),x,6,5/192*x^3/sqrt(x^2+sqrt(x^4+1))+1/8*x^7/sqrt(x^2+sqrt(x^4+1))-5/128*x*sqrt(x^2+sqrt(x^4+1))+1/48*x^5*sqrt(x^2+sqrt(x^4+1))+5/128*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^4/sqrt(x^2+sqrt(x^4+1)),x,5,1/16*x/sqrt(x^2+sqrt(x^4+1))+1/6*x^5/sqrt(x^2+sqrt(x^4+1))+1/24*x^3*sqrt(x^2+sqrt(x^4+1))-1/16*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^2/sqrt(x^2+sqrt(x^4+1)),x,4,1/4*x^3/sqrt(x^2+sqrt(x^4+1))+1/8*x*sqrt(x^2+sqrt(x^4+1))-1/8*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/sqrt(x^2+sqrt(x^4+1)),x,3,1/2*x/sqrt(x^2+sqrt(x^4+1))+1/2*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/x^2/sqrt(x^2+sqrt(x^4+1)),x,3,-1/x/sqrt(x^2+sqrt(x^4+1))-arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/x^4/sqrt(x^2+sqrt(x^4+1)),x,2,-1/3/x^3/sqrt(x^2+sqrt(x^4+1))+1/3*sqrt(x^2+sqrt(x^4+1))/x,1],
[1/x^6/sqrt(x^2+sqrt(x^4+1)),x,2,1/15/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/5/x^5/sqrt(x^2+sqrt(x^4+1)),1],
[1/x^8/sqrt(x^2+sqrt(x^4+1)),x,3,-1/7/x^7/sqrt(x^2+sqrt(x^4+1))+1/35*sqrt(x^2+sqrt(x^4+1))/x^5-4/105*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[1/x^10/sqrt(x^2+sqrt(x^4+1)),x,4,-8/315/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/9/x^9/sqrt(x^2+sqrt(x^4+1))-2/105/x^5/sqrt(x^2+sqrt(x^4+1))+1/63*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[1/x^12/sqrt(x^2+sqrt(x^4+1)),x,5,-1/11/x^11/sqrt(x^2+sqrt(x^4+1))-8/693/x^7/sqrt(x^2+sqrt(x^4+1))+1/99*sqrt(x^2+sqrt(x^4+1))/x^9-16/1155*sqrt(x^2+sqrt(x^4+1))/x^5+64/3465*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[1/(x^2+sqrt(x^4+1))^(3/2),x,3,1/4*x/(x^2+sqrt(x^4+1))^(3/2)+3/4*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/(x^2+sqrt(x^4+1))^(5/2),x,2,1/6*x/(x^2+sqrt(x^4+1))^(5/2)+5/6*x/sqrt(x^2+sqrt(x^4+1)),1],
[x^7*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,1/32*a^4*d^8*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-4+p)/c^4/(4-p)-1/16*a^3*d^6*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-2+p)/c^4/(2-p)-1/16*a*d^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(2+p)/c^4/(2+p)+1/32*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(4+p)/c^4/(4+p),1],
[x^5*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,-1/16*a^3*d^6*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-3+p)/c^3/(3-p)+1/16*a^2*d^4*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-1+p)/c^3/(1-p)-1/16*a*d^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(p+1)/c^3/(p+1)+1/16*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(3+p)/c^3/(3+p),1],
[x^3*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,5,1/8*a^2*d^4*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-2+p)/c^2/(2-p)+1/8*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(2+p)/c^2/(2+p),1],
[x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,-1/4*a*d^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-1+p)/c/(1-p)+1/4*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(p+1)/c/(p+1),1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x,x,4,1/2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/p-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p*hypergeom([1, 1/2*p],[1+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/p,1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^3,x,4,-1/2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^2-c*p*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(p+1)*hypergeom([1, 1/2*p+1/2],[3/2+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/a/d^2/(p+1),1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^5,x,4,-1/4*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^4+c^2*p*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(2+p)*hypergeom([2, 1+1/2*p],[2+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/a^2/d^4/(2+p),1],
[x^4*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,1/4*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-2+p)*(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2)^(5/2)/sqrt(2)/c^2/(5+2*p)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))+a^2*d^4*p*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-2+p)*sqrt(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2)*hypergeom([-3/2, -5/4+1/2*p],[-1/4+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/sqrt(2)/c^2/(-4*p^2+25)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))/sqrt(1-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2),1],
[x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,1/2*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-1+p)*(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2)^(3/2)/sqrt(2)/c/(3+2*p)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))-sqrt(2)*a*d^2*p*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(-1+p)*sqrt(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2)*hypergeom([-1/2, -3/4+1/2*p],[1/4+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/c/(-4*p^2+9)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))/sqrt(1-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2),1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p,x,4,x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/(1-2*p)-2*sqrt(2)*p*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(2+p)*sqrt(1-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)*hypergeom([1/2, 3/4+1/2*p],[7/4+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/(-4*p^2-4*p+3)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))/sqrt(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2),1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^2,x,4,-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x+2*sqrt(2)*c*p*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(p+1)*sqrt(1-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)*hypergeom([1/2, 1/4+1/2*p],[5/4+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/(1+2*p)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))/sqrt(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2),1],
[(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^4,x,4,-1/3*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^p/x^3-4/3*sqrt(2)*c^2*p*x*(c*x^2+d*sqrt(a+c^2*x^4/d^2))^(2+p)*sqrt(1-(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)*hypergeom([3/2, 3/4+1/2*p],[7/4+1/2*p],(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2/a/d^2)/a/d^2/(3+2*p)/sqrt(c*x^2*(c*x^2+d*sqrt(a+c^2*x^4/d^2)))/sqrt(-a*d^2+(c*x^2+d*sqrt(a+c^2*x^4/d^2))^2),1],
[x^7*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,6,-16/35/sqrt(x^2+sqrt(x^4+1))+6/35*x^4/sqrt(x^2+sqrt(x^4+1))-8/35*x^2*sqrt(x^2+sqrt(x^4+1))+1/7*x^6*sqrt(x^2+sqrt(x^4+1)),1],
[x^5*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,5,4/15*x^2/sqrt(x^2+sqrt(x^4+1))-8/15*sqrt(x^2+sqrt(x^4+1))+1/5*x^4*sqrt(x^2+sqrt(x^4+1)),1],
[x^3*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,4,2/3/sqrt(x^2+sqrt(x^4+1))+1/3*x^2*sqrt(x^2+sqrt(x^4+1)),1],
[x*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,3,sqrt(x^2+sqrt(x^4+1)),1],
[sqrt(x^2+sqrt(x^4+1))/x/sqrt(x^4+1),x,4,arctan(sqrt(x^2+sqrt(x^4+1)))-arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[sqrt(x^2+sqrt(x^4+1))/x^3/sqrt(x^4+1),x,5,-1/2/x^2/sqrt(x^2+sqrt(x^4+1))-1/2*arctan(sqrt(x^2+sqrt(x^4+1)))-1/2*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[sqrt(x^2+sqrt(x^4+1))/x^5/sqrt(x^4+1),x,6,-1/4/x^4/sqrt(x^2+sqrt(x^4+1))-3/8*sqrt(x^2+sqrt(x^4+1))/x^2-3/8*arctan(sqrt(x^2+sqrt(x^4+1)))+3/8*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[x^4*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,4,3/8*x/sqrt(x^2+sqrt(x^4+1))+1/4*x^3*sqrt(x^2+sqrt(x^4+1))-3/8*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^2*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,3,1/2*x*sqrt(x^2+sqrt(x^4+1))-1/2*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,2,arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/x^2/sqrt(x^4+1),x,1,-1/x/sqrt(x^2+sqrt(x^4+1)),1],
[sqrt(x^2+sqrt(x^4+1))/x^4/sqrt(x^4+1),x,1,-1/3*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[sqrt(x^2+sqrt(x^4+1))/x^6/sqrt(x^4+1),x,2,-4/15/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/5/x^5/sqrt(x^2+sqrt(x^4+1)),1],
[sqrt(x^2+sqrt(x^4+1))/x^8/sqrt(x^4+1),x,3,-1/7/x^7/sqrt(x^2+sqrt(x^4+1))-6/35*sqrt(x^2+sqrt(x^4+1))/x^5+8/35*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[sqrt(x^2+sqrt(x^4+1))/x^10/sqrt(x^4+1),x,4,64/315/x^3/(x^2+sqrt(x^4+1))^(3/2)-1/9/x^9/sqrt(x^2+sqrt(x^4+1))+16/105/x^5/sqrt(x^2+sqrt(x^4+1))-8/63*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[x^4*(x^2+sqrt(x^4+1))^(3/2)/sqrt(x^4+1),x,5,1/6*x^3/sqrt(x^2+sqrt(x^4+1))-1/4*x*sqrt(x^2+sqrt(x^4+1))+1/3*x^5*sqrt(x^2+sqrt(x^4+1))+1/4*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^2*(x^2+sqrt(x^4+1))^(3/2)/sqrt(x^4+1),x,4,1/4*x/sqrt(x^2+sqrt(x^4+1))+1/2*x^3*sqrt(x^2+sqrt(x^4+1))-1/4*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[(x^2+sqrt(x^4+1))^(3/2)/sqrt(x^4+1),x,1,x*sqrt(x^2+sqrt(x^4+1)),1],
[(x^2+sqrt(x^4+1))^(3/2)/x^2/sqrt(x^4+1),x,3,-sqrt(x^2+sqrt(x^4+1))/x+sqrt(2)*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1))),1],
[(x^2+sqrt(x^4+1))^(3/2)/x^4/sqrt(x^4+1),x,2,-4/3/x/sqrt(x^2+sqrt(x^4+1))-1/3*sqrt(x^2+sqrt(x^4+1))/x^3,1],
[(x^2+sqrt(x^4+1))^(3/2)/x^6/sqrt(x^4+1),x,1,-1/5*(x^2+sqrt(x^4+1))^(5/2)/x^5,1],
[(x^2+sqrt(x^4+1))^(3/2)/x^8/sqrt(x^4+1),x,3,-32/105/x^3/(x^2+sqrt(x^4+1))^(3/2)-8/35/x^5/sqrt(x^2+sqrt(x^4+1))-1/7*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[(x^2+sqrt(x^4+1))^(3/2)/x^10/sqrt(x^4+1),x,4,-10/63/x^7/sqrt(x^2+sqrt(x^4+1))-1/9*sqrt(x^2+sqrt(x^4+1))/x^9-4/21*sqrt(x^2+sqrt(x^4+1))/x^5+16/63*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[(x^2+sqrt(x^4+1))^(3/2)/x^12/sqrt(x^4+1),x,5,256/1155/x^3/(x^2+sqrt(x^4+1))^(3/2)-4/33/x^9/sqrt(x^2+sqrt(x^4+1))+64/385/x^5/sqrt(x^2+sqrt(x^4+1))-1/11*sqrt(x^2+sqrt(x^4+1))/x^11-32/231*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[x^7/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,6,8/35*x^2/sqrt(x^2+sqrt(x^4+1))-1/7*x^6/sqrt(x^2+sqrt(x^4+1))-16/35*sqrt(x^2+sqrt(x^4+1))+6/35*x^4*sqrt(x^2+sqrt(x^4+1)),1],
[x^5/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,5,8/15/sqrt(x^2+sqrt(x^4+1))-1/5*x^4/sqrt(x^2+sqrt(x^4+1))+4/15*x^2*sqrt(x^2+sqrt(x^4+1)),1],
[x^3/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,4,-1/3*x^2/sqrt(x^2+sqrt(x^4+1))+2/3*sqrt(x^2+sqrt(x^4+1)),1],
[x/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,3,-1/sqrt(x^2+sqrt(x^4+1)),1],
[1/x/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,4,-arctan(sqrt(x^2+sqrt(x^4+1)))-arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[1/x^3/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,5,-1/2*sqrt(x^2+sqrt(x^4+1))/x^2-1/2*arctan(sqrt(x^2+sqrt(x^4+1)))+1/2*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[1/x^5/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,6,3/8/x^2/sqrt(x^2+sqrt(x^4+1))-1/4*sqrt(x^2+sqrt(x^4+1))/x^4+3/8*arctan(sqrt(x^2+sqrt(x^4+1)))+3/8*arctanh(sqrt(x^2+sqrt(x^4+1))),1],
[x^6/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,5,5/16*x/sqrt(x^2+sqrt(x^4+1))-1/6*x^5/sqrt(x^2+sqrt(x^4+1))+5/24*x^3*sqrt(x^2+sqrt(x^4+1))-5/16*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^4/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,4,-1/4*x^3/sqrt(x^2+sqrt(x^4+1))+3/8*x*sqrt(x^2+sqrt(x^4+1))-3/8*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[x^2/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,3,-1/2*x/sqrt(x^2+sqrt(x^4+1))+1/2*arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,2,arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[1/x^2/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,1,-sqrt(x^2+sqrt(x^4+1))/x,1],
[1/x^4/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,1,-1/3/x^3/(x^2+sqrt(x^4+1))^(3/2),1],
[1/x^6/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,2,-1/5*sqrt(x^2+sqrt(x^4+1))/x^5+4/15*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[1/x^8/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,3,8/35/x^3/(x^2+sqrt(x^4+1))^(3/2)+6/35/x^5/sqrt(x^2+sqrt(x^4+1))-1/7*sqrt(x^2+sqrt(x^4+1))/x^7,1],
[1/x^10/sqrt(x^4+1)/sqrt(x^2+sqrt(x^4+1)),x,4,8/63/x^7/sqrt(x^2+sqrt(x^4+1))-1/9*sqrt(x^2+sqrt(x^4+1))/x^9+16/105*sqrt(x^2+sqrt(x^4+1))/x^5-64/315*(x^2+sqrt(x^4+1))^(3/2)/x^3,1],
[(1+x)^2*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,10,2*sqrt(x^2+sqrt(x^4+1))+1/2*x*sqrt(x^2+sqrt(x^4+1))-1/2*arctan(sqrt(2)*x*sqrt(x^2+sqrt(x^4+1)))/sqrt(2)+arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[(1+x)*sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,7,sqrt(x^2+sqrt(x^4+1))+arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/sqrt(x^4+1),x,2,arctanh(sqrt(2)*x/sqrt(x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(x^2+sqrt(x^4+1))/(1+x)/sqrt(x^4+1),x,10,sqrt(-1/2+1/2*sqrt(2))*arctan(sqrt(1+sqrt(2))*sqrt(x^2+sqrt(x^4+1)))-arctan(sqrt(2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1-x^2-sqrt(x^4+1)))/sqrt(2+2*sqrt(2))-sqrt(1/2+1/2*sqrt(2))*arctanh(sqrt(-1+sqrt(2))*sqrt(x^2+sqrt(x^4+1)))-arctanh(sqrt(-2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1-x^2-sqrt(x^4+1)))/sqrt(-2+2*sqrt(2)),1],
[(1+x)^2*sqrt(-x^2+sqrt(x^4+1))/sqrt(x^4+1),x,10,-2*sqrt(-x^2+sqrt(x^4+1))-1/2*x*sqrt(-x^2+sqrt(x^4+1))+arctan(sqrt(2)*x/sqrt(-x^2+sqrt(x^4+1)))/sqrt(2)+1/2*arctanh(sqrt(2)*x*sqrt(-x^2+sqrt(x^4+1)))/sqrt(2),1],
[(1+x)*sqrt(-x^2+sqrt(x^4+1))/sqrt(x^4+1),x,7,-sqrt(-x^2+sqrt(x^4+1))+arctan(sqrt(2)*x/sqrt(-x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(-x^2+sqrt(x^4+1))/sqrt(x^4+1),x,2,arctan(sqrt(2)*x/sqrt(-x^2+sqrt(x^4+1)))/sqrt(2),1],
[sqrt(-x^2+sqrt(x^4+1))/(1+x)/sqrt(x^4+1),x,10,sqrt(1/2+1/2*sqrt(2))*arctan(sqrt(-1+sqrt(2))*sqrt(-x^2+sqrt(x^4+1)))+arctan(sqrt(-2+2*sqrt(2))*x*sqrt(-x^2+sqrt(x^4+1))/(1-x^2+sqrt(x^4+1)))/sqrt(-2+2*sqrt(2))-sqrt(-1/2+1/2*sqrt(2))*arctanh(sqrt(1+sqrt(2))*sqrt(-x^2+sqrt(x^4+1)))+arctanh(sqrt(2+2*sqrt(2))*x*sqrt(-x^2+sqrt(x^4+1))/(1-x^2+sqrt(x^4+1)))/sqrt(2+2*sqrt(2)),1],
[sqrt(x^2+sqrt(x^4+1))/(x^2+1)/sqrt(x^4+1),x,4,arctan(sqrt(2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1+x^2+sqrt(x^4+1)))/sqrt(2+2*sqrt(2))+arctanh(sqrt(-2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1+x^2+sqrt(x^4+1)))/sqrt(-2+2*sqrt(2)),1],
[sqrt(x^2+sqrt(x^4+1))/(-x^2+1)/sqrt(x^4+1),x,4,-arctan(sqrt(2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1-x^2-sqrt(x^4+1)))/sqrt(2+2*sqrt(2))-arctanh(sqrt(-2+2*sqrt(2))*x*sqrt(x^2+sqrt(x^4+1))/(1-x^2-sqrt(x^4+1)))/sqrt(-2+2*sqrt(2)),1]]: