lst:=[[(b*x^3+a)^5,x,2,a^5*x+5/4*a^4*b*x^4+10/7*a^3*b^2*x^7+a^2*b^3*x^10+5/13*a*b^4*x^13+1/16*b^5*x^16,1],
[(b*x^3+a)^4,x,2,a^4*x+a^3*b*x^4+6/7*a^2*b^2*x^7+2/5*a*b^3*x^10+1/13*b^4*x^13,1],
[(b*x^3+a)^3,x,2,a^3*x+3/4*a^2*b*x^4+3/7*a*b^2*x^7+1/10*b^3*x^10,1],
[(b*x^3+a)^2,x,2,a^2*x+1/2*a*b*x^4+1/7*b^2*x^7,1],
[b*x^3+a,x,1,a*x+1/4*b*x^4,1],
[1/(b*x^3+a),x,6,-arctan((a^(1/3)-2*b^(1/3)*x)/sqrt(3)/a^(1/3))/sqrt(3)/a^(2/3)/b^(1/3)+1/3*ln(a^(1/3)+b^(1/3)*x)/a^(2/3)/b^(1/3)-1/6*ln(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(2/3)/b^(1/3),1],
[1/(b*x^3+a)^2,x,7,1/3*x/a/(b*x^3+a)-2/3*arctan((a^(1/3)-2*b^(1/3)*x)/sqrt(3)/a^(1/3))/sqrt(3)/a^(5/3)/b^(1/3)+2/9*ln(a^(1/3)+b^(1/3)*x)/a^(5/3)/b^(1/3)-1/9*ln(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)/b^(1/3),1],
[1/(b*x^3+a)^3,x,8,1/6*x/a/(b*x^3+a)^2+5/18*x/a^2/(b*x^3+a)-5/9*arctan((a^(1/3)-2*b^(1/3)*x)/sqrt(3)/a^(1/3))/sqrt(3)/a^(8/3)/b^(1/3)+5/27*ln(a^(1/3)+b^(1/3)*x)/a^(8/3)/b^(1/3)-5/54*ln(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(8/3)/b^(1/3),1],
[1/(b*x^3+a+1),x,6,-arctan((1-2*b^(1/3)*x/(1+a)^(1/3))/sqrt(3))/sqrt(3)/(1+a)^(2/3)/b^(1/3)+1/3*ln((1+a)^(1/3)+b^(1/3)*x)/(1+a)^(2/3)/b^(1/3)-1/6*ln((1+a)^(2/3)-(1+a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(1+a)^(2/3)/b^(1/3),1],
[1/(-b*x^3+a+1),x,6,arctan((1+2*b^(1/3)*x/(1+a)^(1/3))/sqrt(3))/sqrt(3)/(1+a)^(2/3)/b^(1/3)-1/3*ln((1+a)^(1/3)-b^(1/3)*x)/(1+a)^(2/3)/b^(1/3)+1/6*ln((1+a)^(2/3)+(1+a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(1+a)^(2/3)/b^(1/3),1],
[1/(b*x^3+a-1),x,6,-arctan((1+2*b^(1/3)*x/(1-a)^(1/3))/sqrt(3))/sqrt(3)/(1-a)^(2/3)/b^(1/3)+1/3*ln((1-a)^(1/3)-b^(1/3)*x)/(1-a)^(2/3)/b^(1/3)-1/6*ln((1-a)^(2/3)+(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(1-a)^(2/3)/b^(1/3),1],
[1/(-b*x^3+a-1),x,6,arctan((1-2*b^(1/3)*x/(1-a)^(1/3))/sqrt(3))/sqrt(3)/(1-a)^(2/3)/b^(1/3)-1/3*ln((1-a)^(1/3)+b^(1/3)*x)/(1-a)^(2/3)/b^(1/3)+1/6*ln((1-a)^(2/3)-(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(1-a)^(2/3)/b^(1/3),1],
[(b*x^3+a)^(5/2),x,4,54/187*a^2*x*sqrt(b*x^3+a)+30/187*a*x*(b*x^3+a)^(3/2)+2/17*x*(b*x^3+a)^(5/2)+54/187*3^(3/4)*sqrt(2+sqrt(3))*a^3*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[(b*x^3+a)^(3/2),x,3,18/55*a*x*sqrt(b*x^3+a)+2/11*x*(b*x^3+a)^(3/2)+18/55*3^(3/4)*sqrt(2+sqrt(3))*a^2*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[sqrt(b*x^3+a),x,2,2/5*x*sqrt(b*x^3+a)+2/5*3^(3/4)*sqrt(2+sqrt(3))*a*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[1/sqrt(b*x^3+a),x,1,2/3*sqrt(2+sqrt(3))*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[1/(b*x^3+a)^(3/2),x,2,2/3*x/a/sqrt(b*x^3+a)+2/9*sqrt(2+sqrt(3))*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/a/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[1/(b*x^3+a)^(5/2),x,3,2/9*x/a/(b*x^3+a)^(3/2)+14/27*x/a^2/sqrt(b*x^3+a)+14/81*sqrt(2+sqrt(3))*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/a^2/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[1/(b*x^3+a)^(7/2),x,4,2/15*x/a/(b*x^3+a)^(5/2)+26/135*x/a^2/(b*x^3+a)^(3/2)+182/405*x/a^3/sqrt(b*x^3+a)+182/1215*sqrt(2+sqrt(3))*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/a^3/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^3+a),1],
[1/sqrt(x^3+1),x,1,2/3*sqrt(2+sqrt(3))*(1+x)*sqrt((x^2-x+1)/(1+sqrt(3)+x)^2)*InverseJacobiAM(arcsin((1-sqrt(3)+x)/(1+sqrt(3)+x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/sqrt((1+x)/(1+sqrt(3)+x)^2)/sqrt(x^3+1),1],
[1/sqrt(-x^3+1),x,1,-2/3*sqrt(2+sqrt(3))*(1-x)*sqrt((x^2+x+1)/(1+sqrt(3)-x)^2)*InverseJacobiAM(arcsin((1-sqrt(3)-x)/(1+sqrt(3)-x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/sqrt((1-x)/(1+sqrt(3)-x)^2)/sqrt(-x^3+1),1],
[1/sqrt(x^3-1),x,1,-2/3*sqrt(2-sqrt(3))*(1-x)*sqrt((x^2+x+1)/(1-sqrt(3)-x)^2)*InverseJacobiAM(arcsin((1+sqrt(3)-x)/(1-sqrt(3)-x)),sqrt(-7+4*sqrt(3)))*3^(3/4)/sqrt(-(1-x)/(1-sqrt(3)-x)^2)/sqrt(x^3-1),1],
[1/sqrt(-x^3-1),x,1,2/3*sqrt(2-sqrt(3))*(1+x)*sqrt((x^2-x+1)/(1-sqrt(3)+x)^2)*InverseJacobiAM(arcsin((1+sqrt(3)+x)/(1-sqrt(3)+x)),sqrt(-7+4*sqrt(3)))*3^(3/4)/sqrt(-(1+x)/(1-sqrt(3)+x)^2)/sqrt(-x^3-1),1],
[(b*x^3+a)^(5/3),x,3,5/18*a*x*(b*x^3+a)^(2/3)+1/6*x*(b*x^3+a)^(5/3)+5/9*a^2*arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(1/3)-5/18*a^2*ln(-b^(1/3)*x+(b*x^3+a)^(1/3))/b^(1/3),1],
[(b*x^3+a)^(2/3),x,2,1/3*x*(b*x^3+a)^(2/3)+2/3*a*arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(1/3)-1/3*a*ln(-b^(1/3)*x+(b*x^3+a)^(1/3))/b^(1/3),1],
[1/(b*x^3+a)^(1/3),x,1,arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(1/3)-1/2*ln(-b^(1/3)*x+(b*x^3+a)^(1/3))/b^(1/3),1],
[1/(b*x^3+a)^(4/3),x,1,x/a/(b*x^3+a)^(1/3),1],
[1/(b*x^3+a)^(7/3),x,2,1/4*x/a/(b*x^3+a)^(4/3)+3/4*x/a^2/(b*x^3+a)^(1/3),1],
[1/(b*x^3+a)^(10/3),x,3,1/7*x/a/(b*x^3+a)^(7/3)+3/14*x/a^2/(b*x^3+a)^(4/3)+9/14*x/a^3/(b*x^3+a)^(1/3),1],
[1/(b*x^3+a)^(13/3),x,4,1/10*x/a/(b*x^3+a)^(10/3)+9/70*x/a^2/(b*x^3+a)^(7/3)+27/140*x/a^3/(b*x^3+a)^(4/3)+81/140*x/a^4/(b*x^3+a)^(1/3),1],
[(b*x^3+a)^(4/3),x,2,a*x*(b*x^3+a)^(1/3)*hypergeom([-4/3, 1/3],[4/3],-b*x^3/a)/(1+b*x^3/a)^(1/3),1],
[(b*x^3+a)^(1/3),x,2,x*(b*x^3+a)^(1/3)*hypergeom([-1/3, 1/3],[4/3],-b*x^3/a)/(1+b*x^3/a)^(1/3),1],
[1/(b*x^3+a)^(2/3),x,2,x*(1+b*x^3/a)^(2/3)*hypergeom([1/3, 2/3],[4/3],-b*x^3/a)/(b*x^3+a)^(2/3),1],
[1/(b*x^3+a)^(5/3),x,2,x*(1+b*x^3/a)^(2/3)*hypergeom([1/3, 5/3],[4/3],-b*x^3/a)/a/(b*x^3+a)^(2/3),1],
[1/(-b*x^3+a)^(1/3),x,1,-arctan((1-2*b^(1/3)*x/(-b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(1/3)+1/2*ln(b^(1/3)*x+(-b*x^3+a)^(1/3))/b^(1/3),1],
[1/(x^3+2)^(1/3),x,1,arctan((1+2*x/(x^3+2)^(1/3))/sqrt(3))/sqrt(3)-1/2*ln(-x+(x^3+2)^(1/3)),1],
[(b*x^3+a)^(3/4),x,2,x*(b*x^3+a)^(3/4)*hypergeom([-3/4, 1/3],[4/3],-b*x^3/a)/(1+b*x^3/a)^(3/4),1],
[(b*x^3+a)^(1/4),x,2,x*(b*x^3+a)^(1/4)*hypergeom([-1/4, 1/3],[4/3],-b*x^3/a)/(1+b*x^3/a)^(1/4),1],
[1/(b*x^3+a)^(1/4),x,2,x*(1+b*x^3/a)^(1/4)*hypergeom([1/4, 1/3],[4/3],-b*x^3/a)/(b*x^3+a)^(1/4),1],
[1/(b*x^3+a)^(3/4),x,2,x*(1+b*x^3/a)^(3/4)*hypergeom([1/3, 3/4],[4/3],-b*x^3/a)/(b*x^3+a)^(3/4),1],
[1/(b*x^3+a)^(5/4),x,2,x*(1+b*x^3/a)^(1/4)*hypergeom([1/3, 5/4],[4/3],-b*x^3/a)/a/(b*x^3+a)^(1/4),1]]: