lst:=[[1/(x^6-x^3),x,8,1/2/x^2-arctan((1+2*x)/sqrt(3))/sqrt(3)+1/3*ln(1-x)-1/6*ln(x^2+x+1),1],
[(b*x^6+a*x^3)^(11/3),x,4,-81/54740*a^3*(b*x^6+a*x^3)^(14/3)/b^4/x^14+27/3910*a^2*(b*x^6+a*x^3)^(14/3)/b^3/x^11-9/460*a*(b*x^6+a*x^3)^(14/3)/b^2/x^8+1/23*(b*x^6+a*x^3)^(14/3)/b/x^5,1],
[(b*x^6+a*x^3)^(8/3),x,3,9/1309*a^2*(b*x^6+a*x^3)^(11/3)/b^3/x^11-3/119*a*(b*x^6+a*x^3)^(11/3)/b^2/x^8+1/17*(b*x^6+a*x^3)^(11/3)/b/x^5,1],
[(b*x^6+a*x^3)^(5/3),x,2,-3/88*a*(b*x^6+a*x^3)^(8/3)/b^2/x^8+1/11*(b*x^6+a*x^3)^(8/3)/b/x^5,1],
[(b*x^6+a*x^3)^(2/3),x,1,1/5*(b*x^6+a*x^3)^(5/3)/b/x^5,1],
[1/(b*x^6+a*x^3)^(1/3),x,9,x*(b*x^3+a)^(1/3)*arctan((a^(1/3)+2*(b*x^3+a)^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/a^(1/3)/(b*x^6+a*x^3)^(1/3)-1/2*x*(b*x^3+a)^(1/3)*ln(x)/a^(1/3)/(b*x^6+a*x^3)^(1/3)+1/2*x*(b*x^3+a)^(1/3)*ln(a^(1/3)-(b*x^3+a)^(1/3))/a^(1/3)/(b*x^6+a*x^3)^(1/3),1],
[1/(b*x^6+a*x^3)^(4/3),x,11,1/a/x^2/(b*x^6+a*x^3)^(1/3)-4/3*(b*x^6+a*x^3)^(2/3)/a^2/x^5-4/3*b*x*(b*x^3+a)^(1/3)*arctan((a^(1/3)+2*(b*x^3+a)^(1/3))/sqrt(3)/a^(1/3))/sqrt(3)/a^(7/3)/(b*x^6+a*x^3)^(1/3)+2/3*b*x*(b*x^3+a)^(1/3)*ln(x)/a^(7/3)/(b*x^6+a*x^3)^(1/3)-2/3*b*x*(b*x^3+a)^(1/3)*ln(a^(1/3)-(b*x^3+a)^(1/3))/a^(7/3)/(b*x^6+a*x^3)^(1/3),1],
[(b*x^6+a*x^3)^(7/3),x,7,-7/1458*a^4*x*(b*x^6+a*x^3)^(1/3)/b^2+7/2430*a^3*x^4*(b*x^6+a*x^3)^(1/3)/b+7/405*a^2*x^7*(b*x^6+a*x^3)^(1/3)+7/180*a*x^4*(b*x^6+a*x^3)^(4/3)+1/15*x*(b*x^6+a*x^3)^(7/3)-7/729*a^5*x^2*(b*x^3+a)^(2/3)*arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(8/3)/(b*x^6+a*x^3)^(2/3)-7/1458*a^5*x^2*(b*x^3+a)^(2/3)*ln(b^(1/3)*x-(b*x^3+a)^(1/3))/b^(8/3)/(b*x^6+a*x^3)^(2/3),1],
[(b*x^6+a*x^3)^(4/3),x,5,2/81*a^2*x*(b*x^6+a*x^3)^(1/3)/b+2/27*a*x^4*(b*x^6+a*x^3)^(1/3)+1/9*x*(b*x^6+a*x^3)^(4/3)+4/81*a^3*x^2*(b*x^3+a)^(2/3)*arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(5/3)/(b*x^6+a*x^3)^(2/3)+2/81*a^3*x^2*(b*x^3+a)^(2/3)*ln(b^(1/3)*x-(b*x^3+a)^(1/3))/b^(5/3)/(b*x^6+a*x^3)^(2/3),1],
[(b*x^6+a*x^3)^(1/3),x,3,1/3*x*(b*x^6+a*x^3)^(1/3)-1/3*a*x^2*(b*x^3+a)^(2/3)*arctan((1+2*b^(1/3)*x/(b*x^3+a)^(1/3))/sqrt(3))/sqrt(3)/b^(2/3)/(b*x^6+a*x^3)^(2/3)-1/6*a*x^2*(b*x^3+a)^(2/3)*ln(b^(1/3)*x-(b*x^3+a)^(1/3))/b^(2/3)/(b*x^6+a*x^3)^(2/3),1],
[1/(b*x^6+a*x^3)^(2/3),x,1,-(b*x^6+a*x^3)^(1/3)/a/x^2,1],
[1/(b*x^6+a*x^3)^(5/3),x,3,-1/4/a/x^2/(b*x^6+a*x^3)^(2/3)+3/2*b*x/a^2/(b*x^6+a*x^3)^(2/3)+9/4*b^2*x^4/a^3/(b*x^6+a*x^3)^(2/3),1],
[1/(b*x^6+a*x^3)^(8/3),x,5,-1/7/a/x^2/(b*x^6+a*x^3)^(5/3)+3/7*b*x/a^2/(b*x^6+a*x^3)^(5/3)-27/7*b^2*x^4/a^3/(b*x^6+a*x^3)^(5/3)-81/7*b^3*x^7/a^4/(b*x^6+a*x^3)^(5/3)-243/35*b^4*x^10/a^5/(b*x^6+a*x^3)^(5/3),1],
[(a+c/x^2+b/x)^(5/2),x,9,-5/24*(a+c/x^2+b/x)^(3/2)*(7*b+6*c/x)-5/64*sqrt(a+c/x^2+b/x)*(b*(44*a*c+b^2)+2*c*(12*a*c+b^2)/x)/c+(a+c/x^2+b/x)^(5/2)*x+5/2*a^(3/2)*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))+5/128*(-48*a^2*c^2-24*a*b^2*c+b^4)*arctanh(1/2*(b+2*c/x)/sqrt(c)/sqrt(a+c/x^2+b/x))/c^(3/2),1],
[(a+c/x^2+b/x)^(3/2),x,8,-3/4*sqrt(a+c/x^2+b/x)*(3*b+2*c/x)+(a+c/x^2+b/x)^(3/2)*x+3/2*sqrt(a)*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))-3/8*(4*a*c+b^2)*arctanh(1/2*(b+2*c/x)/sqrt(c)/sqrt(a+c/x^2+b/x))/sqrt(c),1],
[sqrt(a+c/x^2+b/x),x,7,sqrt(a+c/x^2+b/x)*x+1/2*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))/sqrt(a)-sqrt(c)*arctanh(1/2*(b+2*c/x)/sqrt(c)/sqrt(a+c/x^2+b/x)),1],
[1/sqrt(a+c/x^2+b/x),x,4,sqrt(a+c/x^2+b/x)*x/a-1/2*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))/a^(3/2),1],
[1/(a+c/x^2+b/x)^(3/2),x,5,(b*(-10*a*c+3*b^2)+c*(-8*a*c+3*b^2)/x)/a^2/(-4*a*c+b^2)/sqrt(a+c/x^2+b/x)+x/a/sqrt(a+c/x^2+b/x)-3/2*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))/a^(5/2),1],
[1/(a+c/x^2+b/x)^(5/2),x,6,1/3*(b*(-18*a*c+5*b^2)+c*(-16*a*c+5*b^2)/x)/a^2/(-4*a*c+b^2)/(a+c/x^2+b/x)^(3/2)+1/3*(b*(184*a^2*c^2-110*a*b^2*c+15*b^4)+c*(128*a^2*c^2-100*a*b^2*c+15*b^4)/x)/a^3/(-4*a*c+b^2)^2/sqrt(a+c/x^2+b/x)+x/a/(a+c/x^2+b/x)^(3/2)-5/2*b*arctanh(1/2*(2*a+b/x)/sqrt(a)/sqrt(a+c/x^2+b/x))/a^(7/2),1],
[sqrt(a^2+b^2/x^2+2*a*b/x),x,2,a*sqrt(a^2+b^2/x^2+2*a*b/x)*x/(a+b/x)+b*sqrt(a^2+b^2/x^2+2*a*b/x)*ln(x)/(a+b/x),1],
[1/(c+a/x^4+b/x^2),x,6,x/c-(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(sqrt(2)*sqrt(c)*x/sqrt(b-sqrt(-4*a*c+b^2)))/sqrt(2)/c^(3/2)/sqrt(b-sqrt(-4*a*c+b^2))-(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(sqrt(2)*sqrt(c)*x/sqrt(b+sqrt(-4*a*c+b^2)))/sqrt(2)/c^(3/2)/sqrt(b+sqrt(-4*a*c+b^2)),1],
[1/(c+a/x^6+b/x^3),x,16,x/c+1/2*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan((1-2*2^(1/3)*c^(1/3)*x/(b-sqrt(-4*a*c+b^2))^(1/3))/sqrt(3))*2^(2/3)/sqrt(3)/c^(4/3)/(b-sqrt(-4*a*c+b^2))^(2/3)+1/2*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan((1-2*2^(1/3)*c^(1/3)*x/(b+sqrt(-4*a*c+b^2))^(1/3))/sqrt(3))*2^(2/3)/sqrt(3)/c^(4/3)/(b+sqrt(-4*a*c+b^2))^(2/3)-1/6*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*ln((b-sqrt(-4*a*c+b^2))^(1/3)+2^(1/3)*c^(1/3)*x)*2^(2/3)/c^(4/3)/(b-sqrt(-4*a*c+b^2))^(2/3)-1/6*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*ln((b+sqrt(-4*a*c+b^2))^(1/3)+2^(1/3)*c^(1/3)*x)*2^(2/3)/c^(4/3)/(b+sqrt(-4*a*c+b^2))^(2/3)+1/12*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*ln((b-sqrt(-4*a*c+b^2))^(2/3)-2^(1/3)*c^(1/3)*(b-sqrt(-4*a*c+b^2))^(1/3)*x+2^(2/3)*c^(2/3)*x^2)*2^(2/3)/c^(4/3)/(b-sqrt(-4*a*c+b^2))^(2/3)+1/12*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*ln((b+sqrt(-4*a*c+b^2))^(2/3)-2^(1/3)*c^(1/3)*(b+sqrt(-4*a*c+b^2))^(1/3)*x+2^(2/3)*c^(2/3)*x^2)*2^(2/3)/c^(4/3)/(b+sqrt(-4*a*c+b^2))^(2/3),1],
[1/(c+a/x^8+b/x^4),x,10,x/c+1/4*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(2^(1/4)*c^(1/4)*x/(-b-sqrt(-4*a*c+b^2))^(1/4))*2^(3/4)/c^(5/4)/(-b-sqrt(-4*a*c+b^2))^(3/4)+1/4*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(2^(1/4)*c^(1/4)*x/(-b+sqrt(-4*a*c+b^2))^(1/4))*2^(3/4)/c^(5/4)/(-b+sqrt(-4*a*c+b^2))^(3/4)+1/4*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctanh(2^(1/4)*c^(1/4)*x/(-b-sqrt(-4*a*c+b^2))^(1/4))*2^(3/4)/c^(5/4)/(-b-sqrt(-4*a*c+b^2))^(3/4)+1/4*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctanh(2^(1/4)*c^(1/4)*x/(-b+sqrt(-4*a*c+b^2))^(1/4))*2^(3/4)/c^(5/4)/(-b+sqrt(-4*a*c+b^2))^(3/4),1],
[(a+b*sqrt(x)+c*x)^3,x,3,a^3*x+2*a^2*b*x^(3/2)+3/2*a*(a*c+b^2)*x^2+2/5*b*(6*a*c+b^2)*x^(5/2)+c*(a*c+b^2)*x^3+6/7*b*c^2*x^(7/2)+1/4*c^3*x^4,1],
[(a+b*sqrt(x)+c*x)^2,x,3,a^2*x+4/3*a*b*x^(3/2)+1/2*(2*a*c+b^2)*x^2+4/5*b*c*x^(5/2)+1/3*c^2*x^3,1],
[a+b*sqrt(x)+c*x,x,1,a*x+2/3*b*x^(3/2)+1/2*c*x^2,1],
[1/(a+b*sqrt(x)+c*x),x,5,2*b*arctanh((b+2*c*sqrt(x))/sqrt(-4*a*c+b^2))/c/sqrt(-4*a*c+b^2)+ln(a+b*sqrt(x)+c*x)/c,1],
[1/(a+b*sqrt(x)+c*x)^2,x,4,2*(2*a+b*sqrt(x))/(-4*a*c+b^2)/(a+b*sqrt(x)+c*x)-4*b*arctanh((b+2*c*sqrt(x))/sqrt(-4*a*c+b^2))/(-4*a*c+b^2)^(3/2),1],
[1/(a+b*sqrt(x)+c*x)^3,x,5,(2*a+b*sqrt(x))/(-4*a*c+b^2)/(a+b*sqrt(x)+c*x)^2-3*b*(b+2*c*sqrt(x))/(-4*a*c+b^2)^2/(a+b*sqrt(x)+c*x)+12*b*c*arctanh((b+2*c*sqrt(x))/sqrt(-4*a*c+b^2))/(-4*a*c+b^2)^(5/2),1],
[(a+b*sqrt(x)+c*x)^(5/2),x,7,-5/512*b*(-4*a*c+b^2)^2*(b+2*c*sqrt(x))*sqrt(a+b*sqrt(x)+c*x)/c^4+5/192*b*(-4*a*c+b^2)*(b+2*c*sqrt(x))*(a+b*sqrt(x)+c*x)^(3/2)/c^3-1/12*b*(b+2*c*sqrt(x))*(a+b*sqrt(x)+c*x)^(5/2)/c^2+2/7*(a+b*sqrt(x)+c*x)^(7/2)/c+5/1024*b*(-4*a*c+b^2)^3*arctanh(1/2*(b+2*c*sqrt(x))/sqrt(c)/sqrt(a+b*sqrt(x)+c*x))/c^(9/2),1],
[(a+b*sqrt(x)+c*x)^(3/2),x,6,3/64*b*(-4*a*c+b^2)*(b+2*c*sqrt(x))*sqrt(a+b*sqrt(x)+c*x)/c^3-1/8*b*(b+2*c*sqrt(x))*(a+b*sqrt(x)+c*x)^(3/2)/c^2+2/5*(a+b*sqrt(x)+c*x)^(5/2)/c-3/128*b*(-4*a*c+b^2)^2*arctanh(1/2*(b+2*c*sqrt(x))/sqrt(c)/sqrt(a+b*sqrt(x)+c*x))/c^(7/2),1],
[sqrt(a+b*sqrt(x)+c*x),x,5,-1/4*b*(b+2*c*sqrt(x))*sqrt(a+b*sqrt(x)+c*x)/c^2+2/3*(a+b*sqrt(x)+c*x)^(3/2)/c+1/8*b*(-4*a*c+b^2)*arctanh(1/2*(b+2*c*sqrt(x))/sqrt(c)/sqrt(a+b*sqrt(x)+c*x))/c^(5/2),1],
[1/sqrt(a+b*sqrt(x)+c*x),x,4,2*sqrt(a+b*sqrt(x)+c*x)/c-b*arctanh(1/2*(b+2*c*sqrt(x))/sqrt(c)/sqrt(a+b*sqrt(x)+c*x))/c^(3/2),1],
[1/(a+b*sqrt(x)+c*x)^(3/2),x,2,4*(2*a+b*sqrt(x))/(-4*a*c+b^2)/sqrt(a+b*sqrt(x)+c*x),1],
[1/(a+b*sqrt(x)+c*x)^(5/2),x,3,4/3*(2*a+b*sqrt(x))/(-4*a*c+b^2)/(a+b*sqrt(x)+c*x)^(3/2)-16/3*b*(b+2*c*sqrt(x))/(-4*a*c+b^2)^2/sqrt(a+b*sqrt(x)+c*x),1],
[(a^2+2*a*c*sqrt(x)+c^2*x)^3,x,4,-2/7*a*(a+c*sqrt(x))^7/c^2+1/4*(a+c*sqrt(x))^8/c^2,1],
[(a^2+2*a*c*sqrt(x)+c^2*x)^2,x,4,-2/5*a*(a+c*sqrt(x))^5/c^2+1/3*(a+c*sqrt(x))^6/c^2,1],
[a^2+2*a*c*sqrt(x)+c^2*x,x,1,a^2*x+4/3*a*c*x^(3/2)+1/2*c^2*x^2,1],
[1/(a^2+2*a*c*sqrt(x)+c^2*x),x,4,2*a/c^2/(a+c*sqrt(x))+2*ln(a+c*sqrt(x))/c^2,1],
[1/(a^2+2*a*c*sqrt(x)+c^2*x)^2,x,4,2/3*a/c^2/(a+c*sqrt(x))^3-1/c^2/(a+c*sqrt(x))^2,1],
[1/(a^2+2*a*c*sqrt(x)+c^2*x)^3,x,4,2/5*a/c^2/(a+c*sqrt(x))^5-1/2/c^2/(a+c*sqrt(x))^4,1],
[(1/4*b^2/c+b*sqrt(x)+c*x)^2,x,4,-1/160*b*(b+2*c*sqrt(x))^5/c^4+1/192*(b+2*c*sqrt(x))^6/c^4,1],
[(a^2+2*a*c*sqrt(x)+c^2*x)^(5/2),x,4,-1/3*a*(a+c*sqrt(x))^5*sqrt(a^2+2*a*c*sqrt(x)+c^2*x)/c^2+2/7*(a^2+2*a*c*sqrt(x)+c^2*x)^(7/2)/c^2,1],
[(a^2+2*a*c*sqrt(x)+c^2*x)^(3/2),x,4,-1/2*a*(a+c*sqrt(x))^3*sqrt(a^2+2*a*c*sqrt(x)+c^2*x)/c^2+2/5*(a^2+2*a*c*sqrt(x)+c^2*x)^(5/2)/c^2,1],
[sqrt(a^2+2*a*c*sqrt(x)+c^2*x),x,4,-a*(a+c*sqrt(x))*sqrt(a^2+2*a*c*sqrt(x)+c^2*x)/c^2+2/3*(a^2+2*a*c*sqrt(x)+c^2*x)^(3/2)/c^2,1],
[1/sqrt(a^2+2*a*c*sqrt(x)+c^2*x),x,4,2*sqrt(a^2+2*a*c*sqrt(x)+c^2*x)/c^2-2*a*(a+c*sqrt(x))*ln(a+c*sqrt(x))/c^2/sqrt(a^2+2*a*c*sqrt(x)+c^2*x),1],
[1/(a^2+2*a*c*sqrt(x)+c^2*x)^(3/2),x,4,-2/c^2/sqrt(a^2+2*a*c*sqrt(x)+c^2*x)+a/c^2/(a+c*sqrt(x))/sqrt(a^2+2*a*c*sqrt(x)+c^2*x),1],
[1/(a^2+2*a*c*sqrt(x)+c^2*x)^(5/2),x,4,-2/3/c^2/(a^2+2*a*c*sqrt(x)+c^2*x)^(3/2)+1/2*a/c^2/(a+c*sqrt(x))^3/sqrt(a^2+2*a*c*sqrt(x)+c^2*x),1],
[1/sqrt(a^2+2*a*b*sqrt(x)+b^2*x),x,4,2*sqrt(a^2+2*a*b*sqrt(x)+b^2*x)/b^2-2*a*(a+b*sqrt(x))*ln(a+b*sqrt(x))/b^2/sqrt(a^2+2*a*b*sqrt(x)+b^2*x),1],
[(a+b*x^(1/3)+c*x^(2/3))^4,x,3,a^4*x+3*a^3*b*x^(4/3)+6/5*a^2*(2*a*c+3*b^2)*x^(5/3)+2*a*b*(3*a*c+b^2)*x^2+3/7*(6*a^2*c^2+12*a*b^2*c+b^4)*x^(7/3)+3/2*b*c*(3*a*c+b^2)*x^(8/3)+2/3*c^2*(2*a*c+3*b^2)*x^3+6/5*b*c^3*x^(10/3)+3/11*c^4*x^(11/3),1],
[(a+b*x^(1/3)+c*x^(2/3))^3,x,3,a^3*x+9/4*a^2*b*x^(4/3)+9/5*a*(a*c+b^2)*x^(5/3)+1/2*b*(6*a*c+b^2)*x^2+9/7*c*(a*c+b^2)*x^(7/3)+9/8*b*c^2*x^(8/3)+1/3*c^3*x^3,1],
[(a+b*x^(1/3)+c*x^(2/3))^2,x,3,a^2*x+3/2*a*b*x^(4/3)+3/5*(2*a*c+b^2)*x^(5/3)+b*c*x^2+3/7*c^2*x^(7/3),1],
[1/(a+b*x^(1/3)+c*x^(2/3)),x,7,3*x^(1/3)/c-3*(-2*a*c+b^2)*arctanh((b+2*c*x^(1/3))/sqrt(-4*a*c+b^2))/c^2/sqrt(-4*a*c+b^2)-3/2*b*ln(a+b*x^(1/3)+c*x^(2/3))/c^2,1],
[1/(a+b*x^(1/3)+c*x^(2/3))^2,x,4,(-3*a*b-3*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))+12*a*arctanh((b+2*c*x^(1/3))/sqrt(-4*a*c+b^2))/(-4*a*c+b^2)^(3/2),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^3,x,5,1/2*(-3*a*b-3*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))^2+3/2*(2*a*c+b^2)*(b+2*c*x^(1/3))/c/(-4*a*c+b^2)^2/(a+b*x^(1/3)+c*x^(2/3))-6*(2*a*c+b^2)*arctanh((b+2*c*x^(1/3))/sqrt(-4*a*c+b^2))/(-4*a*c+b^2)^(5/2),1],
[(a+b*x^(1/3)+c*x^(2/3))^(5/2),x,7,15/16384*(-4*a*c+b^2)^2*(-4*a*c+9*b^2)*(b+2*c*x^(1/3))*sqrt(a+b*x^(1/3)+c*x^(2/3))/c^5-5/2048*(-4*a*c+b^2)*(-4*a*c+9*b^2)*(b+2*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(3/2)/c^4+1/128*(-4*a*c+9*b^2)*(b+2*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(5/2)/c^3-3/112*(9*b-14*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(7/2)/c^2-15/32768*(-4*a*c+b^2)^3*(-4*a*c+9*b^2)*arctanh(1/2*(b+2*c*x^(1/3))/sqrt(c)/sqrt(a+b*x^(1/3)+c*x^(2/3)))/c^(11/2),1],
[(a+b*x^(1/3)+c*x^(2/3))^(3/2),x,6,-3/512*(-4*a*c+b^2)*(-4*a*c+7*b^2)*(b+2*c*x^(1/3))*sqrt(a+b*x^(1/3)+c*x^(2/3))/c^4+1/64*(-4*a*c+7*b^2)*(b+2*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(3/2)/c^3-1/20*(7*b-10*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(5/2)/c^2+3/1024*(-4*a*c+b^2)^2*(-4*a*c+7*b^2)*arctanh(1/2*(b+2*c*x^(1/3))/sqrt(c)/sqrt(a+b*x^(1/3)+c*x^(2/3)))/c^(9/2),1],
[sqrt(a+b*x^(1/3)+c*x^(2/3)),x,5,3/64*(-4*a*c+5*b^2)*(b+2*c*x^(1/3))*sqrt(a+b*x^(1/3)+c*x^(2/3))/c^3-1/8*(5*b-6*c*x^(1/3))*(a+b*x^(1/3)+c*x^(2/3))^(3/2)/c^2-3/128*(-4*a*c+b^2)*(-4*a*c+5*b^2)*arctanh(1/2*(b+2*c*x^(1/3))/sqrt(c)/sqrt(a+b*x^(1/3)+c*x^(2/3)))/c^(7/2),1],
[1/sqrt(a+b*x^(1/3)+c*x^(2/3)),x,4,-3/4*(3*b-2*c*x^(1/3))*sqrt(a+b*x^(1/3)+c*x^(2/3))/c^2+3/8*(-4*a*c+3*b^2)*arctanh(1/2*(b+2*c*x^(1/3))/sqrt(c)/sqrt(a+b*x^(1/3)+c*x^(2/3)))/c^(5/2),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^(3/2),x,4,(-6*a*b-6*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/sqrt(a+b*x^(1/3)+c*x^(2/3))+3*arctanh(1/2*(b+2*c*x^(1/3))/sqrt(c)/sqrt(a+b*x^(1/3)+c*x^(2/3)))/c^(3/2),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^(5/2),x,3,(-2*a*b-2*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))^(3/2)+2*(4*a*c+b^2)*(b+2*c*x^(1/3))/c/(-4*a*c+b^2)^2/sqrt(a+b*x^(1/3)+c*x^(2/3)),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^(7/2),x,4,1/5*(-6*a*b-6*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))^(5/2)+2/5*(4*a*c+3*b^2)*(b+2*c*x^(1/3))/c/(-4*a*c+b^2)^2/(a+b*x^(1/3)+c*x^(2/3))^(3/2)-16/5*(4*a*c+3*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^3/sqrt(a+b*x^(1/3)+c*x^(2/3)),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^(9/2),x,5,1/7*(-6*a*b-6*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))^(7/2)+6/35*(4*a*c+5*b^2)*(b+2*c*x^(1/3))/c/(-4*a*c+b^2)^2/(a+b*x^(1/3)+c*x^(2/3))^(5/2)-32/35*(4*a*c+5*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^3/(a+b*x^(1/3)+c*x^(2/3))^(3/2)+256/35*c*(4*a*c+5*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^4/sqrt(a+b*x^(1/3)+c*x^(2/3)),1],
[1/(a+b*x^(1/3)+c*x^(2/3))^(11/2),x,6,1/3*(-2*a*b-2*(-2*a*c+b^2)*x^(1/3))/c/(-4*a*c+b^2)/(a+b*x^(1/3)+c*x^(2/3))^(9/2)+2/21*(4*a*c+7*b^2)*(b+2*c*x^(1/3))/c/(-4*a*c+b^2)^2/(a+b*x^(1/3)+c*x^(2/3))^(7/2)-16/35*(4*a*c+7*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^3/(a+b*x^(1/3)+c*x^(2/3))^(5/2)+256/105*c*(4*a*c+7*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^4/(a+b*x^(1/3)+c*x^(2/3))^(3/2)-2048/105*c^2*(4*a*c+7*b^2)*(b+2*c*x^(1/3))/(-4*a*c+b^2)^5/sqrt(a+b*x^(1/3)+c*x^(2/3)),1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^3,x,4,3/7*a^2*(a+b*x^(1/3))^7/b^3-3/4*a*(a+b*x^(1/3))^8/b^3+1/3*(a+b*x^(1/3))^9/b^3,1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^2,x,4,3/5*a^2*(a+b*x^(1/3))^5/b^3-a*(a+b*x^(1/3))^6/b^3+3/7*(a+b*x^(1/3))^7/b^3,1],
[a^2+2*a*b*x^(1/3)+b^2*x^(2/3),x,1,a^2*x+3/2*a*b*x^(4/3)+3/5*b^2*x^(5/3),1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),x,4,-3*a^2/b^3/(a+b*x^(1/3))+3*x^(1/3)/b^2-6*a*ln(a+b*x^(1/3))/b^3,1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^2,x,2,x/a/(a+b*x^(1/3))^3,1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^3,x,4,-3/5*a^2/b^3/(a+b*x^(1/3))^5+3/2*a/b^3/(a+b*x^(1/3))^4-1/b^3/(a+b*x^(1/3))^3,1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^4,x,4,-3/7*a^2/b^3/(a+b*x^(1/3))^7+a/b^3/(a+b*x^(1/3))^6-3/5/b^3/(a+b*x^(1/3))^5,1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x,4,3/8*a^2*(a+b*x^(1/3))^7*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3-2/3*a*(a+b*x^(1/3))^8*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3+3/10*(a+b*x^(1/3))^9*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3,1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x,4,1/2*a^2*(a+b*x^(1/3))^5*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3-6/7*a*(a+b*x^(1/3))^6*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3+3/8*(a+b*x^(1/3))^7*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3,1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x,4,3/4*a^2*(a+b*x^(1/3))^3*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3-6/5*a*(a+b*x^(1/3))^4*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3+1/2*(a+b*x^(1/3))^5*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))/b^3,1],
[sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),x,4,a*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))*x/(a+b*x^(1/3))+3*b*sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))*x^(4/3)/(4*a+4*b*x^(1/3)),1],
[1/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),x,4,-3*a*(a+b*x^(1/3))*x^(1/3)/b^2/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))+3/2*(a+b*x^(1/3))*x^(2/3)/b/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))+3*a^2*(a+b*x^(1/3))*ln(a+b*x^(1/3))/b^3/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x,4,6*a/b^3/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))-3/2*a^2/b^3/(a+b*x^(1/3))/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))+3*(a+b*x^(1/3))*ln(a+b*x^(1/3))/b^3/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),1],
[1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x,4,-3/4*a^2/b^3/(a+b*x^(1/3))^3/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))+2*a/b^3/(a+b*x^(1/3))^2/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))-3/2/b^3/(a+b*x^(1/3))/sqrt(a^2+2*a*b*x^(1/3)+b^2*x^(2/3)),1],
[(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p,x,4,3*a^2*(a+b*x^(1/3))*(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/b^3/(1+2*p)-3*a*(a+b*x^(1/3))^2*(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/b^3/(p+1)+3*(a+b*x^(1/3))^3*(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/b^3/(3+2*p),1],
[1/(a^2+2*a*b*x^(1/4)+b^2*sqrt(x))^(3/2),x,4,-12*a^2/b^4/sqrt(a^2+2*a*b*x^(1/4)+b^2*sqrt(x))+2*a^3/b^4/(a+b*x^(1/4))/sqrt(a^2+2*a*b*x^(1/4)+b^2*sqrt(x))+4*(a+b*x^(1/4))*x^(1/4)/b^3/sqrt(a^2+2*a*b*x^(1/4)+b^2*sqrt(x))-12*a*(a+b*x^(1/4))*ln(a+b*x^(1/4))/b^4/sqrt(a^2+2*a*b*x^(1/4)+b^2*sqrt(x)),1],
[1/(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))^(5/2),x,4,-60*a^2/b^6/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))+3/2*a^5/b^6/(a+b*x^(1/6))^3/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))-10*a^4/b^6/(a+b*x^(1/6))^2/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))+30*a^3/b^6/(a+b*x^(1/6))/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))+6*(a+b*x^(1/6))*x^(1/6)/b^5/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))-30*a*(a+b*x^(1/6))*ln(a+b*x^(1/6))/b^6/sqrt(a^2+2*a*b*x^(1/6)+b^2*x^(1/3)),1],
[(a^2+b^2/x+2*a*b/sqrt(x))^(3/2),x,5,-2*b^3*sqrt(a^2+b^2/x+2*a*b/sqrt(x))/(a+b/sqrt(x))/sqrt(x)+6*a^2*b*sqrt(a^2+b^2/x+2*a*b/sqrt(x))*sqrt(x)/(a+b/sqrt(x))+a^3*sqrt(a^2+b^2/x+2*a*b/sqrt(x))*x/(a+b/sqrt(x))+3*a*b^2*sqrt(a^2+b^2/x+2*a*b/sqrt(x))*ln(x)/(a+b/sqrt(x)),1],
[(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(7/2),x,5,-3/4*b^7*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x^(4/3)-7*a*b^6*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x-63/2*a^2*b^5*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x^(2/3)-105*a^3*b^4*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x^(1/3)+63*a^5*b^2*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(1/3)/(a+b/x^(1/3))+21*a^6*b*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(2/3)/(2*a+2*b/x^(1/3))+a^7*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x/(a+b/x^(1/3))+35*a^4*b^3*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*ln(x)/(a+b/x^(1/3)),1],
[(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x,5,-3/2*b^5*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x^(2/3)-15*a*b^4*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(a+b/x^(1/3))/x^(1/3)+30*a^3*b^2*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(1/3)/(a+b/x^(1/3))+15*a^4*b*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(2/3)/(2*a+2*b/x^(1/3))+a^5*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x/(a+b/x^(1/3))+10*a^2*b^3*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*ln(x)/(a+b/x^(1/3)),1],
[(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x,5,9*a*b^2*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(1/3)/(a+b/x^(1/3))+9*a^2*b*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(2/3)/(2*a+2*b/x^(1/3))+a^3*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x/(a+b/x^(1/3))+b^3*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*ln(x)/(a+b/x^(1/3)),1],
[sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3)),x,5,3*b*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x^(2/3)/(2*a+2*b/x^(1/3))+a*sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))*x/(a+b/x^(1/3)),1],
[1/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3)),x,5,3*b^2*(a+b/x^(1/3))*x^(1/3)/a^3/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-3/2*b*(a+b/x^(1/3))*x^(2/3)/a^2/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))+(a+b/x^(1/3))*x/a/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-3*b^3*(a+b/x^(1/3))*ln(b+a*x^(1/3))/a^4/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3)),1],
[1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x,5,3/2*b^5*(a+b/x^(1/3))/a^6/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))^2-15*b^4*(a+b/x^(1/3))/a^6/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))+18*b^2*(a+b/x^(1/3))*x^(1/3)/a^5/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-9/2*b*(a+b/x^(1/3))*x^(2/3)/a^4/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))+(a+b/x^(1/3))*x/a^3/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-30*b^3*(a+b/x^(1/3))*ln(b+a*x^(1/3))/a^6/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3)),1],
[1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x,5,3/4*b^7*(a+b/x^(1/3))/a^8/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))^4-7*b^6*(a+b/x^(1/3))/a^8/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))^3+63/2*b^5*(a+b/x^(1/3))/a^8/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))^2-105*b^4*(a+b/x^(1/3))/a^8/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))/(b+a*x^(1/3))+45*b^2*(a+b/x^(1/3))*x^(1/3)/a^7/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-15/2*b*(a+b/x^(1/3))*x^(2/3)/a^6/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))+(a+b/x^(1/3))*x/a^5/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))-105*b^3*(a+b/x^(1/3))*ln(b+a*x^(1/3))/a^8/sqrt(a^2+b^2/x^(2/3)+2*a*b/x^(1/3)),1],
[(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))^(5/2),x,5,-4*b^5*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))/(a+b/x^(1/4))/x^(1/4)+40*a^2*b^3*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))*x^(1/4)/(a+b/x^(1/4))+20*a^3*b^2*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))*sqrt(x)/(a+b/x^(1/4))+20*a^4*b*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))*x^(3/4)/(3*a+3*b/x^(1/4))+a^5*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))*x/(a+b/x^(1/4))+5*a*b^4*sqrt(a^2+b^2/sqrt(x)+2*a*b/x^(1/4))*ln(x)/(a+b/x^(1/4)),1],
[(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))^(5/2),x,5,25*a*b^4*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*x^(1/5)/(a+b/x^(1/5))+25*a^2*b^3*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*x^(2/5)/(a+b/x^(1/5))+50*a^3*b^2*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*x^(3/5)/(3*a+3*b/x^(1/5))+25*a^4*b*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*x^(4/5)/(4*a+4*b/x^(1/5))+a^5*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*x/(a+b/x^(1/5))+b^5*sqrt(a^2+b^2/x^(2/5)+2*a*b/x^(1/5))*ln(x)/(a+b/x^(1/5)),1],
[1/(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))^(5/2),x,4,20*a/b^5/sqrt(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))-5/4*a^4/b^5/(a+b*x^(1/5))^3/sqrt(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))+20/3*a^3/b^5/(a+b*x^(1/5))^2/sqrt(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))-15*a^2/b^5/(a+b*x^(1/5))/sqrt(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))+5*(a+b*x^(1/5))*ln(a+b*x^(1/5))/b^5/sqrt(a^2+2*a*b*x^(1/5)+b^2*x^(2/5)),1],
[(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))^(7/2),x,5,-6*b^7*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))/(a+b/x^(1/6))/x^(1/6)+126*a^2*b^5*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*x^(1/6)/(a+b/x^(1/6))+105*a^3*b^4*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*x^(1/3)/(a+b/x^(1/6))+70*a^4*b^3*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*sqrt(x)/(a+b/x^(1/6))+63*a^5*b^2*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*x^(2/3)/(2*a+2*b/x^(1/6))+42*a^6*b*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*x^(5/6)/(5*a+5*b/x^(1/6))+a^7*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*x/(a+b/x^(1/6))+7*a*b^6*sqrt(a^2+b^2/x^(1/3)+2*a*b/x^(1/6))*ln(x)/(a+b/x^(1/6)),1],
[(a+b*x^n+c*x^(2*n))^3,x,2,a^3*x+3*a^2*b*x^(1+n)/(1+n)+3*a*(a*c+b^2)*x^(1+2*n)/(1+2*n)+b*(6*a*c+b^2)*x^(1+3*n)/(1+3*n)+3*c*(a*c+b^2)*x^(1+4*n)/(1+4*n)+3*b*c^2*x^(1+5*n)/(1+5*n)+c^3*x^(1+6*n)/(1+6*n),1],
[(a+b*x^n+c*x^(2*n))^2,x,2,a^2*x+2*a*b*x^(1+n)/(1+n)+(2*a*c+b^2)*x^(1+2*n)/(1+2*n)+2*b*c*x^(1+3*n)/(1+3*n)+c^2*x^(1+4*n)/(1+4*n),1],
[a+b*x^n+c*x^(2*n),x,1,a*x+b*x^(1+n)/(1+n)+c*x^(1+2*n)/(1+2*n),1],
[1/(a+b*x^n+c*x^(2*n)),x,3,-2*c*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))-2*c*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2)),1],
[1/(a+b*x^n+c*x^(2*n))^2,x,4,x*(b^2-2*a*c+b*c*x^n)/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))-c*(4*a*c*(1-2*n)-b^2*(1-n)-b*sqrt(-4*a*c+b^2)*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/n-c*(4*a*c*(1-2*n)-b^2*(1-n)+b*sqrt(-4*a*c+b^2)*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/n,1],
[1/(a+b*x^n+c*x^(2*n))^3,x,5,1/2*x*(b^2-2*a*c+b*c*x^n)/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))^2-1/2*x*(4*a^2*c^2*(1-4*n)-5*a*b^2*c*(1-3*n)+b^4*(1-2*n)-b*c*(2*a*c*(2-7*n)-b^2*(1-2*n))*x^n)/a^2/(-4*a*c+b^2)^2/n^2/(a+b*x^n+c*x^(2*n))+1/2*c*(b*sqrt(-4*a*c+b^2)*(2*a*c*(2-7*n)-b^2*(1-2*n))*(1-n)-b^4*(2*n^2-3*n+1)+6*a*b^2*c*(3*n^2-4*n+1)-8*a^2*c^2*(8*n^2-6*n+1))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/a^2/(-4*a*c+b^2)^2/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/n^2-1/2*c*(b*sqrt(-4*a*c+b^2)*(2*a*c*(2-7*n)-b^2*(1-2*n))*(1-n)+b^4*(2*n^2-3*n+1)-6*a*b^2*c*(3*n^2-4*n+1)+8*a^2*c^2*(8*n^2-6*n+1))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/a^2/(-4*a*c+b^2)^2/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/n^2,1],
[(a+b*x^n+c*x^(2*n))^(5/2),x,3,a^2*x*sqrt(a+b*x^n+c*x^(2*n))*AppellF1(1/n,-5/2,-5/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2))),1],
[(a+b*x^n+c*x^(2*n))^(3/2),x,3,a*x*sqrt(a+b*x^n+c*x^(2*n))*AppellF1(1/n,-3/2,-3/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2))),1],
[sqrt(a+b*x^n+c*x^(2*n)),x,3,x*sqrt(a+b*x^n+c*x^(2*n))*AppellF1(1/n,-1/2,-1/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2))),1],
[1/sqrt(a+b*x^n+c*x^(2*n)),x,3,x*sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))*sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))*AppellF1(1/n,1/2,1/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/sqrt(a+b*x^n+c*x^(2*n)),1],
[1/(a+b*x^n+c*x^(2*n))^(3/2),x,3,x*sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))*sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))*AppellF1(1/n,3/2,3/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/a/sqrt(a+b*x^n+c*x^(2*n)),1],
[1/(a+b*x^n+c*x^(2*n))^(5/2),x,3,x*sqrt(1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))*sqrt(1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))*AppellF1(1/n,5/2,5/2,1+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/a^2/sqrt(a+b*x^n+c*x^(2*n)),1],
[(a^2+2*a*c*x^n+c^2*x^(2*n))^3,x,3,a^6*x+6*a^5*c*x^(1+n)/(1+n)+15*a^4*c^2*x^(1+2*n)/(1+2*n)+20*a^3*c^3*x^(1+3*n)/(1+3*n)+15*a^2*c^4*x^(1+4*n)/(1+4*n)+6*a*c^5*x^(1+5*n)/(1+5*n)+c^6*x^(1+6*n)/(1+6*n),1],
[(a^2+2*a*c*x^n+c^2*x^(2*n))^2,x,3,a^4*x+4*a^3*c*x^(1+n)/(1+n)+6*a^2*c^2*x^(1+2*n)/(1+2*n)+4*a*c^3*x^(1+3*n)/(1+3*n)+c^4*x^(1+4*n)/(1+4*n),1],
[a^2+2*a*c*x^n+c^2*x^(2*n),x,1,a^2*x+2*a*c*x^(1+n)/(1+n)+c^2*x^(1+2*n)/(1+2*n),1],
[1/(a^2+2*a*c*x^n+c^2*x^(2*n)),x,2,x*hypergeom([2, 1/n],[1+1/n],-c*x^n/a)/a^2,1],
[1/(a^2+2*a*c*x^n+c^2*x^(2*n))^2,x,2,x*hypergeom([4, 1/n],[1+1/n],-c*x^n/a)/a^4,1],
[1/(a^2+2*a*c*x^n+c^2*x^(2*n))^3,x,2,x*hypergeom([6, 1/n],[1+1/n],-c*x^n/a)/a^6,1],
[(a^2+2*a*c*x^n+c^2*x^(2*n))^(5/2),x,3,a^5*x*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(a+c*x^n)+5*a^4*c^2*x^(1+n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+n)/(a*c+c^2*x^n)+10*a^3*c^3*x^(1+2*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+2*n)/(a*c+c^2*x^n)+10*a^2*c^4*x^(1+3*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+3*n)/(a*c+c^2*x^n)+5*a*c^5*x^(1+4*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+4*n)/(a*c+c^2*x^n)+c^6*x^(1+5*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+5*n)/(a*c+c^2*x^n),1],
[(a^2+2*a*c*x^n+c^2*x^(2*n))^(3/2),x,3,a^3*x*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(a+c*x^n)+3*a^2*c^2*x^(1+n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+n)/(a*c+c^2*x^n)+3*a*c^3*x^(1+2*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+2*n)/(a*c+c^2*x^n)+c^4*x^(1+3*n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+3*n)/(a*c+c^2*x^n),1],
[sqrt(a^2+2*a*c*x^n+c^2*x^(2*n)),x,2,a*x*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(a+c*x^n)+c^2*x^(1+n)*sqrt(a^2+2*a*c*x^n+c^2*x^(2*n))/(1+n)/(a*c+c^2*x^n),1],
[1/sqrt(a^2+2*a*c*x^n+c^2*x^(2*n)),x,2,x*(a+c*x^n)*hypergeom([1, 1/n],[1+1/n],-c*x^n/a)/a/sqrt(a^2+2*a*c*x^n+c^2*x^(2*n)),1],
[1/(a^2+2*a*c*x^n+c^2*x^(2*n))^(3/2),x,2,x*(a+c*x^n)*hypergeom([3, 1/n],[1+1/n],-c*x^n/a)/a^3/sqrt(a^2+2*a*c*x^n+c^2*x^(2*n)),1],
[1/(a^2+2*a*c*x^n+c^2*x^(2*n))^(5/2),x,2,x*(a+c*x^n)*hypergeom([5, 1/n],[1+1/n],-c*x^n/a)/a^5/sqrt(a^2+2*a*c*x^n+c^2*x^(2*n)),1]]: