lst:=[[1/(b*x^5+a)^(1/5)/(d*x^5+c),x,7,-1/5*sqrt(5/2+1/2*sqrt(5))*arctan(sqrt(1-2/5*sqrt(5))-2*sqrt(2/(5+sqrt(5)))*(-a*d+b*c)^(1/5)*x/c^(1/5)/(b*x^5+a)^(1/5))/c^(4/5)/(-a*d+b*c)^(1/5)+1/5*sqrt(5/2-1/2*sqrt(5))*arctan(sqrt(1+2/5*sqrt(5))+sqrt(2+2/5*sqrt(5))*(-a*d+b*c)^(1/5)*x/c^(1/5)/(b*x^5+a)^(1/5))/c^(4/5)/(-a*d+b*c)^(1/5)-1/5*ln(c^(1/5)-(-a*d+b*c)^(1/5)*x/(b*x^5+a)^(1/5))/c^(4/5)/(-a*d+b*c)^(1/5)+1/20*(1-sqrt(5))*ln((2*(-a*d+b*c)^(2/5)*x^2+c^(1/5)*(-a*d+b*c)^(1/5)*x*(b*x^5+a)^(1/5)-sqrt(5)*c^(1/5)*(-a*d+b*c)^(1/5)*x*(b*x^5+a)^(1/5)+2*c^(2/5)*(b*x^5+a)^(2/5))/(b*x^5+a)^(2/5))/c^(4/5)/(-a*d+b*c)^(1/5)+1/20*(1+sqrt(5))*ln((2*(-a*d+b*c)^(2/5)*x^2+c^(1/5)*(-a*d+b*c)^(1/5)*x*(b*x^5+a)^(1/5)+sqrt(5)*c^(1/5)*(-a*d+b*c)^(1/5)*x*(b*x^5+a)^(1/5)+2*c^(2/5)*(b*x^5+a)^(2/5))/(b*x^5+a)^(2/5))/c^(4/5)/(-a*d+b*c)^(1/5),1],
[(x^6+1)/(x^6-1),x,11,x+arctan((1-2*x)/sqrt(3))/sqrt(3)-arctan((1+2*x)/sqrt(3))/sqrt(3)-2/3*arctanh(x)-1/3*arctanh(x/(x^2+1)),1],
[(1/x^3+x^3)/(-1/x^3+x^3),x,13,x+arctan((1-2*x)/sqrt(3))/sqrt(3)-arctan((1+2*x)/sqrt(3))/sqrt(3)-2/3*arctanh(x)-1/3*arctanh(x/(x^2+1)),1],
[sqrt(a+b/x)*(c+d/x)^3,x,6,-6*c^2*d*sqrt(a+b/x)-2/3*d^2*(-a*d+3*b*c)*(a+b/x)^(3/2)/b^2-2/5*d^3*(a+b/x)^(5/2)/b^2+c^3*sqrt(a+b/x)*x+c^2*(6*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a),1],
[sqrt(a+b/x)*(c+d/x)^2,x,6,-4*c*d*sqrt(a+b/x)-2/3*d^2*(a+b/x)^(3/2)/b+c^2*sqrt(a+b/x)*x+c*(4*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a),1],
[sqrt(a+b/x)*(c+d/x),x,5,-2*d*sqrt(a+b/x)+c*sqrt(a+b/x)*x+(2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a),1],
[sqrt(a+b/x),x,4,sqrt(a+b/x)*x+b*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a),1],
[sqrt(a+b/x)/(c+d/x),x,7,sqrt(a+b/x)*x/c+2*sqrt(d)*sqrt(-a*d+b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2+(-2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)/c^2,1],
[sqrt(a+b/x)/(c+d/x)^2,x,8,2*d*sqrt(a+b/x)/c^2/(c+d/x)+sqrt(a+b/x)*x/c/(c+d/x)+sqrt(d)*(-4*a*d+3*b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/sqrt(-a*d+b*c)+(-4*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)/c^3,1],
[sqrt(a+b/x)/(c+d/x)^3,x,9,3/2*d*sqrt(a+b/x)/c^2/(c+d/x)^2+1/4*d*(-12*a*d+11*b*c)*sqrt(a+b/x)/c^3/(-a*d+b*c)/(c+d/x)+sqrt(a+b/x)*x/c/(c+d/x)^2+1/4*sqrt(d)*(24*a^2*d^2-40*a*b*c*d+15*b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/(-a*d+b*c)^(3/2)+(-6*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)/c^4,1],
[(a+b/x)^(3/2)*(c+d/x)^3,x,6,-2*c^2*(3*a*d+b*c)*sqrt(a+b/x)-2*c^2*d*(a+b/x)^(3/2)-2/5*d^2*(-a*d+3*b*c)*(a+b/x)^(5/2)/b^2-2/7*d^3*(a+b/x)^(7/2)/b^2+a*c^3*sqrt(a+b/x)*x+3*sqrt(a)*c^2*(2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(3/2)*(c+d/x)^2,x,6,-2*c*(2*a*d+b*c)*sqrt(a+b/x)-4/3*c*d*(a+b/x)^(3/2)-2/5*d^2*(a+b/x)^(5/2)/b+a*c^2*sqrt(a+b/x)*x+sqrt(a)*c*(4*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(3/2)*(c+d/x),x,6,-2*(a*d+b*c)*sqrt(a+b/x)-2/3*d*(a+b/x)^(3/2)+a*c*sqrt(a+b/x)*x+sqrt(a)*(2*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(3/2),x,5,-2*b*sqrt(a+b/x)+a*sqrt(a+b/x)*x+3*sqrt(a)*b*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(3/2)/(c+d/x),x,7,a*sqrt(a+b/x)*x/c-2*(-a*d+b*c)^(3/2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2/sqrt(d)+sqrt(a)*(-2*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^2,1],
[(a+b/x)^(3/2)/(c+d/x)^2,x,8,-(-2*a*d+b*c)*sqrt(a+b/x)/c^2/(c+d/x)+a*sqrt(a+b/x)*x/c/(c+d/x)-(-4*a*d+b*c)*sqrt(-a*d+b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/sqrt(d)+sqrt(a)*(-4*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^3,1],
[(a+b/x)^(3/2)/(c+d/x)^3,x,9,-1/2*(-3*a*d+b*c)*sqrt(a+b/x)/c^2/(c+d/x)^2-3/4*(-4*a*d+b*c)*sqrt(a+b/x)/c^3/(c+d/x)+a*sqrt(a+b/x)*x/c/(c+d/x)^2-3/4*(8*a^2*d^2-8*a*b*c*d+b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/sqrt(d)/sqrt(-a*d+b*c)+3*sqrt(a)*(-2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^4,1],
[(a+b/x)^(5/2)*(c+d/x)^3,x,6,-2*a*c^2*(3*a*d+2*b*c)*sqrt(a+b/x)-2/3*c^2*(3*a*d+b*c)*(a+b/x)^(3/2)-6/5*c^2*d*(a+b/x)^(5/2)-2/7*d^2*(-a*d+3*b*c)*(a+b/x)^(7/2)/b^2-2/9*d^3*(a+b/x)^(9/2)/b^2+a^2*c^3*sqrt(a+b/x)*x+a^(3/2)*c^2*(6*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(5/2)*(c+d/x)^2,x,6,-4*a*c*(a*d+b*c)*sqrt(a+b/x)-2/3*c*(2*a*d+b*c)*(a+b/x)^(3/2)-4/5*c*d*(a+b/x)^(5/2)-2/7*d^2*(a+b/x)^(7/2)/b+a^2*c^2*sqrt(a+b/x)*x+a^(3/2)*c*(4*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(5/2)*(c+d/x),x,7,-2*a*(a*d+2*b*c)*sqrt(a+b/x)-2/3*(a*d+b*c)*(a+b/x)^(3/2)-2/5*d*(a+b/x)^(5/2)+a^2*c*sqrt(a+b/x)*x+a^(3/2)*(2*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(5/2),x,6,-4*a*b*sqrt(a+b/x)-2/3*b*(a+b/x)^(3/2)+a^2*sqrt(a+b/x)*x+5*a^(3/2)*b*arctanh(sqrt(a+b/x)/sqrt(a)),1],
[(a+b/x)^(5/2)/(c+d/x),x,8,-b*(a*d+2*b*c)*sqrt(a+b/x)/c/d+a*(a+b/x)^(3/2)*x/c+2*(-a*d+b*c)^(5/2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2/d^(3/2)+a^(3/2)*(-2*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^2,1],
[(a+b/x)^(5/2)/(c+d/x)^2,x,8,(-2*a*d+b*c)*(-a*d+b*c)*sqrt(a+b/x)/c^2/d/(c+d/x)+a*(a+b/x)^(3/2)*x/c/(c+d/x)-(-a*d+b*c)^(3/2)*(4*a*d+b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/d^(3/2)+a^(3/2)*(-4*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^3,1],
[(a+b/x)^(5/2)/(c+d/x)^3,x,9,1/2*(-3*a*d+b*c)*(-a*d+b*c)*sqrt(a+b/x)/c^2/d/(c+d/x)^2-1/4*(-12*a^2*d^2+7*a*b*c*d+b^2*c^2)*sqrt(a+b/x)/c^3/d/(c+d/x)+a*(a+b/x)^(3/2)*x/c/(c+d/x)^2-1/4*sqrt(-a*d+b*c)*(-24*a^2*d^2+8*a*b*c*d+b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/d^(3/2)+a^(3/2)*(-6*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/c^4,1],
[(c+d/x)^3/sqrt(a+b/x),x,6,-2*d^2*(-a*d+3*b*c)*sqrt(a+b/x)/b^2-2/3*d^3*(a+b/x)^(3/2)/b^2+c^3*sqrt(a+b/x)*x/a-c^2*(-6*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2),1],
[(c+d/x)^2/sqrt(a+b/x),x,5,-2*d^2*sqrt(a+b/x)/b+c^2*sqrt(a+b/x)*x/a-c*(-4*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2),1],
[(c+d/x)/sqrt(a+b/x),x,4,c*sqrt(a+b/x)*x/a-(-2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2),1],
[1/sqrt(a+b/x),x,4,sqrt(a+b/x)*x/a-b*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2),1],
[1/sqrt(a+b/x)/(c+d/x),x,7,sqrt(a+b/x)*x/a/c-2*d^(3/2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2/sqrt(-a*d+b*c)-(2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)/c^2,1],
[1/sqrt(a+b/x)/(c+d/x)^2,x,8,d*(-2*a*d+b*c)*sqrt(a+b/x)/a/c^2/(-a*d+b*c)/(c+d/x)+sqrt(a+b/x)*x/a/c/(c+d/x)-d^(3/2)*(-4*a*d+5*b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/(-a*d+b*c)^(3/2)-(4*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)/c^3,1],
[1/sqrt(a+b/x)/(c+d/x)^3,x,9,1/2*d*(-3*a*d+2*b*c)*sqrt(a+b/x)/a/c^2/(-a*d+b*c)/(c+d/x)^2+1/4*d*(-4*a*d+b*c)*(-3*a*d+4*b*c)*sqrt(a+b/x)/a/c^3/(-a*d+b*c)^2/(c+d/x)+sqrt(a+b/x)*x/a/c/(c+d/x)^2-1/4*d^(3/2)*(24*a^2*d^2-56*a*b*c*d+35*b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/(-a*d+b*c)^(5/2)-(6*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)/c^4,1],
[(c+d/x)^3/(a+b/x)^(3/2),x,6,2*(-a*d+b*c)^3/a^2/b^2/sqrt(a+b/x)-2*d^3*sqrt(a+b/x)/b^2+c^3*sqrt(a+b/x)*x/a^2-3*c^2*(-2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2),1],
[(c+d/x)^2/(a+b/x)^(3/2),x,5,2*(-a*d+b*c)^2/a^2/b/sqrt(a+b/x)+c^2*sqrt(a+b/x)*x/a^2-c*(-4*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2),1],
[(c+d/x)/(a+b/x)^(3/2),x,5,2*(-a*d+b*c)/a^2/sqrt(a+b/x)+c*sqrt(a+b/x)*x/a^2-(-2*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2),1],
[1/(a+b/x)^(3/2),x,5,3*b/a^2/sqrt(a+b/x)+x/a/sqrt(a+b/x)-3*b*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2),1],
[1/(a+b/x)^(3/2)/(c+d/x),x,8,b*(-a*d+3*b*c)/a^2/c/(-a*d+b*c)/sqrt(a+b/x)+x/a/c/sqrt(a+b/x)+2*d^(5/2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2/(-a*d+b*c)^(3/2)-(2*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)/c^2,1],
[1/(a+b/x)^(3/2)/(c+d/x)^2,x,9,b*(2*a^2*d^2-2*a*b*c*d+3*b^2*c^2)/a^2/c^2/(-a*d+b*c)^2/sqrt(a+b/x)+d*(-2*a*d+b*c)/a/c^2/(-a*d+b*c)/sqrt(a+b/x)/(c+d/x)+x/a/c/sqrt(a+b/x)/(c+d/x)+d^(5/2)*(-4*a*d+7*b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/(-a*d+b*c)^(5/2)-(4*a*d+3*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)/c^3,1],
[1/(a+b/x)^(3/2)/(c+d/x)^3,x,10,3/4*b*(-a*d+2*b*c)*(4*a^2*d^2-a*b*c*d+2*b^2*c^2)/a^2/c^3/(-a*d+b*c)^3/sqrt(a+b/x)+1/2*d*(-3*a*d+2*b*c)/a/c^2/(-a*d+b*c)/sqrt(a+b/x)/(c+d/x)^2+1/4*d*(12*a^2*d^2-21*a*b*c*d+4*b^2*c^2)/a/c^3/(-a*d+b*c)^2/sqrt(a+b/x)/(c+d/x)+x/a/c/sqrt(a+b/x)/(c+d/x)^2+3/4*d^(5/2)*(8*a^2*d^2-24*a*b*c*d+21*b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/(-a*d+b*c)^(7/2)-3*(2*a*d+b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)/c^4,1],
[(c+d/x)^3/(a+b/x)^(5/2),x,6,2/3*(-a*d+b*c)^3/a^2/b^2/(a+b/x)^(3/2)+2*(-a*d+b*c)^2*(a*d+2*b*c)/a^3/b^2/sqrt(a+b/x)+c^3*sqrt(a+b/x)*x/a^3-c^2*(-6*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2),1],
[(c+d/x)^2/(a+b/x)^(5/2),x,6,2/3*(-a*d+b*c)^2/a^2/b/(a+b/x)^(3/2)+4*c*(-a*d+b*c)/a^3/sqrt(a+b/x)+c^2*sqrt(a+b/x)*x/a^3-c*(-4*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2),1],
[(c+d/x)/(a+b/x)^(5/2),x,6,2/3*(-a*d+b*c)/a^2/(a+b/x)^(3/2)+2*(-a*d+2*b*c)/a^3/sqrt(a+b/x)+c*sqrt(a+b/x)*x/a^3-(-2*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2),1],
[1/(a+b/x)^(5/2),x,6,5/3*b/a^2/(a+b/x)^(3/2)+5*b/a^3/sqrt(a+b/x)+x/a/(a+b/x)^(3/2)-5*b*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2),1],
[1/(a+b/x)^(5/2)/(c+d/x),x,9,1/3*b*(-3*a*d+5*b*c)/a^2/c/(-a*d+b*c)/(a+b/x)^(3/2)+b*(a^2*d^2-8*a*b*c*d+5*b^2*c^2)/a^3/c/(-a*d+b*c)^2/sqrt(a+b/x)+x/a/c/(a+b/x)^(3/2)-2*d^(7/2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^2/(-a*d+b*c)^(5/2)-(2*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)/c^2,1],
[1/(a+b/x)^(5/2)/(c+d/x)^2,x,10,1/3*b*(6*a^2*d^2-6*a*b*c*d+5*b^2*c^2)/a^2/c^2/(-a*d+b*c)^2/(a+b/x)^(3/2)+b*(-2*a*d+b*c)*(a^2*d^2-a*b*c*d+5*b^2*c^2)/a^3/c^2/(-a*d+b*c)^3/sqrt(a+b/x)+d*(-2*a*d+b*c)/a/c^2/(-a*d+b*c)/(a+b/x)^(3/2)/(c+d/x)+x/a/c/(a+b/x)^(3/2)/(c+d/x)-d^(7/2)*(-4*a*d+9*b*c)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^3/(-a*d+b*c)^(7/2)-(4*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)/c^3,1],
[1/(a+b/x)^(5/2)/(c+d/x)^3,x,11,1/12*b*(-36*a^3*d^3+87*a^2*b*c*d^2-36*a*b^2*c^2*d+20*b^3*c^3)/a^2/c^3/(-a*d+b*c)^3/(a+b/x)^(3/2)+1/4*b*(12*a^4*d^4-35*a^3*b*c*d^3+24*a^2*b^2*c^2*d^2-56*a*b^3*c^3*d+20*b^4*c^4)/a^3/c^3/(-a*d+b*c)^4/sqrt(a+b/x)+1/2*d*(-3*a*d+2*b*c)/a/c^2/(-a*d+b*c)/(a+b/x)^(3/2)/(c+d/x)^2+1/4*d*(12*a^2*d^2-23*a*b*c*d+4*b^2*c^2)/a/c^3/(-a*d+b*c)^2/(a+b/x)^(3/2)/(c+d/x)+x/a/c/(a+b/x)^(3/2)/(c+d/x)^2-1/4*d^(7/2)*(24*a^2*d^2-88*a*b*c*d+99*b^2*c^2)*arctan(sqrt(d)*sqrt(a+b/x)/sqrt(-a*d+b*c))/c^4/(-a*d+b*c)^(9/2)-(6*a*d+5*b*c)*arctanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)/c^4,1],
[sqrt(a+b/x)*sqrt(c+d/x),x,7,sqrt(a+b/x)*sqrt(c+d/x)*x+(a*d+b*c)*arctanh(sqrt(c)*sqrt(a+b/x)/sqrt(a)/sqrt(c+d/x))/sqrt(a)/sqrt(c)-2*sqrt(b)*sqrt(d)*arctanh(sqrt(d)*sqrt(a+b/x)/sqrt(b)/sqrt(c+d/x)),1],
[sqrt(a+b/x)/sqrt(c+d/x),x,4,sqrt(a+b/x)*sqrt(c+d/x)*x/c+(-a*d+b*c)*arctanh(sqrt(c)*sqrt(a+b/x)/sqrt(a)/sqrt(c+d/x))/sqrt(a)/c^(3/2),1],
[sqrt(a+b/x)/(c+d/x)^(3/2),x,5,-(-3*a*d+b*c)*sqrt(a+b/x)/a/c^2/sqrt(c+d/x)+(a+b/x)^(3/2)*x/a/c/sqrt(c+d/x)+(-3*a*d+b*c)*arctanh(sqrt(c)*sqrt(a+b/x)/sqrt(a)/sqrt(c+d/x))/sqrt(a)/c^(5/2),1],
[(a+b/x)^p*(c+d/x)^q,x,3,-b*(a+b/x)^(p+1)*(c+d/x)^q*AppellF1(p+1,2,-q,2+p,1+b/a/x,-d*(a+b/x)/(-a*d+b*c))/a^2/(p+1)/((b*(c+d/x)/(-a*d+b*c))^q),1],
[(a+b/x^2)/(c+d/x^2),x,3,a*x/c+(-a*d+b*c)*arctan(sqrt(c)*x/sqrt(d))/c^(3/2)/sqrt(d),1],
[sqrt(a+b/x^2)*sqrt(c+d/x^2),x,6,-2*b*sqrt(c+d/x^2)/sqrt(a+b/x^2)/x+sqrt(a+b/x^2)*sqrt(c+d/x^2)*x+2*sqrt(a)*sqrt(b)*sqrt(c+d/x^2)*EllipticE(sin(arccot(sqrt(a)*x/sqrt(b))),sqrt(1-a*d/b/c))/sqrt(a+b/x^2)/sqrt(a*(c+d/x^2)/c/(a+b/x^2))-sqrt(a)*(a*d+b*c)*sqrt(c+d/x^2)*InverseJacobiAM(arccot(sqrt(a)*x/sqrt(b)),sqrt(1-a*d/b/c))/sqrt(b)/c/sqrt(a+b/x^2)/sqrt(a*(c+d/x^2)/c/(a+b/x^2)),1],
[sqrt(a+b/x^2)/sqrt(c+d/x^2),x,3,sqrt(a+b/x^2)*x/sqrt(c+d/x^2)+sqrt(d)*sqrt(a+b/x^2)*EllipticE(sin(arccot(sqrt(c)*x/sqrt(d))),sqrt(1-b*c/a/d))/sqrt(c)/sqrt(c*(a+b/x^2)/a/(c+d/x^2))/sqrt(c+d/x^2)-b*sqrt(c)*sqrt(a+b/x^2)*InverseJacobiAM(arccot(sqrt(c)*x/sqrt(d)),sqrt(1-b*c/a/d))/a/sqrt(d)/sqrt(c*(a+b/x^2)/a/(c+d/x^2))/sqrt(c+d/x^2),1],
[sqrt(a+b/x^2)/(c+d/x^2)^(3/2),x,4,-sqrt(a+b/x^2)*x/c/sqrt(c+d/x^2)+2*a*sqrt(c+d/x^2)*x/c^2/sqrt(a+b/x^2)+2*sqrt(a)*sqrt(b)*sqrt(c+d/x^2)*EllipticE(sin(arccot(sqrt(a)*x/sqrt(b))),sqrt(1-a*d/b/c))/c^2/sqrt(a+b/x^2)/sqrt(a*(c+d/x^2)/c/(a+b/x^2))-sqrt(a)*sqrt(b)*sqrt(c+d/x^2)*InverseJacobiAM(arccot(sqrt(a)*x/sqrt(b)),sqrt(1-a*d/b/c))/c^2/sqrt(a+b/x^2)/sqrt(a*(c+d/x^2)/c/(a+b/x^2)),1],
[(a+b/x^2)^p*(c+d/x^2)^q,x,4,(a+b/x^2)^p*(c+d/x^2)^q*x*AppellF1(-1/2,-p,-q,1/2,-b/a/x^2,-d/c/x^2)/((1+b/a/x^2)^p)/((1+d/c/x^2)^q),1],
[(a+b/x^3)/(c+d/x^3),x,8,a*x/c-(-a*d+b*c)*arctan((d^(1/3)-2*c^(1/3)*x)/sqrt(3)/d^(1/3))/sqrt(3)/c^(4/3)/d^(2/3)+1/3*(-a*d+b*c)*ln(d^(1/3)+c^(1/3)*x)/c^(4/3)/d^(2/3)-1/6*(-a*d+b*c)*ln(d^(2/3)-c^(1/3)*d^(1/3)*x+c^(2/3)*x^2)/c^(4/3)/d^(2/3),1],
[(a+b*sqrt(x))/(c+d*sqrt(x)),x,3,-2*(-a*d+b*c)*sqrt(x)/d^2+b*x/d+2*c*(-a*d+b*c)*ln(c+d*sqrt(x))/d^3,1],
[(-1+x^(1/3))/(1+x^(1/3)),x,3,6*x^(1/3)-3*x^(2/3)+x-6*ln(1+x^(1/3)),1],
[(1+x^(2/3))/(-1+x^(2/3)),x,4,6*x^(1/3)+x-6*arctanh(x^(1/3)),1],
[(-16+x^(3/4))/(16+x^(3/4)),x,9,-128*x^(1/4)+x-256*2^(1/3)*arctan(1/2*(2^(1/3)-x^(1/4))*2^(2/3)/sqrt(3))/sqrt(3)+256/3*2^(1/3)*ln(2*2^(1/3)+x^(1/4))-128/3*2^(1/3)*ln(4*2^(2/3)-2*2^(1/3)*x^(1/4)+sqrt(x)),1],
[(1+1/x^(1/3))/(-1+1/x^(1/3)),x,3,-6*x^(1/3)-3*x^(2/3)-x-6*ln(1-x^(1/3)),1],
[(a+b*x^n)^2*(a*d-b*d*x^n)^2,x,3,a^4*d^2*x-2*a^2*b^2*d^2*x^(1+2*n)/(1+2*n)+b^4*d^2*x^(1+4*n)/(1+4*n),1],
[(a+b*x^n)*(a*d-b*d*x^n),x,2,a^2*d*x-b^2*d*x^(1+2*n)/(1+2*n),1],
[1/(a+b*x^n)/(a*d-b*d*x^n),x,2,x*hypergeom([1, 1/2/n],[1+1/2/n],b^2*x^(2*n)/a^2)/a^2/d,1],
[(a-b*x^n)^(3/2)*(a+b*x^n)^(3/2),x,2,a^2*x*sqrt(a-b*x^n)*sqrt(a+b*x^n)*hypergeom([-3/2, 1/2/n],[1+1/2/n],b^2*x^(2*n)/a^2)/sqrt(1-b^2*x^(2*n)/a^2),1],
[sqrt(a-b*x^n)*sqrt(a+b*x^n),x,2,x*sqrt(a-b*x^n)*sqrt(a+b*x^n)*hypergeom([-1/2, 1/2/n],[1+1/2/n],b^2*x^(2*n)/a^2)/sqrt(1-b^2*x^(2*n)/a^2),1],
[(a-b*x^n)^p*(a+b*x^n)^p,x,2,x*(a-b*x^n)^p*(a+b*x^n)^p*hypergeom([1/2/n, -p],[1+1/2/n],b^2*x^(2*n)/a^2)/((1-b^2*x^(2*n)/a^2)^p),1],
[(a+b*x^n)*(c+d*x^n)^4,x,2,a*c^4*x+c^3*(4*a*d+b*c)*x^(1+n)/(1+n)+2*c^2*d*(3*a*d+2*b*c)*x^(1+2*n)/(1+2*n)+2*c*d^2*(2*a*d+3*b*c)*x^(1+3*n)/(1+3*n)+d^3*(a*d+4*b*c)*x^(1+4*n)/(1+4*n)+b*d^4*x^(1+5*n)/(1+5*n),1],
[(a+b*x^n)*(c+d*x^n)^3,x,2,a*c^3*x+c^2*(3*a*d+b*c)*x^(1+n)/(1+n)+3*c*d*(a*d+b*c)*x^(1+2*n)/(1+2*n)+d^2*(a*d+3*b*c)*x^(1+3*n)/(1+3*n)+b*d^3*x^(1+4*n)/(1+4*n),1],
[(a+b*x^n)*(c+d*x^n)^2,x,2,a*c^2*x+c*(2*a*d+b*c)*x^(1+n)/(1+n)+d*(a*d+2*b*c)*x^(1+2*n)/(1+2*n)+b*d^2*x^(1+3*n)/(1+3*n),1],
[(a+b*x^n)*(c+d*x^n),x,2,a*c*x+(a*d+b*c)*x^(1+n)/(1+n)+b*d*x^(1+2*n)/(1+2*n),1],
[(a+b*x^n)/(c+d*x^n),x,2,b*x/d-(-a*d+b*c)*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c/d,1],
[(a+b*x^n)/(c+d*x^n)^2,x,2,b*x/d/(1-n)/(c+d*x^n)-(b*c-a*d*(1-n))*x*hypergeom([2, 1/n],[1+1/n],-d*x^n/c)/c^2/d/(1-n),1],
[(a+b*x^n)/(c+d*x^n)^3,x,2,b*x/d/(1-2*n)/(c+d*x^n)^2+(a-b*c/(-2*d*n+d))*x*hypergeom([3, 1/n],[1+1/n],-d*x^n/c)/c^3,1],
[(a+b*x^n)/(c+d*x^n)^4,x,2,b*x/d/(1-3*n)/(c+d*x^n)^3+(a-b*c/(-3*d*n+d))*x*hypergeom([4, 1/n],[1+1/n],-d*x^n/c)/c^4,1],
[(a+b*x^n)^2*(d+e*x^n)^3,x,2,a^2*d^3*x+a*d^2*(3*a*e+2*b*d)*x^(1+n)/(1+n)+d*(3*a^2*e^2+6*a*b*d*e+b^2*d^2)*x^(1+2*n)/(1+2*n)+e*(a^2*e^2+6*a*b*d*e+3*b^2*d^2)*x^(1+3*n)/(1+3*n)+b*e^2*(2*a*e+3*b*d)*x^(1+4*n)/(1+4*n)+b^2*e^3*x^(1+5*n)/(1+5*n),1],
[(a+b*x^n)^2*(d+e*x^n)^2,x,2,a^2*d^2*x+2*a*d*(a*e+b*d)*x^(1+n)/(1+n)+(a^2*e^2+4*a*b*d*e+b^2*d^2)*x^(1+2*n)/(1+2*n)+2*b*e*(a*e+b*d)*x^(1+3*n)/(1+3*n)+b^2*e^2*x^(1+4*n)/(1+4*n),1],
[(a+b*x^n)^2*(c+d*x^n),x,2,a^2*c*x+a*(a*d+2*b*c)*x^(1+n)/(1+n)+b*(2*a*d+b*c)*x^(1+2*n)/(1+2*n)+b^2*d*x^(1+3*n)/(1+3*n),1],
[(a+b*x^n)^2/(c+d*x^n),x,3,-b*(b*c*(1+n)-a*d*(1+2*n))*x/d^2/(1+n)+b*x*(a+b*x^n)/d/(1+n)+(-a*d+b*c)^2*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c/d^2,1],
[(a+b*x^n)^2/(c+d*x^n)^2,x,3,-b*(a*d-b*c*(1+n))*x/c/d^2/n-(-a*d+b*c)*x*(a+b*x^n)/c/d/n/(c+d*x^n)+(-a*d+b*c)*(a*d*(1-n)-b*c*(1+n))*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c^2/d^2/n,1],
[(a+b*x^n)^2/(c+d*x^n)^3,x,3,-1/2*(-a*d+b*c)*x*(a+b*x^n)/c/d/n/(c+d*x^n)^2-1/2*b*(a*d*(1-n)-b*c*(1+n))*x/c/d^2/(1-n)/n/(c+d*x^n)+1/2*(2*a*b*c*d*(1-n)-b^2*c^2*(1+n)-a^2*d^2*(2*n^2-3*n+1))*x*hypergeom([2, 1/n],[1+1/n],-d*x^n/c)/c^3/d^2/(1-n)/n,1],
[(c+d*x^n)^4/(a+b*x^n),x,4,-d*(6*a*b^2*c^2*d*(1+3*n)-4*a^2*b*c*d^2*(1+3*n)+a^3*d^3*(1+3*n)-3*b^3*c^3*(1+4*n))*x/b^4/(1+3*n)-d^2*(4*a*b*c*d*(1+3*n)-a^2*d^2*(1+3*n)-3*b^2*c^2*(1+5*n))*x^(1+n)/b^3/(1+n)/(1+3*n)-d^3*(a*d*(1+3*n)-b*(6*c*n+c))*x^(1+2*n)/b^2/(6*n^2+5*n+1)+d*x*(c+d*x^n)^3/b/(1+3*n)+(-a*d+b*c)^4*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/b^4,1],
[(c+d*x^n)^3/(a+b*x^n),x,4,-d*(3*a*b*c*d*(1+2*n)-a^2*d^2*(1+2*n)-2*b^2*c^2*(1+3*n))*x/b^3/(1+2*n)-d^2*(a*d*(1+2*n)-b*(4*c*n+c))*x^(1+n)/b^2/(1+n)/(1+2*n)+d*x*(c+d*x^n)^2/b/(1+2*n)+(-a*d+b*c)^3*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/b^3,1],
[(c+d*x^n)^2/(a+b*x^n),x,3,-d*(a*d*(1+n)-b*(2*c*n+c))*x/b^2/(1+n)+d*x*(c+d*x^n)/b/(1+n)+(-a*d+b*c)^2*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/b^2,1],
[(c+d*x^n)/(a+b*x^n),x,2,d*x/b+(-a*d+b*c)*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/b,1],
[1/(a+b*x^n)/(c+d*x^n),x,3,b*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/(-a*d+b*c)-d*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c/(-a*d+b*c),1],
[1/(a+b*x^n)/(c+d*x^n)^2,x,4,-d*x/c/(-a*d+b*c)/n/(c+d*x^n)+b^2*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/(-a*d+b*c)^2+d*(b*c*(1-2*n)-a*d*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c^2/(-a*d+b*c)^2/n,1],
[1/(a+b*x^n)/(c+d*x^n)^3,x,5,-1/2*d*x/c/(-a*d+b*c)/n/(c+d*x^n)^2-1/2*d*(a*d*(1-2*n)-b*(-4*c*n+c))*x/c^2/(-a*d+b*c)^2/n^2/(c+d*x^n)+b^3*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a/(-a*d+b*c)^3-1/2*d*(a^2*d^2*(2*n^2-3*n+1)-2*a*b*c*d*(3*n^2-4*n+1)+b^2*c^2*(6*n^2-5*n+1))*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c^3/(-a*d+b*c)^3/n^2,1],
[(c+d*x^n)^4/(a+b*x^n)^2,x,4,-d*(3*b^3*c^3-6*a*b^2*c^2*d*(1+n)+4*a^2*b*c*d^2*(1+2*n)-a^3*d^3*(1+3*n))*x/a/b^4/n-d^2*(3*b^2*c^2*(1+n)-4*a*b*c*d*(1+2*n)+a^2*d^2*(1+3*n))*x^(1+n)/a/b^3/n/(1+n)+d^3*(a*d*(1+3*n)-b*(2*c*n+c))*x^(1+2*n)/a/b^2/n/(1+2*n)+(-a*d+b*c)*x*(c+d*x^n)^3/a/b/n/(a+b*x^n)-(-a*d+b*c)^3*(b*c*(1-n)-a*d*(1+3*n))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/b^4/n,1],
[(c+d*x^n)^3/(a+b*x^n)^2,x,4,-d*(2*b^2*c^2-3*a*b*c*d*(1+n)+a^2*d^2*(1+2*n))*x/a/b^3/n-d^2*(b*c*(1+n)-a*d*(1+2*n))*x^(1+n)/a/b^2/n/(1+n)+(-a*d+b*c)*x*(c+d*x^n)^2/a/b/n/(a+b*x^n)-(-a*d+b*c)^2*(b*c*(1-n)-a*d*(1+2*n))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/b^3/n,1],
[(c+d*x^n)^2/(a+b*x^n)^2,x,3,-d*(b*c-a*d*(1+n))*x/a/b^2/n+(-a*d+b*c)*x*(c+d*x^n)/a/b/n/(a+b*x^n)-(-a*d+b*c)*(b*c*(1-n)-a*d*(1+n))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/b^2/n,1],
[(c+d*x^n)/(a+b*x^n)^2,x,2,d*x/b/(1-n)/(a+b*x^n)-(a*d-b*c*(1-n))*x*hypergeom([2, 1/n],[1+1/n],-b*x^n/a)/a^2/b/(1-n),1],
[1/(a+b*x^n)^2/(c+d*x^n),x,4,b*x/a/(-a*d+b*c)/n/(a+b*x^n)+b*(a*d*(1-2*n)-b*c*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/(-a*d+b*c)^2/n+d^2*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c/(-a*d+b*c)^2,1],
[1/(a+b*x^n)^2/(c+d*x^n)^2,x,5,d*(a*d+b*c)*x/a/c/(-a*d+b*c)^2/n/(c+d*x^n)+b*x/a/(-a*d+b*c)/n/(a+b*x^n)/(c+d*x^n)+b^2*(a*d*(1-3*n)-b*(-c*n+c))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/(-a*d+b*c)^3/n-d^2*(b*c*(1-3*n)-a*d*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c^2/(-a*d+b*c)^3/n,1],
[1/(a+b*x^n)^2/(c+d*x^n)^3,x,6,1/2*d*(a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/n/(c+d*x^n)^2+b*x/a/(-a*d+b*c)/n/(a+b*x^n)/(c+d*x^n)^2-1/2*d*(a*b*c*d*(1-6*n)-a^2*d^2*(1-2*n)-2*b^2*c^2*n)*x/a/c^2/(-a*d+b*c)^3/n^2/(c+d*x^n)+b^3*(a*d*(1-4*n)-b*c*(1-n))*x*hypergeom([1, 1/n],[1+1/n],-b*x^n/a)/a^2/(-a*d+b*c)^4/n+1/2*d^2*(a^2*d^2*(2*n^2-3*n+1)-2*a*b*c*d*(4*n^2-5*n+1)+b^2*c^2*(12*n^2-7*n+1))*x*hypergeom([1, 1/n],[1+1/n],-d*x^n/c)/c^3/(-a*d+b*c)^4/n^2,1],
[sqrt(a+b*x^n)*(c+d*x^n)^2,x,4,-2*d*(2*a*d*(1+n)-b*c*(2+7*n))*x*(a+b*x^n)^(3/2)/b^2/(2+3*n)/(2+5*n)+2*d*x*(a+b*x^n)^(3/2)*(c+d*x^n)/b/(2+5*n)+(4*a^2*d^2*(1+n)-4*a*b*c*d*(2+5*n)+b^2*c^2*(15*n^2+16*n+4))*x*sqrt(a+b*x^n)*hypergeom([-1/2, 1/n],[1+1/n],-b*x^n/a)/b^2/(2+3*n)/(2+5*n)/sqrt(1+b*x^n/a),1],
[sqrt(a+b*x^n)*(c+d*x^n),x,3,2*d*x*(a+b*x^n)^(3/2)/b/(2+3*n)+(c-2*a*d/(3*b*n+2*b))*x*sqrt(a+b*x^n)*hypergeom([-1/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(1+b*x^n/a),1],
[sqrt(a+b*x^n)/(c+d*x^n),x,2,x*sqrt(a+b*x^n)*AppellF1(1/n,-1/2,1,1+1/n,-b*x^n/a,-d*x^n/c)/c/sqrt(1+b*x^n/a),1],
[sqrt(a+b*x^n)/(c+d*x^n)^2,x,2,x*sqrt(a+b*x^n)*AppellF1(1/n,-1/2,2,1+1/n,-b*x^n/a,-d*x^n/c)/c^2/sqrt(1+b*x^n/a),1],
[(c+d*x^n)^2/sqrt(a+b*x^n),x,4,-2*d*(2*a*d*(1+n)-b*c*(2+5*n))*x*sqrt(a+b*x^n)/b^2/(2+n)/(2+3*n)+2*d*x*sqrt(a+b*x^n)*(c+d*x^n)/b/(2+3*n)+(4*a^2*d^2*(1+n)-4*a*b*c*d*(2+3*n)+b^2*c^2*(3*n^2+8*n+4))*x*sqrt(1+b*x^n/a)*hypergeom([1/2, 1/n],[1+1/n],-b*x^n/a)/b^2/(2+n)/(2+3*n)/sqrt(a+b*x^n),1],
[(c+d*x^n)/sqrt(a+b*x^n),x,3,2*d*x*sqrt(a+b*x^n)/b/(2+n)+(c-2*a*d/b/(2+n))*x*sqrt(1+b*x^n/a)*hypergeom([1/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(a+b*x^n),1],
[1/sqrt(a+b*x^n)/(c+d*x^n),x,2,x*sqrt(1+b*x^n/a)*AppellF1(1/n,1/2,1,1+1/n,-b*x^n/a,-d*x^n/c)/c/sqrt(a+b*x^n),1],
[1/sqrt(a+b*x^n)/(c+d*x^n)^2,x,2,x*sqrt(1+b*x^n/a)*AppellF1(1/n,1/2,2,1+1/n,-b*x^n/a,-d*x^n/c)/c^2/sqrt(a+b*x^n),1],
[(c+d*x^n)^2/(a+b*x^n)^(3/2),x,4,-2*d*(c-2*a*d*(1+n)/b/(2+n))*x*sqrt(a+b*x^n)/a/b/n+2*(-a*d+b*c)*x*(c+d*x^n)/a/b/n/sqrt(a+b*x^n)-(4*a^2*d^2*(1+n)-4*a*b*c*d*(2+n)+b^2*c^2*(-n^2+4))*x*sqrt(1+b*x^n/a)*hypergeom([1/2, 1/n],[1+1/n],-b*x^n/a)/a/b^2/n/(2+n)/sqrt(a+b*x^n),1],
[(c+d*x^n)/(a+b*x^n)^(3/2),x,3,2*d*x/b/(2-n)/sqrt(a+b*x^n)+(c/a-2*d/b/(2-n))*x*sqrt(1+b*x^n/a)*hypergeom([3/2, 1/n],[1+1/n],-b*x^n/a)/sqrt(a+b*x^n),1],
[1/(a+b*x^n)^(3/2)/(c+d*x^n),x,2,x*sqrt(1+b*x^n/a)*AppellF1(1/n,3/2,1,1+1/n,-b*x^n/a,-d*x^n/c)/a/c/sqrt(a+b*x^n),1],
[1/(a+b*x^n)^(3/2)/(c+d*x^n)^2,x,2,x*sqrt(1+b*x^n/a)*AppellF1(1/n,3/2,2,1+1/n,-b*x^n/a,-d*x^n/c)/a/c^2/sqrt(a+b*x^n),1],
[(a+b*x^n)^(1/3)*(c+d*x^n)^2,x,4,-3*d*(3*a*d*(1+n)-b*c*(3+10*n))*x*(a+b*x^n)^(4/3)/b^2/(3+4*n)/(3+7*n)+3*d*x*(a+b*x^n)^(4/3)*(c+d*x^n)/b/(3+7*n)+(9*a^2*d^2*(1+n)-6*a*b*c*d*(3+7*n)+b^2*c^2*(28*n^2+33*n+9))*x*(a+b*x^n)^(1/3)*hypergeom([-1/3, 1/n],[1+1/n],-b*x^n/a)/b^2/(3+4*n)/(3+7*n)/(1+b*x^n/a)^(1/3),1],
[(a+b*x^n)^(1/3)*(c+d*x^n),x,3,3*d*x*(a+b*x^n)^(4/3)/b/(3+4*n)+(c-3*a*d/(4*b*n+3*b))*x*(a+b*x^n)^(1/3)*hypergeom([-1/3, 1/n],[1+1/n],-b*x^n/a)/(1+b*x^n/a)^(1/3),1],
[(a+b*x^n)^(1/3)/(c+d*x^n),x,2,x*(a+b*x^n)^(1/3)*AppellF1(1/n,-1/3,1,1+1/n,-b*x^n/a,-d*x^n/c)/c/(1+b*x^n/a)^(1/3),1],
[(a+b*x^n)^(1/3)/(c+d*x^n)^2,x,2,x*(a+b*x^n)^(1/3)*AppellF1(1/n,-1/3,2,1+1/n,-b*x^n/a,-d*x^n/c)/c^2/(1+b*x^n/a)^(1/3),1],
[(c+d*x^n)^2/(a+b*x^n)^(1/3),x,4,-3*d*(3*a*d*(1+n)-b*c*(3+8*n))*x*(a+b*x^n)^(2/3)/b^2/(3+2*n)/(3+5*n)+3*d*x*(a+b*x^n)^(2/3)*(c+d*x^n)/b/(3+5*n)+(9*a^2*d^2*(1+n)-6*a*b*c*d*(3+5*n)+b^2*c^2*(10*n^2+21*n+9))*x*(1+b*x^n/a)^(1/3)*hypergeom([1/3, 1/n],[1+1/n],-b*x^n/a)/b^2/(3+2*n)/(3+5*n)/(a+b*x^n)^(1/3),1],
[(c+d*x^n)/(a+b*x^n)^(1/3),x,3,3*d*x*(a+b*x^n)^(2/3)/b/(3+2*n)+(c-3*a*d/(2*b*n+3*b))*x*(1+b*x^n/a)^(1/3)*hypergeom([1/3, 1/n],[1+1/n],-b*x^n/a)/(a+b*x^n)^(1/3),1],
[1/(a+b*x^n)^(1/3)/(c+d*x^n),x,2,x*(1+b*x^n/a)^(1/3)*AppellF1(1/n,1/3,1,1+1/n,-b*x^n/a,-d*x^n/c)/c/(a+b*x^n)^(1/3),1],
[1/(a+b*x^n)^(1/3)/(c+d*x^n)^2,x,2,x*(1+b*x^n/a)^(1/3)*AppellF1(1/n,1/3,2,1+1/n,-b*x^n/a,-d*x^n/c)/c^2/(a+b*x^n)^(1/3),1],
[(c+d*x^n)^2/(a+b*x^n)^(4/3),x,4,-3*d*(c-3*a*d*(1+n)/b/(3+2*n))*x*(a+b*x^n)^(2/3)/a/b/n+3*(-a*d+b*c)*x*(c+d*x^n)/a/b/n/(a+b*x^n)^(1/3)-(9*a^2*d^2*(1+n)-6*a*b*c*d*(3+2*n)+b^2*c^2*(-2*n^2+3*n+9))*x*(1+b*x^n/a)^(1/3)*hypergeom([1/3, 1/n],[1+1/n],-b*x^n/a)/a/b^2/n/(3+2*n)/(a+b*x^n)^(1/3),1],
[(c+d*x^n)/(a+b*x^n)^(4/3),x,3,3*d*x/b/(3-n)/(a+b*x^n)^(1/3)+(c/a-3*d/b/(3-n))*x*(1+b*x^n/a)^(1/3)*hypergeom([4/3, 1/n],[1+1/n],-b*x^n/a)/(a+b*x^n)^(1/3),1],
[1/(a+b*x^n)^(4/3)/(c+d*x^n),x,2,x*(1+b*x^n/a)^(1/3)*AppellF1(1/n,4/3,1,1+1/n,-b*x^n/a,-d*x^n/c)/a/c/(a+b*x^n)^(1/3),1],
[1/(a+b*x^n)^(4/3)/(c+d*x^n)^2,x,2,x*(1+b*x^n/a)^(1/3)*AppellF1(1/n,4/3,2,1+1/n,-b*x^n/a,-d*x^n/c)/a/c^2/(a+b*x^n)^(1/3),1],
[(a+b*x^n)^p*(c+d*x^n)^3,x,5,d*(a^2*d^2*(2*n^2+3*n+1)-3*a*b*c*d*(1+n)*(1+n*(3+p))+2*b^2*c^2*(1+2*n*(3+p)+n^2*(p^2+6*p+8)))*x*(a+b*x^n)^(p+1)/b^3/(n*p+n+1)/(1+n*(2+p))/(1+n*(3+p))-d^2*(a*d*(1+2*n)-b*(c+c*n*(5+p)))*x^(1+n)*(a+b*x^n)^(p+1)/b^2/(1+n*(2+p))/(1+n*(3+p))+d*x*(a+b*x^n)^(p+1)*(c+d*x^n)^2/b/(1+n*(3+p))-(a^3*d^3*(2*n^2+3*n+1)-3*a^2*b*c*d^2*(1+n)*(1+n*(3+p))+3*a*b^2*c^2*d*(1+n*(5+2*p)+n^2*(p^2+5*p+6))-b^3*c^3*(1+3*n*(2+p)+n^2*(3*p^2+12*p+11)+n^3*(p^3+6*p^2+11*p+6)))*x*(a+b*x^n)^p*hypergeom([1/n, -p],[1+1/n],-b*x^n/a)/b^3/(n*p+n+1)/(1+n*(2+p))/(1+n*(3+p))/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p*(c+d*x^n)^2,x,4,-d*(a*d*(1+n)-b*(c+c*n*(3+p)))*x*(a+b*x^n)^(p+1)/b^2/(n*p+n+1)/(1+n*(2+p))+d*x*(a+b*x^n)^(p+1)*(c+d*x^n)/b/(1+n*(2+p))-(c*(a*d-b*(c+c*n*(2+p)))-a*d*(a*d*(1+n)-b*(c+c*n*(3+p)))/b/(n*p+n+1))*x*(a+b*x^n)^p*hypergeom([1/n, -p],[1+1/n],-b*x^n/a)/b/(1+n*(2+p))/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p*(c+d*x^n),x,3,d*x*(a+b*x^n)^(p+1)/b/(n*p+n+1)+(c-a*d/(b*n*p+b*n+b))*x*(a+b*x^n)^p*hypergeom([1/n, -p],[1+1/n],-b*x^n/a)/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p,x,2,x*(a+b*x^n)^p*hypergeom([1/n, -p],[1+1/n],-b*x^n/a)/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p/(c+d*x^n),x,2,x*(a+b*x^n)^p*AppellF1(1/n,-p,1,1+1/n,-b*x^n/a,-d*x^n/c)/c/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p/(c+d*x^n)^2,x,2,x*(a+b*x^n)^p*AppellF1(1/n,-p,2,1+1/n,-b*x^n/a,-d*x^n/c)/c^2/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p/(c+d*x^n)^3,x,2,x*(a+b*x^n)^p*AppellF1(1/n,-p,3,1+1/n,-b*x^n/a,-d*x^n/c)/c^3/((1+b*x^n/a)^p),1],
[(a+b*x^n)^p*(c+d*x^n)^(-1-1/n-p),x,1,x*(a+b*x^n)^p*(c+d*x^n)^(-1/n-p)*hypergeom([1/n, -p],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/c/((c*(a+b*x^n)/a/(c+d*x^n))^p),1],
[(a+b*x^n)^3*(c+d*x^n)^(-4-1/n),x,4,x*(a+b*x^n)^3*(c+d*x^n)^(-3-1/n)/c/(1+3*n)+3*a*n*x*(a+b*x^n)^2*(c+d*x^n)^(-2-1/n)/c^2/(6*n^2+5*n+1)-6*a^2*(-a*d+b*c)*n^2*x*(c+d*x^n)^(-1-1/n)/c^3/d/(1+n)/(1+2*n)/(1+3*n)+6*a^2*n^2*(a*d*n+b*c)*x/c^4/d/(1+n)/(1+2*n)/(1+3*n)/((c+d*x^n)^(1/n)),1],
[(a+b*x^n)^2*(c+d*x^n)^(-3-1/n),x,3,x*(a+b*x^n)^2*(c+d*x^n)^(-2-1/n)/c/(1+2*n)-2*a*(-a*d+b*c)*n*x*(c+d*x^n)^(-1-1/n)/c^2/d/(1+n)/(1+2*n)+2*a*n*(a*d*n+b*c)*x/c^3/d/(1+n)/(1+2*n)/((c+d*x^n)^(1/n)),1],
[(a+b*x^n)*(c+d*x^n)^(-2-1/n),x,2,-(-a*d+b*c)*x*(c+d*x^n)^(-1-1/n)/c/d/(1+n)+(a*d*n+b*c)*x/c^2/d/(1+n)/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(-1-1/n),x,1,x/c/((c+d*x^n)^(1/n)),1],
[1/(a+b*x^n)/((c+d*x^n)^(1/n)),x,1,x*hypergeom([1, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(1-1/n)/(a+b*x^n)^2,x,1,c*x*hypergeom([2, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a^2/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(2-1/n)/(a+b*x^n)^3,x,1,c^2*x*hypergeom([3, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a^3/((c+d*x^n)^(1/n)),1],
[(a+b*x^n)^p*(c+d*x^n)^(-2-1/n-p),x,4,x*(a+b*x^n)^(p+1)*(c+d*x^n)^(-1-1/n-p)/a/c+(a*d*n*(p+1)-b*c*(n*p+n+1))*x^(1+n)*(a+b*x^n)^p*(c+d*x^n)^(-1-1/n-p)*hypergeom([1+1/n, -p],[2+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a/c^2/(1+n)/((c*(a+b*x^n)/a/(c+d*x^n))^p),1],
[(a+b*x^n)^((a*d*n-b*c*(1+n))/(-a*d+b*c)/n)*(c+d*x^n)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x,1,x*(c+d*x^n)^(a*d/(-a*d+b*c)/n)/a/c/((a+b*x^n)^(b*c/(-a*d+b*c)/n)),1],
[(a+b*x^n)^2*(c+d*x^n)^(-4-1/n),x,4,-d*x*(a+b*x^n)^3*(c+d*x^n)^(-3-1/n)/c/(-a*d+b*c)/(1+3*n)-(3*a*d*n-b*(3*c*n+c))*x*(a+b*x^n)^2*(c+d*x^n)^(-2-1/n)/c^2/(-a*d+b*c)/(1+2*n)/(1+3*n)+2*a*n*(3*a*d*n-b*(3*c*n+c))*x*(c+d*x^n)^(-1-1/n)/c^3/d/(1+n)/(1+2*n)/(1+3*n)+2*a*n*(-3*a*d*n+3*b*c*n+b*c)*(a*d*n+b*c)*x/c^4/d/(-a*d+b*c)/(1+n)/(1+2*n)/(1+3*n)/((c+d*x^n)^(1/n)),1],
[(a+b*x^n)*(c+d*x^n)^(-3-1/n),x,3,-(-a*d+b*c)*x*(c+d*x^n)^(-2-1/n)/c/d/(1+2*n)+(2*a*d*n+b*c)*x*(c+d*x^n)^(-1-1/n)/c^2/d/(1+n)/(1+2*n)+n*(2*a*d*n+b*c)*x/c^3/d/(1+n)/(1+2*n)/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(-2-1/n),x,2,x*(c+d*x^n)^(-1-1/n)/c/(1+n)+n*x/c^2/(1+n)/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(-1-1/n)/(a+b*x^n),x,2,x/a/c/((c+d*x^n)^(1/n))-b*x*hypergeom([1, -1/n],[-(1-n)/n],-a*(c+d*x^n)/(-a*d+b*c)/(x^n))/a/(-a*d+b*c)/((c+d*x^n)^(1/n)),1],
[1/(a+b*x^n)^2/((c+d*x^n)^(1/n)),x,2,b*x/a/(-a*d+b*c)/n/(a+b*x^n)/((c+d*x^n)^((1-n)/n))-(a*d*n+b*(-c*n+c))*x*hypergeom([1, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a^2/(-a*d+b*c)/n/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(1-1/n)/(a+b*x^n)^3,x,2,1/2*b*x*(c+d*x^n)^(2-1/n)/a/(-a*d+b*c)/n/(a+b*x^n)^2-1/2*c*(2*a*d-b*c*(2-1/n))*x*hypergeom([2, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a^3/(-a*d+b*c)/((c+d*x^n)^(1/n)),1],
[(c+d*x^n)^(2-1/n)/(a+b*x^n)^4,x,2,1/3*b*x*(c+d*x^n)^(3-1/n)/a/(-a*d+b*c)/n/(a+b*x^n)^3-1/3*c^2*(3*a*d-b*c*(3-1/n))*x*hypergeom([3, 1/n],[1+1/n],-(-a*d+b*c)*x^n/a/(c+d*x^n))/a^4/(-a*d+b*c)/((c+d*x^n)^(1/n)),1],
[(a+b*x^n)^p*(c+d*x^n)^q,x,3,x*(a+b*x^n)^p*(c+d*x^n)^q*AppellF1(1/n,-p,-q,1+1/n,-b*x^n/a,-d*x^n/c)/((1+b*x^n/a)^p)/((1+d*x^n/c)^q),1],
[(2+3*x^n)^p/((5+7*x^n)^p),x,1,(2/5)^p*x*AppellF1(1/n,-p,p,1+1/n,-3/2*x^n,-7/5*x^n),1],
[(2+3*x^n)^p/((5-7*x^n)^p),x,1,(2/5)^p*x*AppellF1(1/n,p,-p,1+1/n,7/5*x^n,-3/2*x^n),1],
[(-2+3*x^n)^p/((5+7*x^n)^p),x,2,x*(-2+3*x^n)^p*AppellF1(1/n,-p,p,1+1/n,3/2*x^n,-7/5*x^n)/(5^p)/((1-3/2*x^n)^p),1],
[(-2+3*x^n)^p/((5-7*x^n)^p),x,2,x*(-2+3*x^n)^p*AppellF1(1/n,p,-p,1+1/n,7/5*x^n,3/2*x^n)/(5^p)/((1-3/2*x^n)^p),1]]: