lst:=[[(e*x^3+d)^5*(c*x^6+b*x^3+a),x,2,a*d^5*x+1/4*d^4*(5*a*e+b*d)*x^4+1/7*d^3*(c*d^2+5*e*(2*a*e+b*d))*x^7+1/2*d^2*e*(c*d^2+2*e*(a*e+b*d))*x^10+5/13*d*e^2*(2*c*d^2+e*(a*e+2*b*d))*x^13+1/16*e^3*(10*c*d^2+e*(a*e+5*b*d))*x^16+1/19*e^4*(b*e+5*c*d)*x^19+1/22*c*e^5*x^22,1],
[(e*x^3+d)^4*(c*x^6+b*x^3+a),x,2,a*d^4*x+1/4*d^3*(4*a*e+b*d)*x^4+1/7*d^2*(6*a*e^2+4*b*d*e+c*d^2)*x^7+1/5*d*e*(2*c*d^2+e*(2*a*e+3*b*d))*x^10+1/13*e^2*(6*c*d^2+e*(a*e+4*b*d))*x^13+1/16*e^3*(b*e+4*c*d)*x^16+1/19*c*e^4*x^19,1],
[(e*x^3+d)^3*(c*x^6+b*x^3+a),x,2,a*d^3*x+1/4*d^2*(3*a*e+b*d)*x^4+1/7*d*(c*d^2+3*e*(a*e+b*d))*x^7+1/10*e*(3*c*d^2+e*(a*e+3*b*d))*x^10+1/13*e^2*(b*e+3*c*d)*x^13+1/16*c*e^3*x^16,1],
[(e*x^3+d)^2*(c*x^6+b*x^3+a),x,2,a*d^2*x+1/4*d*(2*a*e+b*d)*x^4+1/7*(c*d^2+e*(a*e+2*b*d))*x^7+1/10*e*(b*e+2*c*d)*x^10+1/13*c*e^2*x^13,1],
[(e*x^3+d)*(c*x^6+b*x^3+a),x,2,a*d*x+1/4*(a*e+b*d)*x^4+1/7*(b*e+c*d)*x^7+1/10*c*e*x^10,1],
[(c*x^6+b*x^3+a)/(e*x^3+d),x,8,-(-b*e+c*d)*x/e^2+1/4*c*x^4/e-(a*e^2-b*d*e+c*d^2)*arctan((d^(1/3)-2*e^(1/3)*x)/sqrt(3)/d^(1/3))/sqrt(3)/d^(2/3)/e^(7/3)+1/3*(a*e^2-b*d*e+c*d^2)*ln(d^(1/3)+e^(1/3)*x)/d^(2/3)/e^(7/3)-1/6*(a*e^2-b*d*e+c*d^2)*ln(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/d^(2/3)/e^(7/3),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^2,x,8,c*x/e^2+1/3*(a*e^2-b*d*e+c*d^2)*x/d/e^2/(e*x^3+d)+1/3*(4*c*d^2-e*(2*a*e+b*d))*arctan((d^(1/3)-2*e^(1/3)*x)/sqrt(3)/d^(1/3))/sqrt(3)/d^(5/3)/e^(7/3)-1/9*(4*c*d^2-e*(2*a*e+b*d))*ln(d^(1/3)+e^(1/3)*x)/d^(5/3)/e^(7/3)+1/18*(4*c*d^2-e*(2*a*e+b*d))*ln(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/d^(5/3)/e^(7/3),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^3,x,8,1/6*(a*e^2-b*d*e+c*d^2)*x/d/e^2/(e*x^3+d)^2-1/18*(7*c*d^2-e*(5*a*e+b*d))*x/d^2/e^2/(e*x^3+d)-1/9*(2*c*d^2+e*(5*a*e+b*d))*arctan((d^(1/3)-2*e^(1/3)*x)/sqrt(3)/d^(1/3))/sqrt(3)/d^(8/3)/e^(7/3)+1/27*(2*c*d^2+e*(5*a*e+b*d))*ln(d^(1/3)+e^(1/3)*x)/d^(8/3)/e^(7/3)-1/54*(2*c*d^2+e*(5*a*e+b*d))*ln(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/d^(8/3)/e^(7/3),1],
[(e*x^3+d)^(5/2)*(c*x^6+b*x^3+a),x,6,54/124729*d^2*(667*a*e^2-58*b*d*e+16*c*d^2)*x*sqrt(e*x^3+d)/e^2+30/124729*d*(667*a*e^2-58*b*d*e+16*c*d^2)*x*(e*x^3+d)^(3/2)/e^2+2/11339*(667*a*e^2-58*b*d*e+16*c*d^2)*x*(e*x^3+d)^(5/2)/e^2-2/667*(-29*b*e+8*c*d)*x*(e*x^3+d)^(7/2)/e^2+2/29*c*x^4*(e*x^3+d)^(7/2)/e+54/124729*3^(3/4)*sqrt(2+sqrt(3))*d^3*(667*a*e^2-58*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(e*x^3+d)^(3/2)*(c*x^6+b*x^3+a),x,5,18/21505*d*(391*a*e^2-46*b*d*e+16*c*d^2)*x*sqrt(e*x^3+d)/e^2+2/4301*(391*a*e^2-46*b*d*e+16*c*d^2)*x*(e*x^3+d)^(3/2)/e^2-2/391*(-23*b*e+8*c*d)*x*(e*x^3+d)^(5/2)/e^2+2/23*c*x^4*(e*x^3+d)^(5/2)/e+18/21505*3^(3/4)*sqrt(2+sqrt(3))*d^2*(391*a*e^2-46*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[sqrt(e*x^3+d)*(c*x^6+b*x^3+a),x,4,2/935*(187*a*e^2-34*b*d*e+16*c*d^2)*x*sqrt(e*x^3+d)/e^2-2/187*(-17*b*e+8*c*d)*x*(e*x^3+d)^(3/2)/e^2+2/17*c*x^4*(e*x^3+d)^(3/2)/e+2/935*3^(3/4)*sqrt(2+sqrt(3))*d*(187*a*e^2-34*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(c*x^6+b*x^3+a)/sqrt(e*x^3+d),x,3,-2/55*(-11*b*e+8*c*d)*x*sqrt(e*x^3+d)/e^2+2/11*c*x^4*sqrt(e*x^3+d)/e+2/165*sqrt(2+sqrt(3))*(55*a*e^2-22*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^(3/2),x,3,2/3*(a*e^2-b*d*e+c*d^2)*x/d/e^2/sqrt(e*x^3+d)+2/5*c*x*sqrt(e*x^3+d)/e^2-2/45*sqrt(2+sqrt(3))*(16*c*d^2-5*e*(a*e+2*b*d))*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/d/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^(5/2),x,3,2/9*(a*e^2-b*d*e+c*d^2)*x/d/e^2/(e*x^3+d)^(3/2)-2/27*(-7*a*e^2-2*b*d*e+11*c*d^2)*x/d^2/e^2/sqrt(e*x^3+d)+2/81*sqrt(2+sqrt(3))*(16*c*d^2+e*(7*a*e+2*b*d))*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/d^2/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^(7/2),x,4,2/15*(a*e^2-b*d*e+c*d^2)*x/d/e^2/(e*x^3+d)^(5/2)-2/135*(-13*a*e^2-2*b*d*e+17*c*d^2)*x/d^2/e^2/(e*x^3+d)^(3/2)+2/405*(91*a*e^2+14*b*d*e+16*c*d^2)*x/d^3/e^2/sqrt(e*x^3+d)+2/1215*sqrt(2+sqrt(3))*(91*a*e^2+14*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/d^3/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(c*x^6+b*x^3+a)/(e*x^3+d)^(9/2),x,5,2/21*(a*e^2-b*d*e+c*d^2)*x/d/e^2/(e*x^3+d)^(7/2)-2/315*(-19*a*e^2-2*b*d*e+23*c*d^2)*x/d^2/e^2/(e*x^3+d)^(5/2)+2/2835*(247*a*e^2+26*b*d*e+16*c*d^2)*x/d^3/e^2/(e*x^3+d)^(3/2)+2/1215*(247*a*e^2+26*b*d*e+16*c*d^2)*x/d^4/e^2/sqrt(e*x^3+d)+2/3645*sqrt(2+sqrt(3))*(247*a*e^2+26*b*d*e+16*c*d^2)*(d^(1/3)+e^(1/3)*x)*sqrt((d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/d^4/e^(7/3)/sqrt(d^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+sqrt(3))*d^(1/3)+e^(1/3)*x)^2)/sqrt(e*x^3+d),1],
[(e*x^3+d)^(3/2)/(c*x^6+b*x^3+a),x,7,-2*c*d*x*sqrt(e*x^3+d)*AppellF1(1/3,-3/2,1,4/3,-e*x^3/d,-2*c*x^3/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^3/d)-2*c*d*x*sqrt(e*x^3+d)*AppellF1(1/3,-3/2,1,4/3,-e*x^3/d,-2*c*x^3/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^3/d),1],
[sqrt(e*x^3+d)/(c*x^6+b*x^3+a),x,7,-2*c*x*sqrt(e*x^3+d)*AppellF1(1/3,-1/2,1,4/3,-e*x^3/d,-2*c*x^3/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^3/d)-2*c*x*sqrt(e*x^3+d)*AppellF1(1/3,-1/2,1,4/3,-e*x^3/d,-2*c*x^3/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^3/d),1],
[1/sqrt(e*x^3+d)/(c*x^6+b*x^3+a),x,7,-2*c*x*sqrt(1+e*x^3/d)*AppellF1(1/3,1/2,1,4/3,-e*x^3/d,-2*c*x^3/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(e*x^3+d)-2*c*x*sqrt(1+e*x^3/d)*AppellF1(1/3,1/2,1,4/3,-e*x^3/d,-2*c*x^3/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(e*x^3+d),1],
[1/(e*x^3+d)^(3/2)/(c*x^6+b*x^3+a),x,7,-2*c*x*sqrt(1+e*x^3/d)*AppellF1(1/3,3/2,1,4/3,-e*x^3/d,-2*c*x^3/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/d/sqrt(e*x^3+d)-2*c*x*sqrt(1+e*x^3/d)*AppellF1(1/3,3/2,1,4/3,-e*x^3/d,-2*c*x^3/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/d/sqrt(e*x^3+d),1],
[(e*x^3+d)^(1/3)/(c*x^6+b*x^3+a)^2,x,11,1/3*x*(b*c*x^3-2*a*c+b^2)*(e*x^3+d)^(1/3)/a/(-4*a*c+b^2)/(c*x^6+b*x^3+a)-2/3*c*(b^2*d-10*a*c*d+3*a*b*e+sqrt(-4*a*c+b^2)*(-4*a*e+b*d))*x*(1+e*x^3/d)^(2/3)*AppellF1(1/3,2/3,1,4/3,-e*x^3/d,-2*c*x^3/(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))/(e*x^3+d)^(2/3)-2/3*c*(b^2*d-10*a*c*d+3*a*b*e-sqrt(-4*a*c+b^2)*(-4*a*e+b*d))*x*(1+e*x^3/d)^(2/3)*AppellF1(1/3,2/3,1,4/3,-e*x^3/d,-2*c*x^3/(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))/(e*x^3+d)^(2/3)+1/3*b*e*x*(1+e*x^3/d)^(2/3)*hypergeom([1/3, 2/3],[4/3],-e*x^3/d)/a/(-4*a*c+b^2)/(e*x^3+d)^(2/3),1],
[(e*x^4+d)/(e^2*x^8+b*x^4+d^2),x,17,-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b))-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-b))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-b)),1],
[(e*x^4+d)/(e^2*x^8+f*x^4+d^2),x,17,-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f))-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e-f))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e-f)),1],
[(e*x^4+d)/(e^2*x^8-b*x^4+d^2),x,7,-sqrt(e)*arctan(sqrt(2)*sqrt(e)*x/sqrt(sqrt(-2*d*e+b)-sqrt(2*d*e+b)))/sqrt(2)/sqrt(-2*d*e+b)/sqrt(sqrt(-2*d*e+b)-sqrt(2*d*e+b))-sqrt(e)*arctan(sqrt(2)*sqrt(e)*x/sqrt(sqrt(-2*d*e+b)+sqrt(2*d*e+b)))/sqrt(2)/sqrt(-2*d*e+b)/sqrt(sqrt(-2*d*e+b)+sqrt(2*d*e+b))-sqrt(e)*arctanh(sqrt(2)*sqrt(e)*x/sqrt(sqrt(-2*d*e+b)-sqrt(2*d*e+b)))/sqrt(2)/sqrt(-2*d*e+b)/sqrt(sqrt(-2*d*e+b)-sqrt(2*d*e+b))-sqrt(e)*arctanh(sqrt(2)*sqrt(e)*x/sqrt(sqrt(-2*d*e+b)+sqrt(2*d*e+b)))/sqrt(2)/sqrt(-2*d*e+b)/sqrt(sqrt(-2*d*e+b)+sqrt(2*d*e+b)),1],
[(e*x^4+d)/(e^2*x^8-f*x^4+d^2),x,17,-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f))-1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f))-2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f))+1/4*arctan((sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f))+2*sqrt(e)*x)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f)))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)-sqrt(2*d*e+f))+1/4*arctanh(sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f))*x/(sqrt(d)+sqrt(e)*x^2))/sqrt(d)/sqrt(2*sqrt(d)*sqrt(e)+sqrt(2*d*e+f)),1],
[(x^4+1)/(x^8+3*x^4+1),x,17,-1/4*(3+sqrt(5))^(1/4)*arctan(1-2^(3/4)*x/(3-sqrt(5))^(1/4))*2^(1/4)/sqrt(5)+1/4*(3+sqrt(5))^(1/4)*arctan(1+2^(3/4)*x/(3-sqrt(5))^(1/4))*2^(1/4)/sqrt(5)-1/4*(3-sqrt(5))^(1/4)*arctan(1-2^(3/4)*x/(3+sqrt(5))^(1/4))*2^(1/4)/sqrt(5)+1/4*(3-sqrt(5))^(1/4)*arctan(1+2^(3/4)*x/(3+sqrt(5))^(1/4))*2^(1/4)/sqrt(5)+1/4*(3+sqrt(5))^(1/4)*arctanh(2^(3/4)*(3-sqrt(5))^(1/4)*x/(sqrt(3-sqrt(5))+sqrt(2)*x^2))*2^(1/4)/sqrt(5)+1/4*(3-sqrt(5))^(1/4)*arctanh(2^(3/4)*(3+sqrt(5))^(1/4)*x/(sqrt(3+sqrt(5))+sqrt(2)*x^2))*2^(1/4)/sqrt(5),1],
[(x^4+1)/(x^8+2*x^4+1),x,9,-1/2*arctan(1-sqrt(2)*x)/sqrt(2)+1/2*arctan(1+sqrt(2)*x)/sqrt(2)+1/2*arctanh(sqrt(2)*x/(x^2+1))/sqrt(2),1],
[(x^4+1)/(x^8+x^4+1),x,17,-1/4*arctan((1-2*x)/sqrt(3))/sqrt(3)-1/4*arctan(sqrt(3)-2*x)+1/4*arctan((1+2*x)/sqrt(3))/sqrt(3)+1/4*arctan(sqrt(3)+2*x)+1/4*arctanh(x/(x^2+1))+1/4*arctanh(sqrt(3)*x/(x^2+1))/sqrt(3),1],
[(x^4+1)/(x^8+1),x,17,-1/4*arctan((sqrt(2-sqrt(2))-2*x)/sqrt(2+sqrt(2)))/sqrt(2+sqrt(2))-1/4*arctan((sqrt(2+sqrt(2))-2*x)/sqrt(2-sqrt(2)))/sqrt(2-sqrt(2))+1/4*arctan((sqrt(2-sqrt(2))+2*x)/sqrt(2+sqrt(2)))/sqrt(2+sqrt(2))+1/4*arctan((sqrt(2+sqrt(2))+2*x)/sqrt(2-sqrt(2)))/sqrt(2-sqrt(2))+1/4*arctanh(sqrt(2-sqrt(2))*x/(x^2+1))/sqrt(2-sqrt(2))+1/4*arctanh(sqrt(2+sqrt(2))*x/(x^2+1))/sqrt(2+sqrt(2)),1],
[(x^4+1)/(x^8-x^4+1),x,17,-1/4*arctan((sqrt(2-sqrt(3))-2*x)/sqrt(2+sqrt(3)))/sqrt(2+sqrt(3))-1/4*arctan((sqrt(2+sqrt(3))-2*x)/sqrt(2-sqrt(3)))/sqrt(2-sqrt(3))+1/4*arctan((sqrt(2-sqrt(3))+2*x)/sqrt(2+sqrt(3)))/sqrt(2+sqrt(3))+1/4*arctan((sqrt(2+sqrt(3))+2*x)/sqrt(2-sqrt(3)))/sqrt(2-sqrt(3))+1/4*arctanh(sqrt(2-sqrt(3))*x/(x^2+1))/sqrt(2-sqrt(3))+1/4*arctanh(sqrt(2+sqrt(3))*x/(x^2+1))/sqrt(2+sqrt(3)),1],
[(x^4+1)/(x^8-2*x^4+1),x,5,x/(-2*x^4+2)+1/4*arctan(x)+1/4*arctanh(x),1],
[(x^4+1)/(x^8-3*x^4+1),x,7,arctan(sqrt(2/(-1+sqrt(5)))*x)/sqrt(-2+2*sqrt(5))-arctan(sqrt(2/(1+sqrt(5)))*x)/sqrt(2+2*sqrt(5))+arctanh(sqrt(2/(-1+sqrt(5)))*x)/sqrt(-2+2*sqrt(5))-arctanh(sqrt(2/(1+sqrt(5)))*x)/sqrt(2+2*sqrt(5)),1],
[(x^4+1)/(x^8-4*x^4+1),x,7,1/4*arctan(2^(1/4)*x/sqrt(-1+sqrt(3)))*2^(3/4)/sqrt(-1+sqrt(3))-1/4*arctan(2^(1/4)*x/sqrt(1+sqrt(3)))*2^(3/4)/sqrt(1+sqrt(3))+1/4*arctanh(2^(1/4)*x/sqrt(-1+sqrt(3)))*2^(3/4)/sqrt(-1+sqrt(3))-1/4*arctanh(2^(1/4)*x/sqrt(1+sqrt(3)))*2^(3/4)/sqrt(1+sqrt(3)),1],
[(x^4+1)/(x^8-5*x^4+1),x,7,arctan(sqrt(2/(-sqrt(3)+sqrt(7)))*x)/sqrt(-6*sqrt(3)+6*sqrt(7))-arctan(sqrt(2/(sqrt(3)+sqrt(7)))*x)/sqrt(6*sqrt(3)+6*sqrt(7))+arctanh(sqrt(2/(-sqrt(3)+sqrt(7)))*x)/sqrt(-6*sqrt(3)+6*sqrt(7))-arctanh(sqrt(2/(sqrt(3)+sqrt(7)))*x)/sqrt(6*sqrt(3)+6*sqrt(7)),1],
[(x^4+1)/(x^8-6*x^4+1),x,7,1/4*arctan(x/sqrt(-1+sqrt(2)))/sqrt(-1+sqrt(2))-1/4*arctan(x/sqrt(1+sqrt(2)))/sqrt(1+sqrt(2))+1/4*arctanh(x/sqrt(-1+sqrt(2)))/sqrt(-1+sqrt(2))-1/4*arctanh(x/sqrt(1+sqrt(2)))/sqrt(1+sqrt(2)),1],
[(-x^4+1)/(x^8+3*x^4+1),x,17,-1/4*(3+sqrt(5))^(1/4)*arctan(1-2^(3/4)*x/(3-sqrt(5))^(1/4))*2^(1/4)+1/4*(3+sqrt(5))^(1/4)*arctan(1+2^(3/4)*x/(3-sqrt(5))^(1/4))*2^(1/4)+1/4*(3-sqrt(5))^(1/4)*arctan(1-2^(3/4)*x/(3+sqrt(5))^(1/4))*2^(1/4)-1/4*(3-sqrt(5))^(1/4)*arctan(1+2^(3/4)*x/(3+sqrt(5))^(1/4))*2^(1/4)+1/4*(3+sqrt(5))^(1/4)*arctanh(2^(3/4)*(3-sqrt(5))^(1/4)*x/(sqrt(3-sqrt(5))+sqrt(2)*x^2))*2^(1/4)-1/4*(3-sqrt(5))^(1/4)*arctanh(2^(3/4)*(3+sqrt(5))^(1/4)*x/(sqrt(3+sqrt(5))+sqrt(2)*x^2))*2^(1/4),1],
[(-x^4+1)/(x^8+2*x^4+1),x,10,x/(2*x^4+2)-1/4*arctan(1-sqrt(2)*x)/sqrt(2)+1/4*arctan(1+sqrt(2)*x)/sqrt(2)+1/4*arctanh(sqrt(2)*x/(x^2+1))/sqrt(2),1],
[(-x^4+1)/(x^8+x^4+1),x,17,-1/4*sqrt(3)*arctan((1-2*x)/sqrt(3))+1/4*arctan(sqrt(3)-2*x)+1/4*sqrt(3)*arctan((1+2*x)/sqrt(3))-1/4*arctan(sqrt(3)+2*x)-1/4*arctanh(x/(x^2+1))+1/4*sqrt(3)*arctanh(sqrt(3)*x/(x^2+1)),1],
[(-x^4+1)/(x^8+1),x,17,-1/4*sqrt(1+1/2*sqrt(2))*arctan((sqrt(2-sqrt(2))-2*x)/sqrt(2+sqrt(2)))+1/4*sqrt(1-1/2*sqrt(2))*arctan((sqrt(2+sqrt(2))-2*x)/sqrt(2-sqrt(2)))+1/4*sqrt(1+1/2*sqrt(2))*arctan((sqrt(2-sqrt(2))+2*x)/sqrt(2+sqrt(2)))-1/4*sqrt(1-1/2*sqrt(2))*arctan((sqrt(2+sqrt(2))+2*x)/sqrt(2-sqrt(2)))-1/4*sqrt(1-1/2*sqrt(2))*arctanh(sqrt(2-sqrt(2))*x/(x^2+1))+1/4*sqrt(1+1/2*sqrt(2))*arctanh(sqrt(2+sqrt(2))*x/(x^2+1)),1],
[(-x^4+1)/(x^8-x^4+1),x,17,-1/4*sqrt(2/3+1/3*sqrt(3))*arctan((sqrt(2-sqrt(3))-2*x)/sqrt(2+sqrt(3)))+1/4*sqrt(2/3-1/3*sqrt(3))*arctan((sqrt(2+sqrt(3))-2*x)/sqrt(2-sqrt(3)))+1/4*sqrt(2/3+1/3*sqrt(3))*arctan((sqrt(2-sqrt(3))+2*x)/sqrt(2+sqrt(3)))-1/4*sqrt(2/3-1/3*sqrt(3))*arctan((sqrt(2+sqrt(3))+2*x)/sqrt(2-sqrt(3)))-1/4*sqrt(2/3-1/3*sqrt(3))*arctanh(sqrt(2-sqrt(3))*x/(x^2+1))+1/4*sqrt(2/3+1/3*sqrt(3))*arctanh(sqrt(2+sqrt(3))*x/(x^2+1)),1],
[(-x^4+1)/(x^8-2*x^4+1),x,5,1/2*arctan(x)+1/2*arctanh(x),1],
[(-x^4+1)/(x^8-3*x^4+1),x,7,arctan(sqrt(2/(-1+sqrt(5)))*x)/sqrt(-10+10*sqrt(5))+arctan(sqrt(2/(1+sqrt(5)))*x)/sqrt(10+10*sqrt(5))+arctanh(sqrt(2/(-1+sqrt(5)))*x)/sqrt(-10+10*sqrt(5))+arctanh(sqrt(2/(1+sqrt(5)))*x)/sqrt(10+10*sqrt(5)),1],
[(-x^4+1)/(x^8-4*x^4+1),x,7,1/4*arctan(2^(1/4)*x/sqrt(-1+sqrt(3)))*2^(3/4)/sqrt(-3+3*sqrt(3))+1/4*arctan(2^(1/4)*x/sqrt(1+sqrt(3)))*2^(3/4)/sqrt(3+3*sqrt(3))+1/4*arctanh(2^(1/4)*x/sqrt(-1+sqrt(3)))*2^(3/4)/sqrt(-3+3*sqrt(3))+1/4*arctanh(2^(1/4)*x/sqrt(1+sqrt(3)))*2^(3/4)/sqrt(3+3*sqrt(3)),1],
[(-x^4+1)/(x^8-5*x^4+1),x,7,arctan(sqrt(2/(-sqrt(3)+sqrt(7)))*x)/sqrt(-14*sqrt(3)+14*sqrt(7))+arctan(sqrt(2/(sqrt(3)+sqrt(7)))*x)/sqrt(14*sqrt(3)+14*sqrt(7))+arctanh(sqrt(2/(-sqrt(3)+sqrt(7)))*x)/sqrt(-14*sqrt(3)+14*sqrt(7))+arctanh(sqrt(2/(sqrt(3)+sqrt(7)))*x)/sqrt(14*sqrt(3)+14*sqrt(7)),1],
[(-x^4+1)/(x^8-6*x^4+1),x,7,1/4*arctan(x/sqrt(-1+sqrt(2)))/sqrt(-2+2*sqrt(2))+1/4*arctan(x/sqrt(1+sqrt(2)))/sqrt(2+2*sqrt(2))+1/4*arctanh(x/sqrt(-1+sqrt(2)))/sqrt(-2+2*sqrt(2))+1/4*arctanh(x/sqrt(1+sqrt(2)))/sqrt(2+2*sqrt(2)),1],
[(x^4+1)/(x^8+b*x^4+1),x,17,-1/4*arctan((sqrt(2-sqrt(2-b))-2*x)/sqrt(2+sqrt(2-b)))/sqrt(2+sqrt(2-b))-1/4*arctan((sqrt(2+sqrt(2-b))-2*x)/sqrt(2-sqrt(2-b)))/sqrt(2-sqrt(2-b))+1/4*arctan((sqrt(2-sqrt(2-b))+2*x)/sqrt(2+sqrt(2-b)))/sqrt(2+sqrt(2-b))+1/4*arctan((sqrt(2+sqrt(2-b))+2*x)/sqrt(2-sqrt(2-b)))/sqrt(2-sqrt(2-b))+1/4*arctanh(sqrt(2-sqrt(2-b))*x/(x^2+1))/sqrt(2-sqrt(2-b))+1/4*arctanh(sqrt(2+sqrt(2-b))*x/(x^2+1))/sqrt(2+sqrt(2-b)),1],
[(-x^4+1)/(x^8+b*x^4+1),x,17,-1/4*sqrt(2+sqrt(2-b))*arctan((sqrt(2-sqrt(2-b))-2*x)/sqrt(2+sqrt(2-b)))/sqrt(2-b)+1/4*sqrt(2-sqrt(2-b))*arctan((sqrt(2+sqrt(2-b))-2*x)/sqrt(2-sqrt(2-b)))/sqrt(2-b)+1/4*sqrt(2+sqrt(2-b))*arctan((sqrt(2-sqrt(2-b))+2*x)/sqrt(2+sqrt(2-b)))/sqrt(2-b)-1/4*sqrt(2-sqrt(2-b))*arctan((sqrt(2+sqrt(2-b))+2*x)/sqrt(2-sqrt(2-b)))/sqrt(2-b)-1/4*sqrt(2-sqrt(2-b))*arctanh(sqrt(2-sqrt(2-b))*x/(x^2+1))/sqrt(2-b)+1/4*sqrt(2+sqrt(2-b))*arctanh(sqrt(2+sqrt(2-b))*x/(x^2+1))/sqrt(2-b),1],
[(-1+sqrt(3)+2*x^4)/(x^8-x^4+1),x,8,-arctan((sqrt(2+sqrt(3))-2*x)/sqrt(2-sqrt(3)))/sqrt(2)+arctan((sqrt(2+sqrt(3))+2*x)/sqrt(2-sqrt(3)))/sqrt(2)-arctanh(sqrt(42-24*sqrt(3))*x/(3-sqrt(3)+(3-sqrt(3))*x^2))/sqrt(2),1],
[(1+(1+sqrt(3))*x^4)/(x^8-x^4+1),x,8,-1/2*sqrt(2+sqrt(3))*arctan((sqrt(2+sqrt(3))-2*x)/sqrt(2-sqrt(3)))+1/2*sqrt(2+sqrt(3))*arctan((sqrt(2+sqrt(3))+2*x)/sqrt(2-sqrt(3)))+1/2*sqrt(2+sqrt(3))*arctanh(sqrt(2-sqrt(3))*x/(x^2+1)),1],
[(3-2*sqrt(3)+(-3+sqrt(3))*x^4)/(x^8-x^4+1),x,8,1/2*sqrt(6-3*sqrt(3))*arctan((sqrt(2+sqrt(3))-2*x)/sqrt(2-sqrt(3)))-1/2*sqrt(6-3*sqrt(3))*arctan((sqrt(2+sqrt(3))+2*x)/sqrt(2-sqrt(3)))-1/2*sqrt(6-3*sqrt(3))*arctanh(sqrt(26-15*sqrt(3))*x/(2-sqrt(3)+(2-sqrt(3))*x^2)),1],
[(d+e*x^n)^q*(c*d^2-b*d*e-b*e^2*x^n-c*e^2*x^(2*n))^p,x,5,x*(d+e*x^n)^q*(1+e*x^n/d)^(-p-q)*(d*(-b*e+c*d)-b*e^2*x^n-c*e^2*x^(2*n))^p*AppellF1(1/n,-p-q,-p,1+1/n,-e*x^n/d,c*e*x^n/(-b*e+c*d))/((1-c*e*x^n/(-b*e+c*d))^p),1],
[(d+e/x)/(c+a/x^2),x,6,d*x/c-sqrt(a)*d*arctan(sqrt(c)*x/sqrt(a))/c^(3/2)+1/2*e*ln(c*x^2+a)/c,1],
[(d+e/x)/(c+a/x^2+b/x),x,7,d*x/c-(-2*a*c*d+b^2*d-b*c*e)*arctanh((2*c*x+b)/sqrt(-4*a*c+b^2))/c^2/sqrt(-4*a*c+b^2)-1/2*(b*d-c*e)*ln(c*x^2+b*x+a)/c^2,1],
[(d+e/x^2)/(c+a/x^4),x,11,d*x/c+1/2*(sqrt(a)*d-sqrt(c)*e)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(1/4)/c^(5/4)-1/2*(sqrt(a)*d-sqrt(c)*e)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(1/4)/c^(5/4)-1/2*(sqrt(a)*d+sqrt(c)*e)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(1/4)/c^(5/4),1],
[(d+e/x^2)/(c+a/x^4+b/x^2),x,6,d*x/c-(b*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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],
[(d+e/x^3)/(c+a/x^6),x,15,d*x/c-1/3*a^(1/6)*d*arctan(c^(1/6)*x/a^(1/6))/c^(7/6)+1/6*(sqrt(a)*d-sqrt(3)*sqrt(c)*e)*arctan(sqrt(3)-2*c^(1/6)*x/a^(1/6))/a^(1/3)/c^(7/6)-1/6*(sqrt(a)*d+sqrt(3)*sqrt(c)*e)*arctan(sqrt(3)+2*c^(1/6)*x/a^(1/6))/a^(1/3)/c^(7/6)-1/6*e*ln(a^(1/3)+c^(1/3)*x^2)/a^(1/3)/c^(2/3)+1/12*(sqrt(3)*sqrt(a)*d+sqrt(c)*e)*ln(a^(1/3)-sqrt(3)*a^(1/6)*c^(1/6)*x+c^(1/3)*x^2)/a^(1/3)/c^(7/6)-1/12*(sqrt(3)*sqrt(a)*d-sqrt(c)*e)*ln(a^(1/3)+sqrt(3)*a^(1/6)*c^(1/6)*x+c^(1/3)*x^2)/a^(1/3)/c^(7/6),1],
[(d+e/x^3)/(c+a/x^6+b/x^3),x,16,d*x/c+1/2*(b*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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],
[(d+e/x^4)/(c+a/x^8),x,20,d*x/c+1/4*((1+sqrt(2))*sqrt(a)*d+sqrt(c)*e)*arctan((sqrt(2-sqrt(2))*a^(1/8)-2*c^(1/8)*x)/sqrt(2+sqrt(2))/a^(1/8))/sqrt(4+2*sqrt(2))/a^(3/8)/c^(9/8)-1/4*(sqrt(a)*(d-sqrt(2)*d)+sqrt(c)*e)*arctan((sqrt(2+sqrt(2))*a^(1/8)-2*c^(1/8)*x)/sqrt(2-sqrt(2))/a^(1/8))/sqrt(4-2*sqrt(2))/a^(3/8)/c^(9/8)-1/4*((1+sqrt(2))*sqrt(a)*d+sqrt(c)*e)*arctan((sqrt(2-sqrt(2))*a^(1/8)+2*c^(1/8)*x)/sqrt(2+sqrt(2))/a^(1/8))/sqrt(4+2*sqrt(2))/a^(3/8)/c^(9/8)+1/4*(sqrt(a)*(d-sqrt(2)*d)+sqrt(c)*e)*arctan((sqrt(2+sqrt(2))*a^(1/8)+2*c^(1/8)*x)/sqrt(2-sqrt(2))/a^(1/8))/sqrt(4-2*sqrt(2))/a^(3/8)/c^(9/8)+1/4*(sqrt(a)*(d-sqrt(2)*d)+sqrt(c)*e)*arctanh(sqrt(2-sqrt(2))*a^(1/8)*c^(1/8)*x/(a^(1/4)+c^(1/4)*x^2))/sqrt(4-2*sqrt(2))/a^(3/8)/c^(9/8)-1/4*((1+sqrt(2))*sqrt(a)*d+sqrt(c)*e)*arctanh(sqrt(2+sqrt(2))*a^(1/8)*c^(1/8)*x/(a^(1/4)+c^(1/4)*x^2))/sqrt(4+2*sqrt(2))/a^(3/8)/c^(9/8),1],
[(d+e/x^4)/(c+a/x^8+b/x^4),x,10,d*x/c+1/4*(b*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e+(-2*a*c*d+b^2*d-b*c*e)/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*d-c*e-(-2*a*c*d+b^2*d-b*c*e)/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],
[(d+e*x^n)*(a+b*x^n+c*x^(2*n)),x,2,a*d*x+(a*e+b*d)*x^(1+n)/(1+n)+(b*e+c*d)*x^(1+2*n)/(1+2*n)+c*e*x^(1+3*n)/(1+3*n),1],
[(d+e*x^n)*(a+b*x^n+c*x^(2*n))^2,x,2,a^2*d*x+a*(a*e+2*b*d)*x^(1+n)/(1+n)+(2*a*b*e+2*a*c*d+b^2*d)*x^(1+2*n)/(1+2*n)+(2*a*c*e+b^2*e+2*b*c*d)*x^(1+3*n)/(1+3*n)+c*(2*b*e+c*d)*x^(1+4*n)/(1+4*n)+c^2*e*x^(1+5*n)/(1+5*n),1],
[(d+e*x^n)*(a+b*x^n+c*x^(2*n))^3,x,2,a^3*d*x+a^2*(a*e+3*b*d)*x^(1+n)/(1+n)+3*a*(a*b*e+a*c*d+b^2*d)*x^(1+2*n)/(1+2*n)+(3*a^2*c*e+3*a*b^2*e+6*a*b*c*d+b^3*d)*x^(1+3*n)/(1+3*n)+(6*a*b*c*e+3*a*c^2*d+b^3*e+3*b^2*c*d)*x^(1+4*n)/(1+4*n)+3*c*(a*c*e+b^2*e+b*c*d)*x^(1+5*n)/(1+5*n)+c^2*(3*b*e+c*d)*x^(1+6*n)/(1+6*n)+c^3*e*x^(1+7*n)/(1+7*n),1],
[(d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x,6,e^2*(-b*e+3*c*d)*x/c^2+e^3*x^(1+n)/c/(1+n)-(b*e^2*(-b*e+3*c*d)-c*e*(-a*e^2+3*c*d^2)-(-b*e+2*c*d)*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/c^2/(b-sqrt(-4*a*c+b^2))-(2*c^3*d^3-b^2*(b+sqrt(-4*a*c+b^2))*e^3-3*c^2*d*e*(b*d+sqrt(-4*a*c+b^2)*d+2*a*e)+c*e^2*(3*b^2*d+a*sqrt(-4*a*c+b^2)*e+3*b*(sqrt(-4*a*c+b^2)*d+a*e)))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/c^2/(b^2-4*a*c+b*sqrt(-4*a*c+b^2)),1],
[(d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x,4,e^2*x/c+(e*(-b*e+2*c*d)+(2*c^2*d^2+b^2*e^2-2*c*e*(a*e+b*d))/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/c/(b-sqrt(-4*a*c+b^2))+(e*(-b*e+2*c*d)-(2*c^2*d^2+b^2*e^2-2*c*e*(a*e+b*d))/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/c/(b+sqrt(-4*a*c+b^2)),1],
[(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x,3,(e+(-b*e+2*c*d)/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b-sqrt(-4*a*c+b^2))+(e-(-b*e+2*c*d)/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b+sqrt(-4*a*c+b^2)),1],
[1/(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x,5,-c*(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*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))/(a*e^2-b*d*e+c*d^2)-c*(e+(-b*e+2*c*d)/sqrt(-4*a*c+b^2))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b+sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)+e^2*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d/(a*e^2-b*d*e+c*d^2),1],
[1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x,6,e^2*x/d/(a*e^2-b*d*e+c*d^2)/n/(d+e*x^n)-c*(2*c^2*d^2+b*(b+sqrt(-4*a*c+b^2))*e^2-2*c*e*(b*d+sqrt(-4*a*c+b^2)*d+a*e))*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))/(a*e^2-b*d*e+c*d^2)^2-c*(2*c^2*d^2+b*(b-sqrt(-4*a*c+b^2))*e^2-2*c*e*(b*d-sqrt(-4*a*c+b^2)*d+a*e))*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))/(a*e^2-b*d*e+c*d^2)^2-e^2*(c*d^2*(1-3*n)+e*(a*e*(1-n)-b*(-2*d*n+d)))*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d^2/(a*e^2-b*d*e+c*d^2)^2/n,1],
[1/(d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x,7,1/2*e^2*x/d/(a*e^2-b*d*e+c*d^2)/n/(d+e*x^n)^2+1/2*e^2*(e*(b*d*(1-4*n)-a*e*(1-2*n))-c*d^2*(1-6*n))*x/d^2/(a*e^2-b*d*e+c*d^2)^2/n^2/(d+e*x^n)-c*(2*c^3*d^3-b^2*(b+sqrt(-4*a*c+b^2))*e^3-3*c^2*d*e*(b*d+sqrt(-4*a*c+b^2)*d+2*a*e)+c*e^2*(3*b^2*d+a*sqrt(-4*a*c+b^2)*e+3*b*(sqrt(-4*a*c+b^2)*d+a*e)))*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))/(a*e^2-b*d*e+c*d^2)^3-c*(2*c^3*d^3-b^2*(b-sqrt(-4*a*c+b^2))*e^3-3*c^2*d*e*(b*d-sqrt(-4*a*c+b^2)*d+2*a*e)+c*e^2*(3*b^2*d-3*b*sqrt(-4*a*c+b^2)*d+3*a*b*e-a*sqrt(-4*a*c+b^2)*e))*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))/(a*e^2-b*d*e+c*d^2)^3+1/2*e^2*(c^2*d^4*(12*n^2-7*n+1)+e^2*(a^2*e^2*(2*n^2-3*n+1)-2*a*b*d*e*(3*n^2-4*n+1)+b^2*d^2*(6*n^2-5*n+1))+2*c*d^2*e*(a*e*(3*n^2-5*n+1)-b*d*(8*n^2-6*n+1)))*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d^3/(a*e^2-b*d*e+c*d^2)^3/n^2,1],
[(d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^2,x,8,-e*(a*b*e^2-6*a*c*d*e+2*b*c*d^2)*x/a/c/(-4*a*c+b^2)/n-e^2*(-2*a*e+b*d)*x^(1+n)/a/(-4*a*c+b^2)/n-b*e*x*(d+e*x^n)^2/a/(-4*a*c+b^2)/n+x*(b^2-2*a*c+b*c*x^n)*(d+e*x^n)^3/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))+(a*b^3*e^3-b^2*(a*sqrt(-4*a*c+b^2)*e^3-c^2*d^3*(1-n)+3*a*c*d*e^2*(1-n))+2*a*c*(3*c*d*e*(2*a*e-sqrt(-4*a*c+b^2)*d*(1-n))-2*c^2*d^3*(1-2*n)+a*sqrt(-4*a*c+b^2)*e^3*(1+n))+b*c*(c*d^2*(sqrt(-4*a*c+b^2)*d*(1-n)-6*a*e*n)+a*e^2*(3*sqrt(-4*a*c+b^2)*d*(1-n)-2*a*e*(2+n))))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/a/c/(-4*a*c+b^2)/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/n+(a*b^3*e^3+b^2*(a*sqrt(-4*a*c+b^2)*e^3+c^2*d^3*(1-n)-3*a*c*d*e^2*(1-n))+2*a*c*(3*c*d*e*(2*a*e+sqrt(-4*a*c+b^2)*d*(1-n))-2*c^2*d^3*(1-2*n)-a*sqrt(-4*a*c+b^2)*e^3*(1+n))-b*c*(c*d^2*(sqrt(-4*a*c+b^2)*d*(1-n)+6*a*e*n)+a*e^2*(3*sqrt(-4*a*c+b^2)*d*(1-n)+2*a*e*(2+n))))*x*hypergeom([1, 1/n],[1+1/n],-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/a/c/(-4*a*c+b^2)/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/n,1],
[(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x,7,-2*e*(-a*e+b*d)*x/a/(-4*a*c+b^2)/n-b*e^2*x^(1+n)/a/(-4*a*c+b^2)/n+x*(b^2-2*a*c+b*c*x^n)*(d+e*x^n)^2/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))+(4*a*c*(e*(a*e-sqrt(-4*a*c+b^2)*d*(1-n))-c*d^2*(1-2*n))+b^2*(-a*e^2+c*d^2)*(1-n)+b*(a*sqrt(-4*a*c+b^2)*e^2*(1-n)+c*d*(sqrt(-4*a*c+b^2)*d*(1-n)-4*a*e*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+(4*a*c*(e*(a*e+sqrt(-4*a*c+b^2)*d*(1-n))-c*d^2*(1-2*n))+b^2*(-a*e^2+c*d^2)*(1-n)-b*(a*sqrt(-4*a*c+b^2)*e^2*(1-n)+c*d*(sqrt(-4*a*c+b^2)*d*(1-n)+4*a*e*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],
[(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x,4,x*(b^2*d-2*a*c*d-a*b*e+c*(-2*a*e+b*d)*x^n)/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))-c*(2*a*(2*c*d*(1-2*n)+sqrt(-4*a*c+b^2)*e*(1-n))-b^2*(-d*n+d)-b*(sqrt(-4*a*c+b^2)*d*(1-n)-2*a*e*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*(2*a*(c*d*(2-4*n)-sqrt(-4*a*c+b^2)*e*(1-n))-b^2*d*(1-n)+b*(sqrt(-4*a*c+b^2)*d*(1-n)+2*a*e*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/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x,6,x*(c*(-2*a*c+b^2)*d-b*(-3*a*c+b^2)*e+c*(2*a*c*e-b^2*e+b*c*d)*x^n)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/n/(a+b*x^n+c*x^(2*n))+c*(b*c*(a*e^2*(2*a*e*(2-5*n)-sqrt(-4*a*c+b^2)*d*(1-n))+c*d^2*(2*a*e*(4-7*n)+sqrt(-4*a*c+b^2)*d*(1-n)))-2*a*c*(c*d*e*(2*a*e*(1-4*n)-sqrt(-4*a*c+b^2)*d*(1-n))-a*sqrt(-4*a*c+b^2)*e^3*(1-3*n)+2*c^2*d^3*(1-2*n))-b^3*e*(e*(a*e*(1-2*n)-sqrt(-4*a*c+b^2)*d*(1-n))+2*c*d^2*(1-n))-b^2*(a*sqrt(-4*a*c+b^2)*e^3*(1-2*n)-c^2*d^3*(1-n)+c*d*e*(2*sqrt(-4*a*c+b^2)*d+3*a*e)*(1-n))+b^4*d*e^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))/(a*e^2-b*d*e+c*d^2)^2/n+c*(b*c*(c*d^2*(2*a*e*(4-7*n)-sqrt(-4*a*c+b^2)*d*(1-n))+a*e^2*(2*a*e*(2-5*n)+sqrt(-4*a*c+b^2)*d*(1-n)))-2*a*c*(c*d*e*(2*a*e*(1-4*n)+sqrt(-4*a*c+b^2)*d*(1-n))+a*sqrt(-4*a*c+b^2)*e^3*(1-3*n)+2*c^2*d^3*(1-2*n))-b^3*e*(e*(a*e*(1-2*n)+sqrt(-4*a*c+b^2)*d*(1-n))+2*c*d^2*(1-n))+b^2*(a*sqrt(-4*a*c+b^2)*e^3*(1-2*n)+c^2*d^3*(1-n)+c*d*e*(2*sqrt(-4*a*c+b^2)*d-3*a*e)*(1-n))+b^4*d*e^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))/(a*e^2-b*d*e+c*d^2)^2/n+e^4*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d/(a*e^2-b*d*e+c*d^2)^2,1],
[1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x,7,e*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-a*e^2+c*d^2)-b^2*(-a*e^3+2*c*d^2*e))*x/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/n/(d+e*x^n)+x*(c*(-2*a*c+b^2)*d-b*(-3*a*c+b^2)*e+c*(2*a*c*e-b^2*e+b*c*d)*x^n)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/n/(d+e*x^n)/(a+b*x^n+c*x^(2*n))+c*(b*c*(2*a*c*d*e^2*(2*a*e*(1-7*n)-3*sqrt(-4*a*c+b^2)*d*(1-n))+c^2*d^3*(4*a*e*(3-5*n)+sqrt(-4*a*c+b^2)*d*(1-n))-a^2*sqrt(-4*a*c+b^2)*e^4*(3-11*n))+b^4*e^2*(e*(a*e*(1-3*n)-sqrt(-4*a*c+b^2)*d*(1-n))+3*c*d^2*(1-n))-b^5*d*e^3*(1-n)+4*a*c^2*(a*e^3*(sqrt(-4*a*c+b^2)*d*(1-5*n)+a*e*(1-4*n))-c^2*d^4*(1-2*n)+c*d^2*e*(sqrt(-4*a*c+b^2)*d*(1-n)+6*a*e*n))+b^3*e*(a*sqrt(-4*a*c+b^2)*e^3*(1-3*n)-3*c^2*d^3*(1-n)+c*d*e*(3*sqrt(-4*a*c+b^2)*d*(1-n)+a*e*(3+n)))+b^2*c*(c^2*d^4*(1-n)-3*c*d^2*e*(sqrt(-4*a*c+b^2)*d+4*a*e)*(1-n)-a*e^3*(a*e*(5-17*n)-sqrt(-4*a*c+b^2)*d*(1+3*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))/(a*e^2-b*d*e+c*d^2)^3/n+c*(b*c*(c^2*d^3*(4*a*e*(3-5*n)-sqrt(-4*a*c+b^2)*d*(1-n))+2*a*c*d*e^2*(2*a*e*(1-7*n)+3*sqrt(-4*a*c+b^2)*d*(1-n))+a^2*sqrt(-4*a*c+b^2)*e^4*(3-11*n))+b^4*e^2*(e*(a*e*(1-3*n)+sqrt(-4*a*c+b^2)*d*(1-n))+3*c*d^2*(1-n))-b^5*d*e^3*(1-n)-4*a*c^2*(a*e^3*(sqrt(-4*a*c+b^2)*d*(1-5*n)-a*e*(1-4*n))+c^2*d^4*(1-2*n)+c*d^2*e*(sqrt(-4*a*c+b^2)*d*(1-n)-6*a*e*n))-b^3*e*(a*sqrt(-4*a*c+b^2)*e^3*(1-3*n)+3*c^2*d^3*(1-n)+c*d*e*(3*sqrt(-4*a*c+b^2)*d*(1-n)-a*e*(3+n)))+b^2*c*(c^2*d^4*(1-n)+3*c*d^2*e*(sqrt(-4*a*c+b^2)*d-4*a*e)*(1-n)-a*e^3*(a*e*(5-17*n)+sqrt(-4*a*c+b^2)*d*(1+3*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))/(a*e^2-b*d*e+c*d^2)^3/n-e^4*(c*d^2*(1-5*n)+e*(a*e*(1-n)-b*(-3*d*n+d)))*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d^2/(a*e^2-b*d*e+c*d^2)^3/n,1],
[(d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^3,x,6,1/2*x*(b^2-2*a*c+b*c*x^n)*(d+e*x^n)^3/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))^2-1/2*b*e^3*x^(1+2*n)/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))-1/2*x*(4*a^2*c*d*(c*d^2*(1-4*n)-3*a*e^2*(1-2*n))+b^4*d^3*(1-2*n)-3*a*b^3*d^2*e*(1-n)+6*a^2*b*e*(c*d^2*(2-5*n)-a*e^2*n)-a*b^2*d*(5*c*d^2*(1-3*n)-3*a*e^2*(1+n))-(a*b^2*e*(3*c*d^2-a*e^2*(1-4*n))-4*a^2*c*e*(3*c*d^2*(1-3*n)-a*e^2*(1-n))+2*a*b*c*d*(c*d^2*(2-7*n)-3*a*e^2*n)-b^3*(c*d^3*(1-2*n)+3*a*d*e^2*n))*x^n)/a^2/(-4*a*c+b^2)^2/n^2/(a+b*x^n+c*x^(2*n))-1/2*((1-n)*(a*b^2*e*(3*c*d^2-a*e^2*(1-2*n))-b^3*c*d^3*(1-2*n)+2*a*b*c*d*(c*d^2*(2-7*n)-9*a*e^2*n)-4*a^2*c*e*(3*c*d^2*(1-3*n)-a*e^2*(1+n)))+(8*a^2*c^2*d*(3*a*e^2-c*d^2*(1-4*n))*(1-2*n)+a*b^3*e*(3*c*d^2+a*e^2*(1-2*n))*(1-n)-b^4*c*d^3*(2*n^2-3*n+1)-4*a^2*b*c*e*(3*c*d^2*(-3*n^2-n+1)+a*e^2*(-n^2-3*n+1))+6*a*b^2*c*d*(c*d^2*(3*n^2-4*n+1)-a*e^2*(3*n^2-2*n+1)))/sqrt(-4*a*c+b^2))*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-sqrt(-4*a*c+b^2))/n^2-1/2*((1-n)*(a*b^2*e*(3*c*d^2-a*e^2*(1-2*n))-b^3*c*d^3*(1-2*n)+2*a*b*c*d*(c*d^2*(2-7*n)-9*a*e^2*n)-4*a^2*c*e*(3*c*d^2*(1-3*n)-a*e^2*(1+n)))-(8*a^2*c^2*d*(3*a*e^2-c*d^2*(1-4*n))*(1-2*n)+a*b^3*e*(3*c*d^2+a*e^2*(1-2*n))*(1-n)-b^4*c*d^3*(2*n^2-3*n+1)-4*a^2*b*c*e*(3*c*d^2*(-3*n^2-n+1)+a*e^2*(-n^2-3*n+1))+6*a*b^2*c*d*(c*d^2*(3*n^2-4*n+1)-a*e^2*(3*n^2-2*n+1)))/sqrt(-4*a*c+b^2))*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+sqrt(-4*a*c+b^2))/n^2,1],
[(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x,5,1/2*x*(b^2-2*a*c+b*c*x^n)*(d+e*x^n)^2/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))^2-1/2*x*(4*a^2*c*(c*d^2*(1-4*n)-a*e^2*(1-2*n))+4*a^2*b*c*d*e*(2-5*n)+b^4*d^2*(1-2*n)-2*a*b^3*d*e*(1-n)-a*b^2*(5*c*d^2*(1-3*n)-a*e^2*(1+n))-(2*a*b^2*c*d*e-8*a^2*c^2*d*e*(1-3*n)+2*a*b*c*(c*d^2*(2-7*n)-a*e^2*n)-b^3*(c*d^2*(1-2*n)+a*e^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^3*d*(2*a*e-sqrt(-4*a*c+b^2)*d*(1-2*n))*(1-n)-b^4*d^2*(2*n^2-3*n+1)-8*a^2*c*(c*d^2*(8*n^2-6*n+1)-e*(a*e*(1-2*n)-sqrt(-4*a*c+b^2)*d*(3*n^2-4*n+1)))+2*a*b^2*(3*c*d^2*(3*n^2-4*n+1)+e*(sqrt(-4*a*c+b^2)*d*(1-n)-a*e*(3*n^2-2*n+1)))-2*a*b*(3*a*sqrt(-4*a*c+b^2)*e^2*(1-n)*n+c*d*(4*a*e*(-3*n^2-n+1)-sqrt(-4*a*c+b^2)*d*(7*n^2-9*n+2))))*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^3*d*(2*a*e+sqrt(-4*a*c+b^2)*d*(1-2*n))*(1-n)-b^4*d^2*(2*n^2-3*n+1)-8*a^2*c*(c*d^2*(8*n^2-6*n+1)-e*(a*e*(1-2*n)+sqrt(-4*a*c+b^2)*d*(3*n^2-4*n+1)))+2*a*b^2*(3*c*d^2*(3*n^2-4*n+1)-e*(sqrt(-4*a*c+b^2)*d*(1-n)+a*e*(3*n^2-2*n+1)))+2*a*b*(3*a*sqrt(-4*a*c+b^2)*e^2*(1-n)*n-c*d*(4*a*e*(-3*n^2-n+1)+sqrt(-4*a*c+b^2)*d*(7*n^2-9*n+2))))*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],
[(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x,5,1/2*x*(b^2*d-2*a*c*d-a*b*e+c*(-2*a*e+b*d)*x^n)/a/(-4*a*c+b^2)/n/(a+b*x^n+c*x^(2*n))^2+1/2*x*((-2*a*c+b^2)*(a*b*e+2*a*c*d*(1-4*n)-b^2*d*(1-2*n))+a*b*c*(-2*a*e+b*d)*(1-3*n)+c*(a*b^2*e+2*a*b*c*d*(2-7*n)-4*a^2*c*e*(1-3*n)-b^3*d*(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*(a*b^2*(sqrt(-4*a*c+b^2)*e+6*c*d*(1-3*n))*(1-n)+b^3*(a*e-sqrt(-4*a*c+b^2)*d*(1-2*n))*(1-n)-b^4*d*(2*n^2-3*n+1)-2*a*b*c*(2*a*e*(-3*n^2-n+1)-sqrt(-4*a*c+b^2)*d*(7*n^2-9*n+2))-4*a^2*c*(sqrt(-4*a*c+b^2)*e*(3*n^2-4*n+1)+2*c*d*(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*(a*b^2*(sqrt(-4*a*c+b^2)*e-6*c*d*(1-3*n))*(1-n)-b^3*(a*e+sqrt(-4*a*c+b^2)*d*(1-2*n))*(1-n)+b^4*d*(2*n^2-3*n+1)+2*a*b*c*(2*a*e*(-3*n^2-n+1)+sqrt(-4*a*c+b^2)*d*(7*n^2-9*n+2))-4*a^2*c*(sqrt(-4*a*c+b^2)*e*(3*n^2-4*n+1)-2*c*d*(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],
[1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x,11,1/2*x*(c*(-2*a*c+b^2)*d-b*(-3*a*c+b^2)*e+c*(2*a*c*e-b^2*e+b*c*d)*x^n)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/n/(a+b*x^n+c*x^(2*n))^2-1/2*x*(a*b^3*c*e*(c*d^2*(11-30*n)+a*e^2*(6-29*n))-2*a^2*b*c^2*e*(a*e^2*(4-23*n)+c*d^2*(6-19*n))+4*a^2*c^3*d*(a*e^2*(1-8*n)+c*d^2*(1-4*n))-b^4*c*d*(a*e^2*(5-11*n)-c*d^2*(1-2*n))-b^5*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))+b^6*d*e^2*(1-2*n)-a*b^2*c^2*d*(5*c*d^2*(1-3*n)-a*e^2*(3+5*n))+c*(a*b^2*c*e*(c*d^2*(9-28*n)+a*e^2*(5-26*n))-4*a^2*c^2*e*(a*e^2*(1-7*n)+c*d^2*(1-3*n))-b^3*c*d*(2*a*e^2*(2-5*n)-c*d^2*(1-2*n))-b^4*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))+b^5*d*e^2*(1-2*n)-2*a*b*c^2*d*(c*d^2*(2-7*n)-5*a*e^2*n))*x^n)/a^2/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^2/n^2/(a+b*x^n+c*x^(2*n))-c*e^4*(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*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))/(a*e^2-b*d*e+c*d^2)^3+1/2*c*((1-n)*(a*b^2*c*e*(c*d^2*(9-28*n)+a*e^2*(5-26*n))-4*a^2*c^2*e*(a*e^2*(1-7*n)+c*d^2*(1-3*n))-b^3*c*d*(2*a*e^2*(2-5*n)-c*d^2*(1-2*n))-b^4*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))+b^5*d*e^2*(1-2*n)-2*a*b*c^2*d*(c*d^2*(2-7*n)-5*a*e^2*n))+(8*a^2*c^3*d*(a*e^2*(1-8*n)+c*d^2*(1-4*n))*(1-2*n)-b^4*c*d*(2*a*e^2*(3-7*n)-c*d^2*(1-2*n))*(1-n)-b^5*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))*(1-n)+b^6*d*e^2*(2*n^2-3*n+1)-2*a*b^2*c^2*d*(3*c*d^2*(3*n^2-4*n+1)-a*e^2*(5*n^2-6*n+3))-4*a^2*b*c^2*e*(a*e^2*(25*n^2-21*n+3)+c*d^2*(29*n^2-25*n+5))+a*b^3*c*e*(c*d^2*(36*n^2-49*n+13)+a*e^2*(38*n^2-41*n+7)))/sqrt(-4*a*c+b^2))*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-sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)^2/n^2-c*e^4*(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*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))/(a*e^2-b*d*e+c*d^2)^3+1/2*c*((1-n)*(a*b^2*c*e*(c*d^2*(9-28*n)+a*e^2*(5-26*n))-4*a^2*c^2*e*(a*e^2*(1-7*n)+c*d^2*(1-3*n))-b^3*c*d*(2*a*e^2*(2-5*n)-c*d^2*(1-2*n))-b^4*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))+b^5*d*e^2*(1-2*n)-2*a*b*c^2*d*(c*d^2*(2-7*n)-5*a*e^2*n))-(8*a^2*c^3*d*(a*e^2*(1-8*n)+c*d^2*(1-4*n))*(1-2*n)-b^4*c*d*(2*a*e^2*(3-7*n)-c*d^2*(1-2*n))*(1-n)-b^5*e*(a*e^2*(1-4*n)+2*c*d^2*(1-2*n))*(1-n)+b^6*d*e^2*(2*n^2-3*n+1)-2*a*b^2*c^2*d*(3*c*d^2*(3*n^2-4*n+1)-a*e^2*(5*n^2-6*n+3))-4*a^2*b*c^2*e*(a*e^2*(25*n^2-21*n+3)+c*d^2*(29*n^2-25*n+5))+a*b^3*c*e*(c*d^2*(36*n^2-49*n+13)+a*e^2*(38*n^2-41*n+7)))/sqrt(-4*a*c+b^2))*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+sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)^2/n^2+e^6*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/d/(a*e^2-b*d*e+c*d^2)^3,1],
[1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x,12,1/2*x*(c*(-2*a*c+b^2)*d-b*(-3*a*c+b^2)*e+c*(2*a*c*e-b^2*e+b*c*d)*x^n)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/n/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2+1/2*x*(4*a^2*b*c^3*d*e*(a*e^2*(3-28*n)+c*d^2*(5-16*n))-a*b^2*c^2*(a^2*e^4*(13-85*n)+2*a*c*d^2*e^2*(12-23*n)-5*c^2*d^4*(1-3*n))-b^5*c*d*e*(a*e^2*(5-6*n)-3*c*d^2*(1-2*n))-b^6*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))+b^4*c*(a^2*e^4*(7-40*n)+6*a*c*d^2*e^2*(3-7*n)-c^2*d^4*(1-2*n))+b^7*d*e^3*(1-2*n)+4*a^2*c^3*(a^2*e^4*(1-8*n)-c^2*d^4*(1-4*n)+8*a*c*d^2*e^2*n)-a*b^3*c^2*d*e*(c*d^2*(17-46*n)-a*e^2*(1+42*n))-c*(2*a*b*c^2*(a^2*e^4*(4-27*n)-c^2*d^4*(2-7*n)+2*a*c*d^2*e^2*(3-4*n))-8*a^2*c^3*d*e*(a*e^2*(1-9*n)+c*d^2*(1-3*n))+2*a*b^2*c^2*d*e*(a*e^2*(1-23*n)+7*c*d^2*(1-3*n))+b^5*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))-b^3*c*(a*c*d^2*e^2*(15-37*n)+a^2*e^4*(6-35*n)-c^2*d^4*(1-2*n))-b^4*c*d*e*(3*c*d^2*(1-2*n)-4*a*e^2*(1-n))-b^6*d*e^3*(1-2*n))*x^n)/a^2/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^3/n^2/(a+b*x^n+c*x^(2*n))+1/2*c*e*(b^4*e^3*(e*(a*e*(1-7*n)-sqrt(-4*a*c+b^2)*d*(1-n))+c*d^2*(5-7*n))-b^3*e^2*(c*d*e*(a*e*(1-23*n)-3*sqrt(-4*a*c+b^2)*d*(1-n))-a*sqrt(-4*a*c+b^2)*e^3*(1-7*n)+3*c^2*d^3*(3-5*n))+b*c*(2*a*c*d*e^3*(a*e*(5-48*n)-3*sqrt(-4*a*c+b^2)*d*(1-n))+c^2*d^3*e*(4*a*e*(4-7*n)+sqrt(-4*a*c+b^2)*d*(1-n))-3*a^2*sqrt(-4*a*c+b^2)*e^5*(1-9*n)-2*c^3*d^5*(1-2*n))-b^5*d*e^4*(1-n)-4*a*c^2*e*(c*d^2*e*(2*a*e*(1-12*n)-sqrt(-4*a*c+b^2)*d*(1-n))+2*c^2*d^4*(1-2*n)-a*e^3*(sqrt(-4*a*c+b^2)*d*(1-13*n)-4*a*e*n))+b^2*c*e*(c^2*d^4*(7-13*n)-c*d^2*e*(3*sqrt(-4*a*c+b^2)*d*(1-n)+2*a*e*(4+5*n))-a*e^3*(a*e*(3-31*n)-sqrt(-4*a*c+b^2)*d*(1+11*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))/(a*e^2-b*d*e+c*d^2)^4/n+1/2*c*((2*a*b*c^2*(a^2*e^4*(4-27*n)-c^2*d^4*(2-7*n)+2*a*c*d^2*e^2*(3-4*n))-8*a^2*c^3*d*e*(a*e^2*(1-9*n)+c*d^2*(1-3*n))+2*a*b^2*c^2*d*e*(a*e^2*(1-23*n)+7*c*d^2*(1-3*n))+b^5*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))-b^3*c*(a*c*d^2*e^2*(15-37*n)+a^2*e^4*(6-35*n)-c^2*d^4*(1-2*n))-b^4*c*d*e*(3*c*d^2*(1-2*n)-4*a*e^2*(1-n))-b^6*d*e^3*(1-2*n))*(1-n)+(b^6*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))*(1-n)-8*a^2*c^3*(1-2*n)*(a^2*e^4*(1-8*n)-c^2*d^4*(1-4*n)+8*a*c*d^2*e^2*n)-b^7*d*e^3*(2*n^2-3*n+1)-b^5*c*d*e*(3*c*d^2*(2*n^2-3*n+1)-2*a*e^2*(6*n^2-8*n+3))-2*a*b^3*c^2*d*e*(a*e^2*(-15*n^2+14*n+2)-c*d^2*(29*n^2-38*n+10))-8*a^2*b*c^3*d*e*(c*d^2*(23*n^2-20*n+4)+a*e^2*(29*n^2-22*n+2))+b^4*c*(c^2*d^4*(2*n^2-3*n+1)-a^2*e^4*(55*n^2-55*n+8)-a*c*d^2*e^2*(57*n^2-74*n+21))-2*a*b^2*c^2*(3*c^2*d^4*(3*n^2-4*n+1)-2*a*c*d^2*e^2*(34*n^2-34*n+9)-a^2*e^4*(89*n^2-72*n+9)))/sqrt(-4*a*c+b^2))*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-sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)^3/n^2+1/2*c*e*(b^4*e^3*(e*(a*e*(1-7*n)+sqrt(-4*a*c+b^2)*d*(1-n))+c*d^2*(5-7*n))-b^3*e^2*(c*d*e*(a*e*(1-23*n)+3*sqrt(-4*a*c+b^2)*d*(1-n))+a*sqrt(-4*a*c+b^2)*e^3*(1-7*n)+3*c^2*d^3*(3-5*n))+b*c*(c^2*d^3*e*(4*a*e*(4-7*n)-sqrt(-4*a*c+b^2)*d*(1-n))+2*a*c*d*e^3*(a*e*(5-48*n)+3*sqrt(-4*a*c+b^2)*d*(1-n))+3*a^2*sqrt(-4*a*c+b^2)*e^5*(1-9*n)-2*c^3*d^5*(1-2*n))-b^5*d*e^4*(1-n)-4*a*c^2*e*(c*d^2*e*(2*a*e*(1-12*n)+sqrt(-4*a*c+b^2)*d*(1-n))+2*c^2*d^4*(1-2*n)+a*e^3*(sqrt(-4*a*c+b^2)*d*(1-13*n)+4*a*e*n))+b^2*c*e*(c^2*d^4*(7-13*n)+c*d^2*e*(3*sqrt(-4*a*c+b^2)*d*(1-n)-2*a*e*(4+5*n))-a*e^3*(a*e*(3-31*n)+sqrt(-4*a*c+b^2)*d*(1+11*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))/(a*e^2-b*d*e+c*d^2)^4/n+1/2*c*((2*a*b*c^2*(a^2*e^4*(4-27*n)-c^2*d^4*(2-7*n)+2*a*c*d^2*e^2*(3-4*n))-8*a^2*c^3*d*e*(a*e^2*(1-9*n)+c*d^2*(1-3*n))+2*a*b^2*c^2*d*e*(a*e^2*(1-23*n)+7*c*d^2*(1-3*n))+b^5*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))-b^3*c*(a*c*d^2*e^2*(15-37*n)+a^2*e^4*(6-35*n)-c^2*d^4*(1-2*n))-b^4*c*d*e*(3*c*d^2*(1-2*n)-4*a*e^2*(1-n))-b^6*d*e^3*(1-2*n))*(1-n)-(b^6*e^2*(a*e^2*(1-5*n)+3*c*d^2*(1-2*n))*(1-n)-8*a^2*c^3*(1-2*n)*(a^2*e^4*(1-8*n)-c^2*d^4*(1-4*n)+8*a*c*d^2*e^2*n)-b^7*d*e^3*(2*n^2-3*n+1)-b^5*c*d*e*(3*c*d^2*(2*n^2-3*n+1)-2*a*e^2*(6*n^2-8*n+3))-2*a*b^3*c^2*d*e*(a*e^2*(-15*n^2+14*n+2)-c*d^2*(29*n^2-38*n+10))-8*a^2*b*c^3*d*e*(c*d^2*(23*n^2-20*n+4)+a*e^2*(29*n^2-22*n+2))+b^4*c*(c^2*d^4*(2*n^2-3*n+1)-a^2*e^4*(55*n^2-55*n+8)-a*c*d^2*e^2*(57*n^2-74*n+21))-2*a*b^2*c^2*(3*c^2*d^4*(3*n^2-4*n+1)-2*a*c*d^2*e^2*(34*n^2-34*n+9)-a^2*e^4*(89*n^2-72*n+9)))/sqrt(-4*a*c+b^2))*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+sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)^3/n^2+1/2*e^3*(4*a*c^2*d*e*(a*e^2*(1-13*n)+c*d^2*(1-n))+b^3*e^2*(a*e^2*(1-7*n)+3*c*d^2*(1-n))-b*c*(3*a^2*e^4*(1-9*n)-c^2*d^4*(1-n)+6*a*c*d^2*e^2*(1-n))-b^4*d*e^3*(1-n)-b^2*c*d*e*(3*c*d^2*(1-n)-a*e^2*(1+11*n)))*x*hypergeom([1, 1/n],[1+1/n],-e*x^n/d)/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^4/n+1/2*e^3*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-2*a*e^2+c*d^2)-b^2*(-2*a*e^3+2*c*d^2*e))*x*hypergeom([2, 1/n],[1+1/n],-e*x^n/d)/a/(-4*a*c+b^2)/d^2/(a*e^2-b*d*e+c*d^2)^3,1],
[(d+e*x^n)^(3/2)/(a+b*x^n+c*x^(2*n)),x,7,-2*c*d*x*sqrt(d+e*x^n)*AppellF1(1/n,-3/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^n/d)-2*c*d*x*sqrt(d+e*x^n)*AppellF1(1/n,-3/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^n/d),1],
[sqrt(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x,7,-2*c*x*sqrt(d+e*x^n)*AppellF1(1/n,-1/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^n/d)-2*c*x*sqrt(d+e*x^n)*AppellF1(1/n,-1/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(1+e*x^n/d),1],
[1/sqrt(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x,7,-2*c*x*sqrt(1+e*x^n/d)*AppellF1(1/n,1/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/sqrt(d+e*x^n)-2*c*x*sqrt(1+e*x^n/d)*AppellF1(1/n,1/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/sqrt(d+e*x^n),1],
[1/(d+e*x^n)^(3/2)/(a+b*x^n+c*x^(2*n)),x,7,-2*c*x*sqrt(1+e*x^n/d)*AppellF1(1/n,3/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b-sqrt(-4*a*c+b^2)))/(b^2-4*a*c-b*sqrt(-4*a*c+b^2))/d/sqrt(d+e*x^n)-2*c*x*sqrt(1+e*x^n/d)*AppellF1(1/n,3/2,1,1+1/n,-e*x^n/d,-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(b^2-4*a*c+b*sqrt(-4*a*c+b^2))/d/sqrt(d+e*x^n),1],
[(d+e*x^n)*sqrt(a+b*x^n+c*x^(2*n)),x,7,e*x^(1+n)*sqrt(a+b*x^n+c*x^(2*n))*AppellF1(1+1/n,-1/2,-1/2,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(1+n)/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)))+d*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],
[(d+e*x^n)*(a+b*x^n+c*x^(2*n))^(3/2),x,7,a*e*x^(1+n)*sqrt(a+b*x^n+c*x^(2*n))*AppellF1(1+1/n,-3/2,-3/2,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(1+n)/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)))+a*d*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],
[(d+e*x^n)/sqrt(a+b*x^n+c*x^(2*n)),x,7,e*x^(1+n)*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+1/n,1/2,1/2,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(1+n)/sqrt(a+b*x^n+c*x^(2*n))+d*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],
[(d+e*x^n)/(a+b*x^n+c*x^(2*n))^(3/2),x,7,e*x^(1+n)*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+1/n,3/2,3/2,2+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/(1+n)/sqrt(a+b*x^n+c*x^(2*n))+d*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],
[(d+e*x^n)/(a+b*x^n+c*x^(2*n))^(5/2),x,7,e*x^(1+n)*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+1/n,5/2,5/2,2+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/(1+n)/sqrt(a+b*x^n+c*x^(2*n))+d*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],
[(d+e*x^n)^q*(a+b*x^n+c*x^(2*n))^p,x,0,Defer(Int)((d+e*x^n)^q*(a+b*x^n+c*x^(2*n))^p,x),0],
[(d+e*x^n)^3*(a+b*x^n+c*x^(2*n))^p,x,10,-e^2*(b*e*(1+n*(2+p))-3*c*d*(1+n*(3+2*p)))*x*(a+b*x^n+c*x^(2*n))^(p+1)/c^2/(1+2*n*(p+1))/(1+n*(3+2*p))+e^3*x^(1+n)*(a+b*x^n+c*x^(2*n))^(p+1)/c/(2*n*p+3*n+1)+e*(b*e*(n*p+n+1)*(b*e*(1+n*(2+p))-3*c*d*(1+n*(3+2*p)))-c*(1+2*n*(p+1))*(a*e^2*(1+n)-3*c*d^2*(1+n*(3+2*p))))*x^(1+n)*(a+b*x^n+c*x^(2*n))^p*AppellF1(1+1/n,-p,-p,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/c^2/(1+n)/(1+2*n*(p+1))/(1+n*(3+2*p))/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p)+(c^2*d^3*(1+2*n*(p+1))*(1+n*(3+2*p))+a*e^2*(b*e*(1+n*(2+p))-3*c*d*(1+n*(3+2*p))))*x*(a+b*x^n+c*x^(2*n))^p*AppellF1(1/n,-p,-p,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)))/c^2/(1+2*n*(p+1))/(1+n*(3+2*p))/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p),1],
[(d+e*x^n)^2*(a+b*x^n+c*x^(2*n))^p,x,8,e^2*x*(a+b*x^n+c*x^(2*n))^(p+1)/c/(2*n*p+2*n+1)-e*(b*e*(n*p+n+1)-2*c*d*(1+2*n*(p+1)))*x^(1+n)*(a+b*x^n+c*x^(2*n))^p*AppellF1(1+1/n,-p,-p,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/c/(1+n)/(1+2*n*(p+1))/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p)-(a*e^2-c*d^2*(1+2*n*(p+1)))*x*(a+b*x^n+c*x^(2*n))^p*AppellF1(1/n,-p,-p,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)))/c/(1+2*n*(p+1))/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p),1],
[(d+e*x^n)*(a+b*x^n+c*x^(2*n))^p,x,7,e*x^(1+n)*(a+b*x^n+c*x^(2*n))^p*AppellF1(1+1/n,-p,-p,2+1/n,-2*c*x^n/(b-sqrt(-4*a*c+b^2)),-2*c*x^n/(b+sqrt(-4*a*c+b^2)))/(1+n)/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p)+d*x*(a+b*x^n+c*x^(2*n))^p*AppellF1(1/n,-p,-p,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)))/((1+2*c*x^n/(b-sqrt(-4*a*c+b^2)))^p)/((1+2*c*x^n/(b+sqrt(-4*a*c+b^2)))^p),1],
[(a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x,0,Defer(Int)((a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x),0],
[(a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x,0,Defer(Int)((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x),0]]: