lst:=[[sin(x)^5/(a+b*cos(x)+c*cos(x)^2),x,7,(b^4+2*c^2*(a+c)^2-2*b^2*c*(2*a+c))*arctanh((b+2*c*cos(x))/sqrt(-4*a*c+b^2))/c^4/sqrt(-4*a*c+b^2)-(b^2-c*(a+2*c))*cos(x)/c^3+1/2*b*cos(x)^2/c^2-1/3*cos(x)^3/c+1/2*b*(b^2-2*c*(a+c))*ln(a+b*cos(x)+c*cos(x)^2)/c^4,1],
[sin(x)^3/(a+b*cos(x)+c*cos(x)^2),x,7,-(b^2-2*c*(a+c))*arctanh((b+2*c*cos(x))/sqrt(-4*a*c+b^2))/c^2/sqrt(-4*a*c+b^2)+cos(x)/c-1/2*b*ln(a+b*cos(x)+c*cos(x)^2)/c^2,1],
[sin(x)/(a+b*cos(x)+c*cos(x)^2),x,3,2*arctanh((b+2*c*cos(x))/sqrt(-4*a*c+b^2))/sqrt(-4*a*c+b^2),1],
[csc(x)/(a+b*cos(x)+c*cos(x)^2),x,9,-(b^2-2*c*(a+c))*arctanh((b+2*c*cos(x))/sqrt(-4*a*c+b^2))/(a-b+c)/(a+b+c)/sqrt(-4*a*c+b^2)+ln(1-cos(x))/(2*a+2*b+2*c)-ln(1+cos(x))/(2*a-2*b+2*c)+1/2*b*ln(a+b*cos(x)+c*cos(x)^2)/(a-b+c)/(a+b+c),1],
[csc(x)^3/(a+b*cos(x)+c*cos(x)^2),x,7,(b^4+2*c^2*(a+c)^2-2*b^2*c*(2*a+c))*arctanh((b+2*c*cos(x))/sqrt(-4*a*c+b^2))/(a-b+c)^2/(a+b+c)^2/sqrt(-4*a*c+b^2)-1/4/(a+b+c)/(1-cos(x))+1/4/(a-b+c)/(1+cos(x))+1/4*(a+2*b+3*c)*ln(1-cos(x))/(a+b+c)^2-1/4*(a-2*b+3*c)*ln(1+cos(x))/(a-b+c)^2-1/2*b*(b^2-2*c*(a+c))*ln(a+b*cos(x)+c*cos(x)^2)/(a-b+c)^2/(a+b+c)^2,1],
[sin(x)^4/(a+b*cos(x)+c*cos(x)^2),x,10,1/2*x/c+(b^2-c*(a+2*c))*x/c^3+2*(b^2*(b^2-2*c*(a+c))-b*sqrt(-4*a*c+b^2)*(b^2-2*c*(a+c))-2*c*(a*b^2-c*(a+c)^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/c^3/sqrt(-4*a*c+b^2)/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-2*(b^4+2*c^2*(a+c)^2-2*b^2*c*(2*a+c)+b^3*sqrt(-4*a*c+b^2)-2*b*c*(a+c)*sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/c^3/sqrt(-4*a*c+b^2)/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))-b*sin(x)/c^2+1/2*cos(x)*sin(x)/c,1],
[sin(x)^2/(a+b*cos(x)+c*cos(x)^2),x,7,-x/c+2*(b-(b^2-2*c*(a+c))/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/c/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))+2*(b+(b^2-2*c*(a+c))/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/c/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2)),1],
[csc(x)^2/(a+b*cos(x)+c*cos(x)^2),x,9,-2*b*c*(1+(b^2-2*c*(a+c))/b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/(a-b+c)/(a+b+c)/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-2*b*c*(1-(b^2-2*c*(a+c))/b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/(a-b+c)/(a+b+c)/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))-1/2*sin(x)/(a+b+c)/(1-cos(x))+1/2*sin(x)/(a-b+c)/(1+cos(x)),1],
[sin(x)/(-2+cos(x)+cos(x)^2),x,4,-1/3*ln(1-cos(x))+1/3*ln(2+cos(x)),1],
[sin(x)/(4-5*cos(x)+cos(x)^2),x,4,1/3*ln(1-cos(x))-1/3*ln(4-cos(x)),1],
[sin(x)/(3-2*cos(x)+cos(x)^2),x,3,arctan((1-cos(x))/sqrt(2))/sqrt(2),1],
[sin(x)/(13-4*cos(x)+cos(x)^2)^2,x,4,-1/54*arctan(-2/3+1/3*cos(x))+(2-cos(x))/(234-72*cos(x)+18*cos(x)^2),1],
[cos(x)^4/(a+b*cos(x)+c*cos(x)^2),x,10,1/2*x/c+(-a*c+b^2)*x/c^3-2*(b^3-2*a*b*c-(2*a^2*c^2-4*a*b^2*c+b^4)/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/c^3/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-2*(b^3-2*a*b*c+(2*a^2*c^2-4*a*b^2*c+b^4)/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/c^3/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))-b*sin(x)/c^2+1/2*cos(x)*sin(x)/c,1],
[cos(x)^3/(a+b*cos(x)+c*cos(x)^2),x,8,-b*x/c^2+2*(b^2-a*c-b^3/sqrt(-4*a*c+b^2)+3*a*b*c/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/c^2/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))+2*(b^2-a*c+b^3/sqrt(-4*a*c+b^2)-3*a*b*c/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/c^2/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))+sin(x)/c,1],
[cos(x)^2/(a+b*cos(x)+c*cos(x)^2),x,7,x/c-2*(b-(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/c/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-2*(b+(-2*a*c+b^2)/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/c/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2)),1],
[cos(x)/(a+b*cos(x)+c*cos(x)^2),x,6,2*(1-b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))+2*(1+b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2)),1],
[1/(a+b*cos(x)+c*cos(x)^2),x,5,4*c*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/sqrt(-4*a*c+b^2)/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-4*c*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/sqrt(-4*a*c+b^2)/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2)),1],
[sec(x)/(a+b*cos(x)+c*cos(x)^2),x,8,-2*c*(1+b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/a/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))-2*c*(1-b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/a/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))+arctanh(sin(x))/a,1],
[sec(x)^2/(a+b*cos(x)+c*cos(x)^2),x,10,2*b*c*(1+(-2*a*c+b^2)/b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/a^2/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))+2*b*c*(1-(-2*a*c+b^2)/b/sqrt(-4*a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/a^2/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))-b*arctanh(sin(x))/a^2+tan(x)/a,1],
[sec(x)^3/(a+b*cos(x)+c*cos(x)^2),x,12,-2*c*(b^3-3*a*b*c+sqrt(-4*a*c+b^2)*(-a*c+b^2))*arctan(sqrt(b-2*c-sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c-sqrt(-4*a*c+b^2)))/a^3/sqrt(-4*a*c+b^2)/sqrt(b-2*c-sqrt(-4*a*c+b^2))/sqrt(b+2*c-sqrt(-4*a*c+b^2))+2*c*(b^3-3*a*b*c-sqrt(-4*a*c+b^2)*(-a*c+b^2))*arctan(sqrt(b-2*c+sqrt(-4*a*c+b^2))*tan(1/2*x)/sqrt(b+2*c+sqrt(-4*a*c+b^2)))/a^3/sqrt(-4*a*c+b^2)/sqrt(b-2*c+sqrt(-4*a*c+b^2))/sqrt(b+2*c+sqrt(-4*a*c+b^2))+1/2*arctanh(sin(x))/a+(-a*c+b^2)*arctanh(sin(x))/a^3-b*tan(x)/a^2+1/2*sec(x)*tan(x)/a,1]]: