lst:=[[sin(x)^6/(a-a*cos(x)^2),x,4,3/8*x/a-3/8*cos(x)*sin(x)/a-1/4*cos(x)*sin(x)^3/a,1],
[sin(x)^5/(a-a*cos(x)^2),x,3,-cos(x)/a+1/3*cos(x)^3/a,1],
[sin(x)^4/(a-a*cos(x)^2),x,3,1/2*x/a-1/2*cos(x)*sin(x)/a,1],
[sin(x)^3/(a-a*cos(x)^2),x,2,-cos(x)/a,1],
[sin(x)^2/(a-a*cos(x)^2),x,2,x/a,1],
[sin(x)/(a-a*cos(x)^2),x,2,-arctanh(cos(x))/a,1],
[csc(x)/(a-a*cos(x)^2),x,3,-1/2*arctanh(cos(x))/a-1/2*cot(x)*csc(x)/a,1],
[csc(x)^2/(a-a*cos(x)^2),x,3,-cot(x)/a-1/3*cot(x)^3/a,1],
[csc(x)^3/(a-a*cos(x)^2),x,4,-3/8*arctanh(cos(x))/a-3/8*cot(x)*csc(x)/a-1/4*cot(x)*csc(x)^3/a,1],
[sin(x)^7/(a+b*cos(x)^2),x,4,-(a+b)^3*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/b^(7/2)+(a^2+3*a*b+3*b^2)*cos(x)/b^3-1/3*(a+3*b)*cos(x)^3/b^2+1/5*cos(x)^5/b,1],
[sin(x)^5/(a+b*cos(x)^2),x,4,-(a+b)^2*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/b^(5/2)+(a+2*b)*cos(x)/b^2-1/3*cos(x)^3/b,1],
[sin(x)^3/(a+b*cos(x)^2),x,3,-(a+b)*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/b^(3/2)+cos(x)/b,1],
[sin(x)/(a+b*cos(x)^2),x,2,-arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/sqrt(b),1],
[csc(x)/(a+b*cos(x)^2),x,4,-sqrt(b)*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/(a+b)-arctanh(cos(x))/(a+b),1],
[csc(x)^3/(a+b*cos(x)^2),x,5,-b^(3/2)*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/(a+b)^2-1/2*(a+3*b)*arctanh(cos(x))/(a+b)^2-cot(x)*csc(x)/(2*a+2*b),1],
[csc(x)^5/(a+b*cos(x)^2),x,6,-b^(5/2)*arctan(sqrt(b)*cos(x)/sqrt(a))/sqrt(a)/(a+b)^3-1/8*(3*a^2+10*a*b+15*b^2)*arctanh(cos(x))/(a+b)^3-1/8*(3*a+7*b)*cot(x)*csc(x)/(a+b)^2-cot(x)*csc(x)^3/(4*a+4*b),1],
[sin(x)^6/(a+b*cos(x)^2),x,6,-1/8*(8*a^2+20*a*b+15*b^2)*x/b^3-(a+b)^(5/2)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/b^3+1/8*(4*a+7*b)*cos(x)*sin(x)/b^2+1/4*cos(x)*sin(x)^3/b,1],
[sin(x)^4/(a+b*cos(x)^2),x,5,-1/2*(2*a+3*b)*x/b^2-(a+b)^(3/2)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/b^2+1/2*cos(x)*sin(x)/b,1],
[sin(x)^2/(a+b*cos(x)^2),x,4,-x/b-sqrt(a+b)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/b,1],
[1/(a+b*cos(x)^2),x,2,-arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/sqrt(a+b),1],
[csc(x)^2/(a+b*cos(x)^2),x,3,-b*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/(a+b)^(3/2)-cot(x)/(a+b),1],
[csc(x)^4/(a+b*cos(x)^2),x,4,-b^2*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/(a+b)^(5/2)-(a+2*b)*cot(x)/(a+b)^2-cot(x)^3/(3*a+3*b),1],
[csc(x)^6/(a+b*cos(x)^2),x,4,-b^3*arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/(a+b)^(7/2)-(a^2+3*a*b+3*b^2)*cot(x)/(a+b)^3-1/3*(2*a+3*b)*cot(x)^3/(a+b)^2-cot(x)^5/(5*a+5*b),1],
[sin(x)/(4-3*cos(x)^3),x,7,-1/12*arctan((1+6^(1/3)*cos(x))/sqrt(3))*2^(2/3)*3^(1/6)+1/36*ln(6^(2/3)-3*cos(x))*6^(2/3)-1/72*ln(2*6^(1/3)+6^(2/3)*cos(x)+3*cos(x)^2)*6^(2/3),1],
[cos(x)^7/(a+b*cos(x)^2),x,4,-a^3*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/b^(7/2)/sqrt(a+b)+(a^2-a*b+b^2)*sin(x)/b^3+1/3*(a-2*b)*sin(x)^3/b^2+1/5*sin(x)^5/b,1],
[cos(x)^5/(a+b*cos(x)^2),x,4,a^2*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/b^(5/2)/sqrt(a+b)-(a-b)*sin(x)/b^2-1/3*sin(x)^3/b,1],
[cos(x)^3/(a+b*cos(x)^2),x,3,-a*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/b^(3/2)/sqrt(a+b)+sin(x)/b,1],
[cos(x)/(a+b*cos(x)^2),x,2,arctanh(sqrt(b)*sin(x)/sqrt(a+b))/sqrt(b)/sqrt(a+b),1],
[sec(x)/(a+b*cos(x)^2),x,4,arctanh(sin(x))/a-sqrt(b)*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/a/sqrt(a+b),1],
[sec(x)^3/(a+b*cos(x)^2),x,5,1/2*(a-2*b)*arctanh(sin(x))/a^2+b^(3/2)*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/a^2/sqrt(a+b)+1/2*sec(x)*tan(x)/a,1],
[sec(x)^5/(a+b*cos(x)^2),x,6,1/8*(3*a^2-4*a*b+8*b^2)*arctanh(sin(x))/a^3-b^(5/2)*arctanh(sqrt(b)*sin(x)/sqrt(a+b))/a^3/sqrt(a+b)+1/8*(3*a-4*b)*sec(x)*tan(x)/a^2+1/4*sec(x)^3*tan(x)/a,1],
[cos(x)^6/(a+b*cos(x)^2),x,6,1/8*(8*a^2-4*a*b+3*b^2)*x/b^3+a^(5/2)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/b^3/sqrt(a+b)-1/8*(4*a-3*b)*cos(x)*sin(x)/b^2+1/4*cos(x)^3*sin(x)/b,1],
[cos(x)^4/(a+b*cos(x)^2),x,5,-1/2*(2*a-b)*x/b^2-a^(3/2)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/b^2/sqrt(a+b)+1/2*cos(x)*sin(x)/b,1],
[cos(x)^2/(a+b*cos(x)^2),x,3,x/b+sqrt(a)*arctan(sqrt(a+b)*cot(x)/sqrt(a))/b/sqrt(a+b),1],
[1/(a+b*cos(x)^2),x,2,-arctan(sqrt(a+b)*cot(x)/sqrt(a))/sqrt(a)/sqrt(a+b),1],
[sec(x)^2/(a+b*cos(x)^2),x,3,b*arctan(sqrt(a+b)*cot(x)/sqrt(a))/a^(3/2)/sqrt(a+b)+tan(x)/a,1],
[sec(x)^4/(a+b*cos(x)^2),x,4,-b^2*arctan(sqrt(a+b)*cot(x)/sqrt(a))/a^(5/2)/sqrt(a+b)+(a-b)*tan(x)/a^2+1/3*tan(x)^3/a,1],
[sec(x)^6/(a+b*cos(x)^2),x,4,b^3*arctan(sqrt(a+b)*cot(x)/sqrt(a))/a^(7/2)/sqrt(a+b)+(a^2-a*b+b^2)*tan(x)/a^3+1/3*(2*a-b)*tan(x)^3/a^2+1/5*tan(x)^5/a,1],
[cos(x)/sqrt(1+cos(x)^2),x,2,arcsin(sin(x)/sqrt(2)),1],
[cos(5+3*x)/sqrt(3+cos(5+3*x)^2),x,2,1/3*arcsin(1/2*sin(5+3*x)),1],
[cos(x)/sqrt(4-cos(x)^2),x,2,arcsinh(sin(x)/sqrt(3)),1],
[tan(x)/(1+cos(x)^2),x,4,-ln(cos(x))+1/2*ln(1+cos(x)^2),1],
[sqrt(a+b*cos(x)^2)*tan(x),x,4,sqrt(a)*arctanh(sqrt(a+b*cos(x)^2)/sqrt(a))-sqrt(a+b*cos(x)^2),1],
[sqrt(1-cos(x)^2)*tan(x),x,5,arctanh(sqrt(sin(x)^2))-sqrt(sin(x)^2),1],
[tan(x)/sqrt(a+b*cos(x)^2),x,3,arctanh(sqrt(a+b*cos(x)^2)/sqrt(a))/sqrt(a),1],
[tan(x)/sqrt(1+cos(x)^2),x,3,arctanh(sqrt(1+cos(x)^2)),1],
[tan(x)/sqrt(1-cos(x)^2),x,4,arctanh(sqrt(sin(x)^2)),1],
[tan(x)^3/(a+b*cos(x)^3),x,12,-b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*cos(x))/sqrt(3)/a^(1/3))/sqrt(3)/a^(5/3)+ln(cos(x))/a+1/3*b^(2/3)*ln(a^(1/3)+b^(1/3)*cos(x))/a^(5/3)-1/6*b^(2/3)*ln(a^(2/3)-a^(1/3)*b^(1/3)*cos(x)+b^(2/3)*cos(x)^2)/a^(5/3)-1/3*ln(a+b*cos(x)^3)/a+1/2*sec(x)^2/a,1],
[sqrt(a+b*cos(x)^3)*tan(x),x,5,2/3*sqrt(a)*arctanh(sqrt(a+b*cos(x)^3)/sqrt(a))-2/3*sqrt(a+b*cos(x)^3),1],
[tan(x)/sqrt(a+b*cos(x)^3),x,4,2/3*arctanh(sqrt(a+b*cos(x)^3)/sqrt(a))/sqrt(a),1],
[sqrt(a+b*cos(x)^4)*tan(x),x,5,1/2*sqrt(a)*arctanh(sqrt(a+b*cos(x)^4)/sqrt(a))-1/2*sqrt(a+b*cos(x)^4),1],
[tan(x)/sqrt(a+b*cos(x)^4),x,4,1/2*arctanh(sqrt(a+b*cos(x)^4)/sqrt(a))/sqrt(a),1],
[sqrt(a+b*cos(x)^n)*tan(x),x,5,2*sqrt(a)*arctanh(sqrt(a+b*cos(x)^n)/sqrt(a))/n-2*sqrt(a+b*cos(x)^n)/n,1],
[tan(x)/sqrt(a+b*cos(x)^n),x,4,2*arctanh(sqrt(a+b*cos(x)^n)/sqrt(a))/sqrt(a)/n,1]]: