lst:=[[(A+B*sin(x))/(a+b*cos(x)),x,6,2*A*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)-B*ln(a+b*cos(x))/b,1],
[(A+B*sin(x))/(1+cos(x)),x,5,-B*ln(1+cos(x))+A*sin(x)/(1+cos(x)),1],
[(A+B*sin(x))/(1-cos(x)),x,5,B*ln(1-cos(x))-A*sin(x)/(1-cos(x)),1],
[(b+c+sin(x))/(a+b*cos(x)),x,6,2*(b+c)*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)-ln(a+b*cos(x))/b,1],
[(b+c+sin(x))/(a-b*cos(x)),x,6,2*(b+c)*arctan(sqrt(a+b)*tan(1/2*x)/sqrt(a-b))/sqrt(a-b)/sqrt(a+b)+ln(a-b*cos(x))/b,1],
[(A+B*tan(x))/(a+b*cos(x)),x,8,2*A*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)-B*ln(cos(x))/a+B*ln(a+b*cos(x))/a,1],
[(A+B*cot(x))/(a+b*cos(x)),x,7,2*A*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)+B*ln(1-cos(x))/(2*a+2*b)+B*ln(1+cos(x))/(2*a-2*b)-a*B*ln(a+b*cos(x))/(a^2-b^2),1],
[(A+B*csc(x))/(a+b*cos(x)),x,8,2*A*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)+B*ln(1-cos(x))/(2*a+2*b)-B*ln(1+cos(x))/(2*a-2*b)+b*B*ln(a+b*cos(x))/(a^2-b^2),1],
[(c+d*sec(f*x+e))^4/(a+b*cos(f*x+e)),x,12,2*(a*c-b*d)^4*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/a^4/sqrt(a-b)/sqrt(a+b)/f+1/2*d^3*(4*a*c-b*d)*arctanh(sin(f*x+e))/a^2/f+d*(2*a*c-b*d)*(2*a^2*c^2-2*a*b*c*d+b^2*d^2)*arctanh(sin(f*x+e))/a^4/f+d^4*tan(f*x+e)/a/f+d^2*(6*a^2*c^2-4*a*b*c*d+b^2*d^2)*tan(f*x+e)/a^3/f+1/2*d^3*(4*a*c-b*d)*sec(f*x+e)*tan(f*x+e)/a^2/f+1/3*d^4*tan(f*x+e)^3/a/f,1],
[(c+d*sec(f*x+e))^3/(a+b*cos(f*x+e)),x,10,2*(a*c-b*d)^3*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/a^3/sqrt(a-b)/sqrt(a+b)/f+1/2*d^3*arctanh(sin(f*x+e))/a/f+d*(3*a^2*c^2-3*a*b*c*d+b^2*d^2)*arctanh(sin(f*x+e))/a^3/f+d^2*(3*a*c-b*d)*tan(f*x+e)/a^2/f+1/2*d^3*sec(f*x+e)*tan(f*x+e)/a/f,1],
[(c+d*sec(f*x+e))^2/(a+b*cos(f*x+e)),x,8,2*(a*c-b*d)^2*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/a^2/sqrt(a-b)/sqrt(a+b)/f+d*(2*a*c-b*d)*arctanh(sin(f*x+e))/a^2/f+d^2*tan(f*x+e)/a/f,1],
[(c+d*sec(f*x+e))/(a+b*cos(f*x+e)),x,5,2*(a*c-b*d)*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/a/sqrt(a-b)/sqrt(a+b)/f+d*arctanh(sin(f*x+e))/a/f,1],
[1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e)),x,6,2*a*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)/(a*c-b*d)/f-2*d*arctanh(sqrt(c-d)*tan(1/2*f*x+1/2*e)/sqrt(c+d))/sqrt(c-d)/sqrt(c+d)/(a*c-b*d)/f,1],
[1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^2,x,7,2*a^2*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)/(a*c-b*d)^2/f-2*d*(2*a*c^2-a*d^2-b*c*d)*arctanh(sqrt(c-d)*tan(1/2*f*x+1/2*e)/sqrt(c+d))/(c-d)^(3/2)/(c+d)^(3/2)/(a*c-b*d)^2/f+d^2*sin(f*x+e)/(a*c-b*d)/(c^2-d^2)/f/(d+c*cos(f*x+e)),1],
[1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^3,x,16,2*a^3*arctan(sqrt(a-b)*tan(1/2*f*x+1/2*e)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)/(a*c-b*d)^3/f-2*d^3*(3*a*c-2*b*d)*arctanh(sqrt(c-d)*tan(1/2*f*x+1/2*e)/sqrt(c+d))/c^2/(c-d)^(3/2)/(c+d)^(3/2)/(a*c-b*d)^2/f-d^3*(c^2+2*d^2)*arctanh(sqrt(c-d)*tan(1/2*f*x+1/2*e)/sqrt(c+d))/c^2/(c-d)^(5/2)/(c+d)^(5/2)/(a*c-b*d)/f-2*d*(3*a^2*c^2-3*a*b*c*d+b^2*d^2)*arctanh(sqrt(c-d)*tan(1/2*f*x+1/2*e)/sqrt(c+d))/c^2/sqrt(c-d)/sqrt(c+d)/(a*c-b*d)^3/f-1/2*d^3*sin(f*x+e)/c/(a*c-b*d)/(c^2-d^2)/f/(d+c*cos(f*x+e))^2+3/2*d^4*sin(f*x+e)/c/(a*c-b*d)/(c^2-d^2)^2/f/(d+c*cos(f*x+e))+d^2*(3*a*c-2*b*d)*sin(f*x+e)/c/(a*c-b*d)^2/(c^2-d^2)/f/(d+c*cos(f*x+e)),1],
[sqrt(c+d*sec(f*x+e))/(a+b*cos(f*x+e)),x,4,2*sqrt(c+d)*cot(f*x+e)*InverseJacobiAM(arcsin(sqrt(c+d*sec(f*x+e))/sqrt(c+d)),sqrt((c+d)/(c-d)))*sqrt(d*(1-sec(f*x+e))/(c+d))*sqrt(-d*(1+sec(f*x+e))/(c-d))/a/f+2*(a*c-b*d)*EllipticPi(sin(arcsin(sqrt(1-sec(f*x+e))/sqrt(2))),2*a/(a+b),sqrt(2*d/(c+d)))*sqrt((c+d*sec(f*x+e))/(c+d))*tan(f*x+e)/a/(a+b)/f/sqrt(c+d*sec(f*x+e))/sqrt(-tan(f*x+e)^2),1],
[1/(a+b*cos(f*x+e))/sqrt(c+d*sec(f*x+e)),x,2,2*EllipticPi(sin(arcsin(sqrt(1-sec(f*x+e))/sqrt(2))),2*a/(a+b),sqrt(2*d/(c+d)))*sqrt((c+d*sec(f*x+e))/(c+d))*tan(f*x+e)/(a+b)/f/sqrt(c+d*sec(f*x+e))/sqrt(-tan(f*x+e)^2),1],
[(A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d)),x,6,B*x/b+2*(A*b-B*a)*arctan(sqrt(a-b)*tan(1/2*e*x+1/2*d)/sqrt(a+b))/sqrt(a-b)/b/sqrt(a+b)/e-C*ln(a+b*cos(e*x+d))/b/e,1],
[(A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^2,x,7,2*(A*a-B*b)*arctan(sqrt(a-b)*tan(1/2*e*x+1/2*d)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/e+C/b/e/(a+b*cos(e*x+d))-(A*b-B*a)*sin(e*x+d)/(a^2-b^2)/e/(a+b*cos(e*x+d)),1],
[(A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^3,x,8,(2*A*a^2+A*b^2-3*B*a*b)*arctan(sqrt(a-b)*tan(1/2*e*x+1/2*d)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/e+1/2*C/b/e/(a+b*cos(e*x+d))^2-1/2*(A*b-B*a)*sin(e*x+d)/(a^2-b^2)/e/(a+b*cos(e*x+d))^2-1/2*(3*A*a*b-B*a^2-2*B*b^2)*sin(e*x+d)/(a^2-b^2)^2/e/(a+b*cos(e*x+d)),1],
[(A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^4,x,9,(2*A*a^3+3*A*a*b^2-4*B*a^2*b-B*b^3)*arctan(sqrt(a-b)*tan(1/2*e*x+1/2*d)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/e+1/3*C/b/e/(a+b*cos(e*x+d))^3-1/3*(A*b-B*a)*sin(e*x+d)/(a^2-b^2)/e/(a+b*cos(e*x+d))^3-1/6*(5*A*a*b-2*B*a^2-3*B*b^2)*sin(e*x+d)/(a^2-b^2)^2/e/(a+b*cos(e*x+d))^2-1/6*(11*A*a^2*b+4*A*b^3-2*B*a^3-13*B*a*b^2)*sin(e*x+d)/(a^2-b^2)^3/e/(a+b*cos(e*x+d)),1]]: