lst:=[[tan(e*x+d)^3*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,16,-sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-1/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(c)/e+1/16*b*(-4*a*c+b^2)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(5/2)/e+sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))+b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/e-1/8*b*(b+2*c*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^2/e+1/3*(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2)/c/e,1],
[tan(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,10,sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b*sqrt(a^2-2*a*c+b^2+c^2)-(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-1/8*(b^2-4*(a-2*c)*c)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(3/2)/e+sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b*sqrt(a^2-2*a*c+b^2+c^2)+(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e+1/4*(b+2*c*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/e,1],
[tan(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,10,sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e+1/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(c)/e-sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))+b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e+sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/e,1],
[sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,9,-sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b*sqrt(a^2-2*a*c+b^2+c^2)-(b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e+sqrt(c)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/e-sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b*sqrt(a^2-2*a*c+b^2+c^2)+(b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e,1],
[cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,18,-sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-sqrt(a)*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/e+sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))+b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e,1],
[cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,17,sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b*sqrt(a^2-2*a*c+b^2+c^2)-(b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-1/2*b*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(a)/e+sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b*sqrt(a^2-2*a*c+b^2+c^2)+(b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/e,1],
[cot(e*x+d)^3*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,21,sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))*arctan((b^2+(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c+sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c+sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e+sqrt(a)*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/e+1/8*(-4*a*c+b^2)*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(3/2)/e-sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))*arctanh((b^2+(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))+b*sqrt(a^2-2*a*c+b^2+c^2)*tan(e*x+d))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/sqrt(a^2+b^2+c*(c-sqrt(a^2-2*a*c+b^2+c^2))-a*(2*c-sqrt(a^2-2*a*c+b^2+c^2)))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(1/4)/e-1/4*cot(e*x+d)^2*(2*a+b*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a/e,1],
[tan(e*x+d)^5/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,15,sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c-sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c+sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+1/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(3/2)/e-1/16*b*(-12*a*c+5*b^2)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(7/2)/e-sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/e+1/3*tan(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/e+1/24*(15*b^2-16*a*c-10*b*c*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^3/e,1],
[tan(e*x+d)^4/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,14,sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(c)/e+1/8*(-4*a*c+3*b^2)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(5/2)/e-3/4*b*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^2/e+1/2*tan(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/e,1],
[tan(e*x+d)^3/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,11,-sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c-sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c+sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-1/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(3/2)/e+sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/e,1],
[tan(e*x+d)^2/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,9,-sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(c)/e,1],
[tan(e*x+d)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,6,sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c-sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c+sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e,1],
[1/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,6,sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e,1],
[cot(e*x+d)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,10,-arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(a)/e-sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c-sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c+sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e,1],
[cot(e*x+d)^2/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,11,-sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctan((b-(a-c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+1/2*b*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(3/2)/e-cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a/e,1],
[cot(e*x+d)^3/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),x,14,arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(a)/e-1/8*(-4*a*c+3*b^2)*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(5/2)/e+sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c-sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e-sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))*arctanh((a-c+sqrt(a^2-2*a*c+b^2+c^2)+b*tan(e*x+d))/sqrt(2)/sqrt(a-c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/sqrt(a^2-2*a*c+b^2+c^2)/e+3/4*b*cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a^2/e-1/2*cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a/e,1],
[tan(e*x+d)^7/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,20,3/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(5/2)/e-5/16*b*(-12*a*c+7*b^2)*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(9/2)/e-sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+2*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)-2*tan(e*x+d)^2*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*tan(e*x+d)^4*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)-2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+1/3*(-16*a*c+7*b^2)*tan(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^2/(-4*a*c+b^2)/e-2*b*tan(e*x+d)^3*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c/(-4*a*c+b^2)/e-(3*b^2-8*a*c-2*b*c*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^2/(-4*a*c+b^2)/e+1/24*(105*b^4-460*a*b^2*c+256*a^2*c^2-2*b*c*(-116*a*c+35*b^2)*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^4/(-4*a*c+b^2)/e,1],
[tan(e*x+d)^5/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,14,-3/2*b*arctanh(1/2*(b+2*c*tan(e*x+d))/sqrt(c)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/c^(5/2)/e+sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-2*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*tan(e*x+d)^2*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+(3*b^2-8*a*c-2*b*c*tan(e*x+d))*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/c^2/(-4*a*c+b^2)/e,1],
[tan(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,10,-sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+2*(2*a+b*tan(e*x+d))/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)-2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),1],
[tan(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,7,-sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctan((b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))+(b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctan((b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))+(b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-2*(a*b*(a+c)+c*(2*a^2-2*a*c+b^2)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),1],
[tan(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,7,sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),1],
[cot(e*x+d)/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,13,-arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(3/2)/e-sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+2*(b^2-2*a*c+b*c*tan(e*x+d))/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)-2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2),1],
[cot(e*x+d)^2/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,13,-sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctan((b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))+(b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctan((b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))+(b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2)))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e+3/2*b*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(5/2)/e+2*cot(e*x+d)*(b^2-2*a*c+b*c*tan(e*x+d))/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*(b*(b^2-(3*a-c)*c)+c*(b^2-2*(a-c)*c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)-(-8*a*c+3*b^2)*cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a^2/(-4*a*c+b^2)/e,1],
[cot(e*x+d)^3/(a+b*tan(e*x+d)+c*tan(e*x+d)^2)^(3/2),x,18,arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(3/2)/e-3/8*(-4*a*c+5*b^2)*arctanh(1/2*(2*a+b*tan(e*x+d))/sqrt(a)/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/a^(7/2)/e+sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c+sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c-sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2+(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))*arctanh((b^2-(a-c)*(a-c-sqrt(a^2-2*a*c+b^2+c^2))-b*(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))*tan(e*x+d))/sqrt(2)/sqrt(2*a-2*c+sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a^2-b^2-2*a*c+c^2-(a-c)*sqrt(a^2-2*a*c+b^2+c^2))/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2))/sqrt(2)/(a^2-2*a*c+b^2+c^2)^(3/2)/e-2*(b^2-2*a*c+b*c*tan(e*x+d))/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*cot(e*x+d)^2*(b^2-2*a*c+b*c*tan(e*x+d))/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+2*(a*(b^2-2*(a-c)*c)+b*c*(a+c)*tan(e*x+d))/(b^2+(a-c)^2)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)+1/4*b*(-52*a*c+15*b^2)*cot(e*x+d)*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a^3/(-4*a*c+b^2)/e-1/2*(-12*a*c+5*b^2)*cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)+c*tan(e*x+d)^2)/a^2/(-4*a*c+b^2)/e,1],
[tan(e*x+d)^5*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,9,-1/2*sqrt(a-b+c)*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/32*(b^3+2*b^2*c-4*b*(a-2*c)*c-8*c^2*(a+2*c))*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/c^(5/2)/e-1/16*((b-2*c)*(b+4*c)+2*c*(b+2*c)*tan(e*x+d)^2)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/c^2/e+1/6*(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2)/c/e,1],
[tan(e*x+d)^3*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,1/2*sqrt(a-b+c)*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e-1/16*(b^2+4*b*c-4*c*(a+2*c))*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/c^(3/2)/e+1/8*(b-4*c+2*c*tan(e*x+d)^2)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/c/e,1],
[tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*sqrt(a-b+c)*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/4*(b-2*c)*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(c)/e+1/2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e,1],
[cot(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,10,-1/2*sqrt(a)*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/2*sqrt(a-b+c)*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/2*sqrt(c)*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e,1],
[cot(e*x+d)^3*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,22,1/2*sqrt(a)*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e-1/4*b*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a)/e-1/2*sqrt(a-b+c)*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e-1/4*b*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(c)/e+1/4*(b-2*c)*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(c)/e+1/2*sqrt(c)*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e-1/2*cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e,1],
[tan(e*x+d)^2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*sqrt(a-b+c)*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/3*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e+1/3*(b-3*c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/sqrt(c)/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)-1/3*a^(1/4)*(b-3*c)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/c^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/6*a^(1/4)*(sqrt(a)*(b-2*c)+2*a*sqrt(c)-2*(2*b-3*c)*sqrt(c))*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/(sqrt(a)-sqrt(c))/c^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/4*(sqrt(a)+sqrt(c))*(a-b+c)*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,7,1/2*sqrt(a-b+c)*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+sqrt(c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)-a^(1/4)*c^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/2*a^(1/4)*(b-2*c)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/4*(sqrt(a)+sqrt(c))*(a-b+c)*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*sqrt(a-b+c)*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e-cot(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e+sqrt(c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)-a^(1/4)*c^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/2*(2*a-b)*c^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/4*(sqrt(a)+sqrt(c))*(a-b+c)*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[cot(e*x+d)^4*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,9,1/2*sqrt(a-b+c)*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/e+1/3*(3*a-b)*cot(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a/e-1/3*cot(e*x+d)^3*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/e-1/3*(3*a-b)*sqrt(c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)+1/3*(3*a-b)*c^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/6*(6*a^(3/2)-sqrt(a)*(4*b-2*c)-2*a*sqrt(c)+b*sqrt(c))*c^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(3/4)/(sqrt(a)-sqrt(c))/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/4*(sqrt(a)+sqrt(c))*(a-b+c)*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)^5/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e-1/4*(b+2*c)*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/c^(3/2)/e+1/2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/c/e,1],
[tan(e*x+d)^3/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,7,1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e+1/2*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(c)/e,1],
[tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,4,-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e,1],
[cot(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a)/e+1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e,1],
[cot(e*x+d)^3/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,11,1/2*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a)/e+1/4*b*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/a^(3/2)/e-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e-1/2*cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a/e,1],
[tan(e*x+d)^4/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,7,1/2*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e+tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/sqrt(c)/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)-a^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/c^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/2*a^(1/4)*(sqrt(a)-2*sqrt(c))*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/(sqrt(a)-sqrt(c))/c^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/4*(sqrt(a)+sqrt(c))*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)^2/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,4,-1/2*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e+1/2*a^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/4*(sqrt(a)+sqrt(c))*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[1/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,4,1/2*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e-1/2*c^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/4*(sqrt(a)+sqrt(c))*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[cot(e*x+d)^2/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),x,8,-1/2*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/sqrt(a-b+c)/e-cot(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a/e+sqrt(c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)-c^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(3/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+1/2*(2*sqrt(a)-sqrt(c))*c^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(3/4)/(sqrt(a)-sqrt(c))/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/4*(sqrt(a)+sqrt(c))*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)^7/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,8,1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e+1/2*arctanh(1/2*(b+2*c*tan(e*x+d)^2)/sqrt(c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/c^(3/2)/e+(a*(b^2-a*(b+2*c))+(b^3+2*a^2*c-a*b*(b+3*c))*tan(e*x+d)^2)/c/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)^5/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,6,-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e+(a*(2*a-b)+((a-b)*b+2*a*c)*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,6,1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e-(a*(b-2*c)+(2*a-b)*c*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[tan(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,6,-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e+(b^2-2*a*c-b*c+(b-2*c)*c*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[cot(e*x+d)/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,12,-1/2*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/a^(3/2)/e+1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e+(b^2-2*a*c+b*c*tan(e*x+d)^2)/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-(b^2-2*a*c-b*c+(b-2*c)*c*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1],
[cot(e*x+d)^3/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,16,1/2*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/a^(3/2)/e+3/4*b*arctanh(1/2*(2*a+b*tan(e*x+d)^2)/sqrt(a)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/a^(5/2)/e-1/2*arctanh(1/2*(2*a-b+(b-2*c)*tan(e*x+d)^2)/sqrt(a-b+c)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e-(b^2-2*a*c+b*c*tan(e*x+d)^2)/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+cot(e*x+d)^2*(b^2-2*a*c+b*c*tan(e*x+d)^2)/a/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)+(b^2-2*a*c-b*c+(b-2*c)*c*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/2*(-8*a*c+3*b^2)*cot(e*x+d)^2*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/a^2/(-4*a*c+b^2)/e,1],
[tan(e*x+d)^2/(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)^(3/2),x,8,-1/2*arctan(sqrt(a-b+c)*tan(e*x+d)/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4))/(a-b+c)^(3/2)/e+tan(e*x+d)*(b^2-2*a*c-b*c+(b-2*c)*c*tan(e*x+d)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-(b-2*c)*sqrt(c)*tan(e*x+d)*sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(a-b+c)/(-4*a*c+b^2)/e/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)+a^(1/4)*(b-2*c)*c^(1/4)*EllipticE(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/(a-b+c)/(-4*a*c+b^2)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/2*c^(1/4)*InverseJacobiAM(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)*b-2*a*sqrt(c)-b*sqrt(c)+2*sqrt(a)*c)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)-1/4*(sqrt(a)+sqrt(c))*EllipticPi(sin(2*arctan(c^(1/4)*tan(e*x+d)/a^(1/4))),-1/4*(sqrt(a)-sqrt(c))^2/sqrt(a)/sqrt(c),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))*(sqrt(a)+sqrt(c)*tan(e*x+d)^2)*sqrt((a+b*tan(e*x+d)^2+c*tan(e*x+d)^4)/(sqrt(a)+sqrt(c)*tan(e*x+d)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(c))/c^(1/4)/(a-b+c)/e/sqrt(a+b*tan(e*x+d)^2+c*tan(e*x+d)^4),1]]: