1,1,186,182,1.578000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x)","-\frac{11 a^{2} c^{5} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{24 f}+\frac{29 a^{2} c^{5} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}-\frac{19 c^{5} a^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}-\frac{11 a^{2} c^{5} \tan \left(f x +e \right)}{15 f}-\frac{13 c^{5} a^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+a^{2} c^{5} x +\frac{a^{2} c^{5} e}{f}+\frac{3 c^{5} a^{2} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}-\frac{c^{5} a^{2} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"-11/24*a^2*c^5*sec(f*x+e)^3*tan(f*x+e)/f+29/16*a^2*c^5*sec(f*x+e)*tan(f*x+e)/f-19/16/f*c^5*a^2*ln(sec(f*x+e)+tan(f*x+e))-11/15*a^2*c^5*tan(f*x+e)/f-13/15/f*c^5*a^2*tan(f*x+e)*sec(f*x+e)^2+a^2*c^5*x+1/f*a^2*c^5*e+3/5/f*c^5*a^2*tan(f*x+e)*sec(f*x+e)^4-1/6/f*c^5*a^2*tan(f*x+e)*sec(f*x+e)^5","A"
2,1,161,130,1.406000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,x)","-\frac{17 a^{2} c^{4} \tan \left(f x +e \right)}{15 f}-\frac{a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{5 a^{2} c^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{4 f}-\frac{3 a^{2} c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+a^{2} c^{4} x +\frac{a^{2} c^{4} e}{f}-\frac{a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{2 f}+\frac{a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"-17/15*a^2*c^4*tan(f*x+e)/f-1/15/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^2+5/4*a^2*c^4*sec(f*x+e)*tan(f*x+e)/f-3/4/f*a^2*c^4*ln(sec(f*x+e)+tan(f*x+e))+a^2*c^4*x+1/f*a^2*c^4*e-1/2/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^3+1/5/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^4","A"
3,1,136,91,1.219000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,x)","\frac{5 c^{3} a^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}-\frac{3 c^{3} a^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}-\frac{4 a^{2} c^{3} \tan \left(f x +e \right)}{3 f}+a^{2} c^{3} x +\frac{a^{2} c^{3} e}{f}+\frac{c^{3} a^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}-\frac{c^{3} a^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"5/8/f*c^3*a^2*sec(f*x+e)*tan(f*x+e)-3/8/f*c^3*a^2*ln(sec(f*x+e)+tan(f*x+e))-4/3*a^2*c^3*tan(f*x+e)/f+a^2*c^3*x+1/f*a^2*c^3*e+1/3/f*c^3*a^2*tan(f*x+e)*sec(f*x+e)^2-1/4/f*c^3*a^2*tan(f*x+e)*sec(f*x+e)^3","A"
4,1,58,45,0.820000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x)","\frac{-2 a^{2} c^{2} \tan \left(f x +e \right)+\left(f x +e \right) a^{2} c^{2}-a^{2} c^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-2*a^2*c^2*tan(f*x+e)+(f*x+e)*a^2*c^2-a^2*c^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
5,1,76,51,0.856000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x)","\frac{a^{2} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+a^{2} c x +\frac{a^{2} c e}{f}-\frac{a^{2} c \tan \left(f x +e \right)}{f}-\frac{a^{2} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}"," ",0,"1/2/f*a^2*c*ln(sec(f*x+e)+tan(f*x+e))+a^2*c*x+1/f*a^2*c*e-a^2*c*tan(f*x+e)/f-1/2/f*a^2*c*sec(f*x+e)*tan(f*x+e)","A"
6,1,90,56,0.777000," ","int((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x)","\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f c}-\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f c}+\frac{4 a^{2}}{f c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f c}"," ",0,"1/f*a^2/c*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a^2/c*ln(tan(1/2*e+1/2*f*x)+1)+4/f*a^2/c/tan(1/2*e+1/2*f*x)+2/f*a^2/c*arctan(tan(1/2*e+1/2*f*x))","A"
7,1,67,67,0.862000," ","int((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x)","-\frac{2 a^{2}}{3 f \,c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{2}}{f \,c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{2}}"," ",0,"-2/3/f*a^2/c^2/tan(1/2*e+1/2*f*x)^3+2/f*a^2/c^2/tan(1/2*e+1/2*f*x)+2/f*a^2/c^2*arctan(tan(1/2*e+1/2*f*x))","A"
8,1,89,96,1.046000," ","int((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x)","\frac{a^{2}}{5 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{2 a^{2}}{3 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{2}}{f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{3}}"," ",0,"1/5/f*a^2/c^3/tan(1/2*e+1/2*f*x)^5-2/3/f*a^2/c^3/tan(1/2*e+1/2*f*x)^3+2/f*a^2/c^3/tan(1/2*e+1/2*f*x)+2/f*a^2/c^3*arctan(tan(1/2*e+1/2*f*x))","A"
9,1,111,125,0.904000," ","int((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x)","-\frac{a^{2}}{14 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{3 a^{2}}{10 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{2 a^{2}}{3 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{2}}{f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{4}}"," ",0,"-1/14/f*a^2/c^4/tan(1/2*e+1/2*f*x)^7+3/10/f*a^2/c^4/tan(1/2*e+1/2*f*x)^5-2/3/f*a^2/c^4/tan(1/2*e+1/2*f*x)^3+2/f*a^2/c^4/tan(1/2*e+1/2*f*x)+2/f*a^2/c^4*arctan(tan(1/2*e+1/2*f*x))","A"
10,1,133,154,0.845000," ","int((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x)","\frac{a^{2}}{36 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{a^{2}}{7 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{7 a^{2}}{20 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{2 a^{2}}{3 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{2}}{f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{5}}"," ",0,"1/36/f*a^2/c^5/tan(1/2*e+1/2*f*x)^9-1/7/f*a^2/c^5/tan(1/2*e+1/2*f*x)^7+7/20/f*a^2/c^5/tan(1/2*e+1/2*f*x)^5-2/3/f*a^2/c^5/tan(1/2*e+1/2*f*x)^3+2/f*a^2/c^5/tan(1/2*e+1/2*f*x)+2/f*a^2/c^5*arctan(tan(1/2*e+1/2*f*x))","A"
11,1,211,174,1.621000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x)","-\frac{13 c^{5} a^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{12 f}+\frac{11 a^{3} c^{5} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}-\frac{5 c^{5} a^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}-\frac{146 a^{3} c^{5} \tan \left(f x +e \right)}{105 f}+a^{3} c^{5} x +\frac{a^{3} c^{5} e}{f}+\frac{8 c^{5} a^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{35 f}+\frac{32 c^{5} a^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{105 f}+\frac{c^{5} a^{3} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{3 f}-\frac{c^{5} a^{3} \tan \left(f x +e \right) \left(\sec^{6}\left(f x +e \right)\right)}{7 f}"," ",0,"-13/12/f*c^5*a^3*tan(f*x+e)*sec(f*x+e)^3+11/8*a^3*c^5*sec(f*x+e)*tan(f*x+e)/f-5/8/f*c^5*a^3*ln(sec(f*x+e)+tan(f*x+e))-146/105*a^3*c^5*tan(f*x+e)/f+a^3*c^5*x+1/f*a^3*c^5*e+8/35/f*c^5*a^3*tan(f*x+e)*sec(f*x+e)^4+32/105/f*c^5*a^3*tan(f*x+e)*sec(f*x+e)^2+1/3/f*c^5*a^3*tan(f*x+e)*sec(f*x+e)^5-1/7/f*c^5*a^3*tan(f*x+e)*sec(f*x+e)^6","A"
12,1,186,124,1.646000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x)","-\frac{23 a^{3} c^{4} \tan \left(f x +e \right)}{15 f}+\frac{11 c^{4} a^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{11 c^{4} a^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}-\frac{5 c^{4} a^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}+a^{3} c^{4} x +\frac{a^{3} c^{4} e}{f}-\frac{13 c^{4} a^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}-\frac{c^{4} a^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{c^{4} a^{3} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"-23/15*a^3*c^4*tan(f*x+e)/f+11/15/f*c^4*a^3*tan(f*x+e)*sec(f*x+e)^2+11/16/f*c^4*a^3*sec(f*x+e)*tan(f*x+e)-5/16/f*c^4*a^3*ln(sec(f*x+e)+tan(f*x+e))+a^3*c^4*x+1/f*a^3*c^4*e-13/24/f*c^4*a^3*tan(f*x+e)*sec(f*x+e)^3-1/5/f*c^4*a^3*tan(f*x+e)*sec(f*x+e)^4+1/6/f*c^4*a^3*tan(f*x+e)*sec(f*x+e)^5","A"
13,1,93,64,1.056000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x)","\frac{-3 a^{3} c^{3} \tan \left(f x +e \right)+\left(f x +e \right) a^{3} c^{3}-3 a^{3} c^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)+a^{3} c^{3} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-3*a^3*c^3*tan(f*x+e)+(f*x+e)*a^3*c^3-3*a^3*c^3*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)+a^3*c^3*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e))","A"
14,1,136,91,1.254000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x)","-\frac{4 a^{3} c^{2} \tan \left(f x +e \right)}{3 f}+\frac{3 c^{2} a^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+a^{3} c^{2} x +\frac{a^{3} c^{2} e}{f}-\frac{5 c^{2} a^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{c^{2} a^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{c^{2} a^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"-4/3*a^3*c^2*tan(f*x+e)/f+3/8/f*c^2*a^3*ln(sec(f*x+e)+tan(f*x+e))+a^3*c^2*x+1/f*a^3*c^2*e-5/8/f*c^2*a^3*sec(f*x+e)*tan(f*x+e)+1/3/f*c^2*a^3*tan(f*x+e)*sec(f*x+e)^2+1/4/f*c^2*a^3*tan(f*x+e)*sec(f*x+e)^3","A"
15,1,98,75,0.863000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x)","\frac{a^{3} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+a^{3} c x +\frac{a^{3} c e}{f}-\frac{a^{3} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}-\frac{2 a^{3} c \tan \left(f x +e \right)}{3 f}-\frac{a^{3} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"1/f*a^3*c*ln(sec(f*x+e)+tan(f*x+e))+a^3*c*x+1/f*a^3*c*e-a^3*c*sec(f*x+e)*tan(f*x+e)/f-2/3*a^3*c*tan(f*x+e)/f-1/3/f*a^3*c*tan(f*x+e)*sec(f*x+e)^2","A"
16,1,137,78,0.701000," ","int((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x)","\frac{8 a^{3}}{f c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{a^{3}}{f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{4 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f c}+\frac{a^{3}}{f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{4 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f c}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f c}"," ",0,"8/f*a^3/c/tan(1/2*e+1/2*f*x)+1/f*a^3/c/(tan(1/2*e+1/2*f*x)-1)+4/f*a^3/c*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^3/c/(tan(1/2*e+1/2*f*x)+1)-4/f*a^3/c*ln(tan(1/2*e+1/2*f*x)+1)+2/f*a^3/c*arctan(tan(1/2*e+1/2*f*x))","A"
17,1,90,84,0.833000," ","int((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x)","-\frac{4 a^{3}}{3 f \,c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}-\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,c^{2}}+\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,c^{2}}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{2}}"," ",0,"-4/3/f*a^3/c^2/tan(1/2*e+1/2*f*x)^3-1/f*a^3/c^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^3/c^2*ln(tan(1/2*e+1/2*f*x)+1)+2/f*a^3/c^2*arctan(tan(1/2*e+1/2*f*x))","A"
18,1,89,96,0.819000," ","int((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","-\frac{2 a^{3}}{3 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{3}}{5 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{2 a^{3}}{f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{3}}"," ",0,"-2/3/f*a^3/c^3/tan(1/2*e+1/2*f*x)^3+2/5/f*a^3/c^3/tan(1/2*e+1/2*f*x)^5+2/f*a^3/c^3/tan(1/2*e+1/2*f*x)+2/f*a^3/c^3*arctan(tan(1/2*e+1/2*f*x))","A"
19,1,111,125,0.881000," ","int((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x)","-\frac{a^{3}}{7 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{2 a^{3}}{5 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{2 a^{3}}{3 f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{3}}{f \,c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{4}}"," ",0,"-1/7/f*a^3/c^4/tan(1/2*e+1/2*f*x)^7+2/5/f*a^3/c^4/tan(1/2*e+1/2*f*x)^5-2/3/f*a^3/c^4/tan(1/2*e+1/2*f*x)^3+2/f*a^3/c^4/tan(1/2*e+1/2*f*x)+2/f*a^3/c^4*arctan(tan(1/2*e+1/2*f*x))","A"
20,1,133,154,0.893000," ","int((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x)","\frac{a^{3}}{18 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{3 a^{3}}{14 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{2 a^{3}}{5 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{2 a^{3}}{3 f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{3}}{f \,c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{5}}"," ",0,"1/18/f*a^3/c^5/tan(1/2*e+1/2*f*x)^9-3/14/f*a^3/c^5/tan(1/2*e+1/2*f*x)^7+2/5/f*a^3/c^5/tan(1/2*e+1/2*f*x)^5-2/3/f*a^3/c^5/tan(1/2*e+1/2*f*x)^3+2/f*a^3/c^5/tan(1/2*e+1/2*f*x)+2/f*a^3/c^5*arctan(tan(1/2*e+1/2*f*x))","A"
21,1,207,126,0.708000," ","int((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x)","\frac{16 c^{5} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{2}}+\frac{32 c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}-\frac{c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{15 c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{47 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,a^{2}}+\frac{c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{15 c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{47 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,a^{2}}+\frac{2 c^{5} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2}}"," ",0,"16/3/f*c^5/a^2*tan(1/2*e+1/2*f*x)^3+32/f*c^5/a^2*tan(1/2*e+1/2*f*x)-1/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)-1)^2-15/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)-1)+47/2/f*c^5/a^2*ln(tan(1/2*e+1/2*f*x)-1)+1/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)+1)^2-15/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)+1)-47/2/f*c^5/a^2*ln(tan(1/2*e+1/2*f*x)+1)+2/f*c^5/a^2*arctan(tan(1/2*e+1/2*f*x))","A"
22,1,159,98,0.679000," ","int((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x)","\frac{8 c^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{2}}+\frac{8 c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}-\frac{c^{4}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{6 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}-\frac{c^{4}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{6 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{2}}+\frac{2 c^{4} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2}}"," ",0,"8/3/f*c^4/a^2*tan(1/2*e+1/2*f*x)^3+8/f*c^4/a^2*tan(1/2*e+1/2*f*x)-1/f*c^4/a^2/(tan(1/2*e+1/2*f*x)-1)+6/f*c^4/a^2*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c^4/a^2/(tan(1/2*e+1/2*f*x)+1)-6/f*c^4/a^2*ln(tan(1/2*e+1/2*f*x)+1)+2/f*c^4/a^2*arctan(tan(1/2*e+1/2*f*x))","A"
23,1,90,81,0.818000," ","int((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x)","\frac{4 c^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{2}}+\frac{c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}-\frac{c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{2}}+\frac{2 c^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2}}"," ",0,"4/3/f*c^3/a^2*tan(1/2*e+1/2*f*x)^3+1/f*c^3/a^2*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c^3/a^2*ln(tan(1/2*e+1/2*f*x)+1)+2/f*c^3/a^2*arctan(tan(1/2*e+1/2*f*x))","A"
24,1,65,63,0.859000," ","int((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x)","\frac{2 c^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{2}}-\frac{2 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{2 c^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2}}"," ",0,"2/3/f*c^2/a^2*tan(1/2*e+1/2*f*x)^3-2/f*c^2/a^2*tan(1/2*e+1/2*f*x)+2/f*c^2/a^2*arctan(tan(1/2*e+1/2*f*x))","A"
25,1,59,57,0.900000," ","int((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x)","\frac{c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{2}}-\frac{2 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{2 c \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2}}"," ",0,"1/3/f*c/a^2*tan(1/2*e+1/2*f*x)^3-2/f*c/a^2*tan(1/2*e+1/2*f*x)+2/f*c/a^2*arctan(tan(1/2*e+1/2*f*x))","A"
26,1,87,65,0.840000," ","int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x)","\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{12 f \,a^{2} c}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2} c}+\frac{1}{4 f \,a^{2} c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2} c}"," ",0,"1/12/f/a^2/c*tan(1/2*e+1/2*f*x)^3-1/f/a^2/c*tan(1/2*e+1/2*f*x)+1/4/f/a^2/c/tan(1/2*e+1/2*f*x)+2/f/a^2/c*arctan(tan(1/2*e+1/2*f*x))","A"
27,-2,0,44,180.000000," ","int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x)","\int \frac{1}{\left(a +a \sec \left(f x +e \right)\right)^{2} \left(c -c \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x)","F"
28,1,130,92,1.100000," ","int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x)","\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{48 f \,a^{2} c^{3}}-\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{8 f \,a^{2} c^{3}}+\frac{1}{80 f \,a^{2} c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{1}{8 f \,a^{2} c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{f \,a^{2} c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2} c^{3}}"," ",0,"1/48/f/a^2/c^3*tan(1/2*e+1/2*f*x)^3-3/8/f/a^2/c^3*tan(1/2*e+1/2*f*x)+1/80/f/a^2/c^3/tan(1/2*e+1/2*f*x)^5-1/8/f/a^2/c^3/tan(1/2*e+1/2*f*x)^3+1/f/a^2/c^3/tan(1/2*e+1/2*f*x)+2/f/a^2/c^3*arctan(tan(1/2*e+1/2*f*x))","A"
29,1,153,156,0.950000," ","int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x)","\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{96 f \,a^{2} c^{4}}-\frac{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{32 f \,a^{2} c^{4}}-\frac{1}{224 f \,a^{2} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{7}{160 f \,a^{2} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{11}{48 f \,a^{2} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{21}{16 f \,a^{2} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2} c^{4}}"," ",0,"1/96/f/a^2/c^4*tan(1/2*e+1/2*f*x)^3-7/32/f/a^2/c^4*tan(1/2*e+1/2*f*x)-1/224/f/a^2/c^4/tan(1/2*e+1/2*f*x)^7+7/160/f/a^2/c^4/tan(1/2*e+1/2*f*x)^5-11/48/f/a^2/c^4/tan(1/2*e+1/2*f*x)^3+21/16/f/a^2/c^4/tan(1/2*e+1/2*f*x)+2/f/a^2/c^4*arctan(tan(1/2*e+1/2*f*x))","A"
30,1,175,194,0.945000," ","int(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x)","\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{192 f \,a^{2} c^{5}}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{8 f \,a^{2} c^{5}}+\frac{1}{576 f \,a^{2} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{1}{56 f \,a^{2} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{29}{320 f \,a^{2} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{1}{3 f \,a^{2} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{99}{64 f \,a^{2} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{2} c^{5}}"," ",0,"1/192/f/a^2/c^5*tan(1/2*e+1/2*f*x)^3-1/8/f/a^2/c^5*tan(1/2*e+1/2*f*x)+1/576/f/a^2/c^5/tan(1/2*e+1/2*f*x)^9-1/56/f/a^2/c^5/tan(1/2*e+1/2*f*x)^7+29/320/f/a^2/c^5/tan(1/2*e+1/2*f*x)^5-1/3/f/a^2/c^5/tan(1/2*e+1/2*f*x)^3+99/64/f/a^2/c^5/tan(1/2*e+1/2*f*x)+2/f/a^2/c^5*arctan(tan(1/2*e+1/2*f*x))","A"
31,1,179,154,0.641000," ","int((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x)","-\frac{8 c^{5} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5 f \,a^{3}}-\frac{8 c^{5} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{3}}-\frac{16 c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}+\frac{c^{5}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{8 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}+\frac{8 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{3}}+\frac{c^{5}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 c^{5} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3}}"," ",0,"-8/5/f*c^5/a^3*tan(1/2*e+1/2*f*x)^5-8/3/f*c^5/a^3*tan(1/2*e+1/2*f*x)^3-16/f*c^5/a^3*tan(1/2*e+1/2*f*x)+1/f*c^5/a^3/(tan(1/2*e+1/2*f*x)-1)-8/f*c^5/a^3*ln(tan(1/2*e+1/2*f*x)-1)+8/f*c^5/a^3*ln(tan(1/2*e+1/2*f*x)+1)+1/f*c^5/a^3/(tan(1/2*e+1/2*f*x)+1)+2/f*c^5/a^3*arctan(tan(1/2*e+1/2*f*x))","A"
32,1,110,142,0.772000," ","int((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x)","-\frac{4 c^{4} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5 f \,a^{3}}-\frac{4 c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}-\frac{c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}+\frac{c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{3}}+\frac{2 c^{4} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3}}"," ",0,"-4/5/f*c^4/a^3*tan(1/2*e+1/2*f*x)^5-4/f*c^4/a^3*tan(1/2*e+1/2*f*x)-1/f*c^4/a^3*ln(tan(1/2*e+1/2*f*x)-1)+1/f*c^4/a^3*ln(tan(1/2*e+1/2*f*x)+1)+2/f*c^4/a^3*arctan(tan(1/2*e+1/2*f*x))","A"
33,1,87,90,0.794000," ","int((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x)","-\frac{2 c^{3} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5 f \,a^{3}}+\frac{2 c^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{3}}-\frac{2 c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}+\frac{2 c^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3}}"," ",0,"-2/5/f*c^3/a^3*tan(1/2*e+1/2*f*x)^5+2/3/f*c^3/a^3*tan(1/2*e+1/2*f*x)^3-2/f*c^3/a^3*tan(1/2*e+1/2*f*x)+2/f*c^3/a^3*arctan(tan(1/2*e+1/2*f*x))","A"
34,1,87,90,0.768000," ","int((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x)","-\frac{c^{2} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5 f \,a^{3}}+\frac{2 c^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{3}}-\frac{2 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}+\frac{2 c^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3}}"," ",0,"-1/5/f*c^2/a^3*tan(1/2*e+1/2*f*x)^5+2/3/f*c^2/a^3*tan(1/2*e+1/2*f*x)^3-2/f*c^2/a^3*tan(1/2*e+1/2*f*x)+2/f*c^2/a^3*arctan(tan(1/2*e+1/2*f*x))","A"
35,1,79,82,0.752000," ","int((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x)","-\frac{c \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{10 f \,a^{3}}+\frac{c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{2 f \,a^{3}}-\frac{2 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}+\frac{2 c \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3}}"," ",0,"-1/10/f*c/a^3*tan(1/2*e+1/2*f*x)^5+1/2/f*c/a^3*tan(1/2*e+1/2*f*x)^3-2/f*c/a^3*tan(1/2*e+1/2*f*x)+2/f*c/a^3*arctan(tan(1/2*e+1/2*f*x))","A"
36,1,109,118,0.985000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x)","-\frac{\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)}{40 f \,a^{3} c}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{24 f \,a^{3} c}-\frac{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{8 f \,a^{3} c}+\frac{1}{8 f \,a^{3} c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3} c}"," ",0,"-1/40/f/a^3/c*tan(1/2*e+1/2*f*x)^5+5/24/f/a^3/c*tan(1/2*e+1/2*f*x)^3-11/8/f/a^3/c*tan(1/2*e+1/2*f*x)+1/8/f/a^3/c/tan(1/2*e+1/2*f*x)+2/f/a^3/c*arctan(tan(1/2*e+1/2*f*x))","A"
37,1,131,94,1.083000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x)","-\frac{\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)}{80 f \,a^{3} c^{2}}+\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{8 f \,a^{3} c^{2}}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3} c^{2}}-\frac{1}{48 f \,a^{3} c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{3}{8 f \,a^{3} c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3} c^{2}}"," ",0,"-1/80/f/a^3/c^2*tan(1/2*e+1/2*f*x)^5+1/8/f/a^3/c^2*tan(1/2*e+1/2*f*x)^3-1/f/a^3/c^2*tan(1/2*e+1/2*f*x)-1/48/f/a^3/c^2/tan(1/2*e+1/2*f*x)^3+3/8/f/a^3/c^2/tan(1/2*e+1/2*f*x)+2/f/a^3/c^2*arctan(tan(1/2*e+1/2*f*x))","A"
38,-2,0,63,180.000000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","\int \frac{1}{\left(a +a \sec \left(f x +e \right)\right)^{3} \left(c -c \sec \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","F"
39,1,174,121,0.981000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x)","-\frac{\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)}{320 f \,a^{3} c^{4}}+\frac{\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)}{24 f \,a^{3} c^{4}}-\frac{29 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{64 f \,a^{3} c^{4}}-\frac{1}{448 f \,a^{3} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{40 f \,a^{3} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{29}{192 f \,a^{3} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{f \,a^{3} c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3} c^{4}}"," ",0,"-1/320/f/a^3/c^4*tan(1/2*e+1/2*f*x)^5+1/24/f/a^3/c^4*tan(1/2*e+1/2*f*x)^3-29/64/f/a^3/c^4*tan(1/2*e+1/2*f*x)-1/448/f/a^3/c^4/tan(1/2*e+1/2*f*x)^7+1/40/f/a^3/c^4/tan(1/2*e+1/2*f*x)^5-29/192/f/a^3/c^4/tan(1/2*e+1/2*f*x)^3+1/f/a^3/c^4/tan(1/2*e+1/2*f*x)+2/f/a^3/c^4*arctan(tan(1/2*e+1/2*f*x))","A"
40,1,197,194,0.982000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x)","-\frac{\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)}{640 f \,a^{3} c^{5}}+\frac{3 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{128 f \,a^{3} c^{5}}-\frac{37 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{128 f \,a^{3} c^{5}}+\frac{1}{1152 f \,a^{3} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{9}{896 f \,a^{3} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{37}{640 f \,a^{3} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{31}{128 f \,a^{3} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{163}{128 f \,a^{3} c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3} c^{5}}"," ",0,"-1/640/f/a^3/c^5*tan(1/2*e+1/2*f*x)^5+3/128/f/a^3/c^5*tan(1/2*e+1/2*f*x)^3-37/128/f/a^3/c^5*tan(1/2*e+1/2*f*x)+1/1152/f/a^3/c^5/tan(1/2*e+1/2*f*x)^9-9/896/f/a^3/c^5/tan(1/2*e+1/2*f*x)^7+37/640/f/a^3/c^5/tan(1/2*e+1/2*f*x)^5-31/128/f/a^3/c^5/tan(1/2*e+1/2*f*x)^3+163/128/f/a^3/c^5/tan(1/2*e+1/2*f*x)+2/f/a^3/c^5*arctan(tan(1/2*e+1/2*f*x))","A"
41,1,219,232,0.999000," ","int(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x)","-\frac{\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)}{1280 f \,a^{3} c^{6}}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{384 f \,a^{3} c^{6}}-\frac{23 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{128 f \,a^{3} c^{6}}-\frac{1}{2816 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}+\frac{5}{1152 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{23}{896 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{13}{128 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}-\frac{1}{3 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{191}{128 f \,a^{3} c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,a^{3} c^{6}}"," ",0,"-1/1280/f/a^3/c^6*tan(1/2*e+1/2*f*x)^5+5/384/f/a^3/c^6*tan(1/2*e+1/2*f*x)^3-23/128/f/a^3/c^6*tan(1/2*e+1/2*f*x)-1/2816/f/a^3/c^6/tan(1/2*e+1/2*f*x)^11+5/1152/f/a^3/c^6/tan(1/2*e+1/2*f*x)^9-23/896/f/a^3/c^6/tan(1/2*e+1/2*f*x)^7+13/128/f/a^3/c^6/tan(1/2*e+1/2*f*x)^5-1/3/f/a^3/c^6/tan(1/2*e+1/2*f*x)^3+191/128/f/a^3/c^6/tan(1/2*e+1/2*f*x)+2/f/a^3/c^6*arctan(tan(1/2*e+1/2*f*x))","A"
42,1,391,155,1.896000," ","int((c-c*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x)","\frac{c^{4} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}+315 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}+315 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}+105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right)+2816 \left(\cos^{4}\left(f x +e \right)\right)-4768 \left(\cos^{3}\left(f x +e \right)\right)+3008 \left(\cos^{2}\left(f x +e \right)\right)-1296 \cos \left(f x +e \right)+240\right)}{840 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"1/840*c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)+315*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)+315*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)*sin(f*x+e)*2^(1/2)+105*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*sin(f*x+e)+2816*cos(f*x+e)^4-4768*cos(f*x+e)^3+3008*cos(f*x+e)^2-1296*cos(f*x+e)+240)/cos(f*x+e)^3/sin(f*x+e)","B"
43,1,302,124,1.747000," ","int((c-c*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x)","-\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(15 \sin \left(f x +e \right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+30 \sin \left(f x +e \right) \sqrt{2}\, \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)-184 \left(\cos^{3}\left(f x +e \right)\right)+272 \left(\cos^{2}\left(f x +e \right)\right)-112 \cos \left(f x +e \right)+24\right)}{60 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{2}}"," ",0,"-1/60*c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(15*sin(f*x+e)*2^(1/2)*cos(f*x+e)^2*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+30*sin(f*x+e)*2^(1/2)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+15*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)-184*cos(f*x+e)^3+272*cos(f*x+e)^2-112*cos(f*x+e)+24)/sin(f*x+e)/cos(f*x+e)^2","B"
44,1,142,93,1.714000," ","int((c-c*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x)","-\frac{c^{2} \left(3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-8 \left(\cos^{2}\left(f x +e \right)\right)+10 \cos \left(f x +e \right)-2\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{3 f \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"-1/3*c^2/f*(3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-8*cos(f*x+e)^2+10*cos(f*x+e)-2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)","A"
45,1,115,58,1.420000," ","int((c-c*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x)","\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-\sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+2 \cos \left(f x +e \right)-2\right)}{f \sin \left(f x +e \right)}"," ",0,"c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+2*cos(f*x+e)-2)/sin(f*x+e)","A"
46,1,116,61,1.585000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-2 \cos \left(f x +e \right)\right)}{c f \sin \left(f x +e \right)}"," ",0,"-1/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-2*cos(f*x+e))/sin(f*x+e)","A"
47,1,214,92,1.682000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^2,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+3 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+8 \left(\cos^{2}\left(f x +e \right)\right)-6 \cos \left(f x +e \right)\right)}{3 c^{2} f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/3/c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+3*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+8*cos(f*x+e)^2-6*cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e))","B"
48,1,311,123,1.899000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right) \left(15 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-30 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+15 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-46 \left(\cos^{3}\left(f x +e \right)\right)+70 \left(\cos^{2}\left(f x +e \right)\right)-30 \cos \left(f x +e \right)\right)}{15 c^{3} f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/15/c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))*(15*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-30*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+15*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-46*cos(f*x+e)^3+70*cos(f*x+e)^2-30*cos(f*x+e))/sin(f*x+e)^3/(-1+cos(f*x+e))","B"
49,1,402,154,2.200000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^4,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-105 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+315 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-315 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+352 \left(\cos^{4}\left(f x +e \right)\right)+105 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-812 \left(\cos^{3}\left(f x +e \right)\right)+700 \left(\cos^{2}\left(f x +e \right)\right)-210 \cos \left(f x +e \right)\right)}{105 c^{4} f \sin \left(f x +e \right)^{5} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/105/c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-105*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+315*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-315*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+352*cos(f*x+e)^4+105*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-812*cos(f*x+e)^3+700*cos(f*x+e)^2-210*cos(f*x+e))/sin(f*x+e)^5/(-1+cos(f*x+e))","B"
50,1,392,157,2.332000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^3,x)","\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}+315 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}+315 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}+105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right)+2336 \left(\cos^{4}\left(f x +e \right)\right)-2848 \left(\cos^{3}\left(f x +e \right)\right)+128 \left(\cos^{2}\left(f x +e \right)\right)+624 \cos \left(f x +e \right)-240\right) a}{840 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"1/840*c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)+315*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)+315*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)*sin(f*x+e)*2^(1/2)+105*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*sin(f*x+e)+2336*cos(f*x+e)^4-2848*cos(f*x+e)^3+128*cos(f*x+e)^2+624*cos(f*x+e)-240)/cos(f*x+e)^3/sin(f*x+e)*a","B"
51,1,232,126,1.840000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^2,x)","\frac{c^{2} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(15 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+15 \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}+68 \left(\cos^{3}\left(f x +e \right)\right)-64 \left(\cos^{2}\left(f x +e \right)\right)-16 \cos \left(f x +e \right)+12\right) a}{30 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"1/30*c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(15*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)+15*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)+68*cos(f*x+e)^3-64*cos(f*x+e)^2-16*cos(f*x+e)+12)/cos(f*x+e)^2/sin(f*x+e)*a","A"
52,1,212,89,1.431000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e)),x)","\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(3 \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)-4 \cos \left(f x +e \right)-4\right) a}{6 f \cos \left(f x +e \right) \sin \left(f x +e \right)}"," ",0,"1/6*c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(3*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)+3*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)+8*cos(f*x+e)^2-4*cos(f*x+e)-4)/cos(f*x+e)/sin(f*x+e)*a","B"
53,1,194,62,1.374000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}+4 \sin \left(f x +e \right) \cos \left(f x +e \right)\right) a}{c f \left(-1+\cos^{2}\left(f x +e \right)\right)}"," ",0,"-1/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)+4*sin(f*x+e)*cos(f*x+e))/(-1+cos(f*x+e)^2)*a","B"
54,1,215,90,1.550000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+3 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+10 \left(\cos^{2}\left(f x +e \right)\right)-6 \cos \left(f x +e \right)\right) a}{3 c^{2} f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/3/c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-3*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+3*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+10*cos(f*x+e)^2-6*cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e))*a","B"
55,1,304,121,1.762000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-15 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+30 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-15 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+52 \left(\cos^{3}\left(f x +e \right)\right)-70 \left(\cos^{2}\left(f x +e \right)\right)+30 \cos \left(f x +e \right)\right) a}{15 c^{3} f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/15/c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-15*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+30*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-15*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+52*cos(f*x+e)^3-70*cos(f*x+e)^2+30*cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e))^2*a","B"
56,1,401,152,1.768000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^4,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right) \left(105 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-315 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+315 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-105 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-382 \left(\cos^{4}\left(f x +e \right)\right)+812 \left(\cos^{3}\left(f x +e \right)\right)-700 \left(\cos^{2}\left(f x +e \right)\right)+210 \cos \left(f x +e \right)\right) a}{105 c^{4} f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/105/c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))*(105*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-315*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+315*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-105*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-382*cos(f*x+e)^4+812*cos(f*x+e)^3-700*cos(f*x+e)^2+210*cos(f*x+e))/sin(f*x+e)^3/(-1+cos(f*x+e))^2*a","B"
57,1,483,188,1.837000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^3,x)","\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-315 \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}-1260 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}-1890 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}-1260 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}-315 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \sin \left(f x +e \right)+12256 \left(\cos^{5}\left(f x +e \right)\right)-11168 \left(\cos^{4}\left(f x +e \right)\right)-5312 \left(\cos^{3}\left(f x +e \right)\right)+4064 \left(\cos^{2}\left(f x +e \right)\right)+1280 \cos \left(f x +e \right)-1120\right) a^{2}}{5040 f \cos \left(f x +e \right)^{4} \sin \left(f x +e \right)}"," ",0,"1/5040*c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-315*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)-1260*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)-1890*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)-1260*cos(f*x+e)*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)-315*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*sin(f*x+e)+12256*cos(f*x+e)^5-11168*cos(f*x+e)^4-5312*cos(f*x+e)^3+4064*cos(f*x+e)^2+1280*cos(f*x+e)-1120)/cos(f*x+e)^4/sin(f*x+e)*a^2","B"
58,1,323,157,1.572000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^2,x)","-\frac{c^{2} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+210 \sin \left(f x +e \right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+105 \sin \left(f x +e \right) \sqrt{2}\, \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}-736 \left(\cos^{4}\left(f x +e \right)\right)+368 \left(\cos^{3}\left(f x +e \right)\right)+512 \left(\cos^{2}\left(f x +e \right)\right)-24 \cos \left(f x +e \right)-120\right) a^{2}}{420 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-1/420*c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)^3*2^(1/2)+210*sin(f*x+e)*2^(1/2)*cos(f*x+e)^2*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+105*sin(f*x+e)*2^(1/2)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-736*cos(f*x+e)^4+368*cos(f*x+e)^3+512*cos(f*x+e)^2-24*cos(f*x+e)-120)/sin(f*x+e)/cos(f*x+e)^3*a^2","B"
59,1,303,118,1.368000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e)),x)","-\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(5 \sin \left(f x +e \right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+10 \sin \left(f x +e \right) \sqrt{2}\, \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)-8 \left(\cos^{3}\left(f x +e \right)\right)-16 \left(\cos^{2}\left(f x +e \right)\right)+16 \cos \left(f x +e \right)+8\right) a^{2}}{20 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"-1/20*c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(5*sin(f*x+e)*2^(1/2)*cos(f*x+e)^2*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+10*sin(f*x+e)*2^(1/2)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+5*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)-8*cos(f*x+e)^3-16*cos(f*x+e)^2+16*cos(f*x+e)+8)/cos(f*x+e)^2/sin(f*x+e)*a^2","B"
60,1,120,93,1.356000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x)","\frac{\left(-\sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+10 \cos \left(f x +e \right)-2\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{c f \sin \left(f x +e \right)}"," ",0,"1/c/f*(-2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+10*cos(f*x+e)-2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)*a^2","A"
61,1,351,64,1.419000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x)","-\frac{\left(3 \sqrt{2}\, \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}-3 \sqrt{2}\, \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{3 c^{2} f \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\cos \left(f x +e \right)\right)}"," ",0,"-1/3/c^2/f*(3*2^(1/2)*cos(f*x+e)^3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-3*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)-3*2^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+8*cos(f*x+e)^2*sin(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2))*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))^2/(1+cos(f*x+e))*a^2","B"
62,1,306,92,1.619000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-5 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+10 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-5 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+18 \left(\cos^{3}\left(f x +e \right)\right)-20 \left(\cos^{2}\left(f x +e \right)\right)+10 \cos \left(f x +e \right)\right) a^{2}}{5 c^{3} f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/5/c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-5*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+10*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-5*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+18*cos(f*x+e)^3-20*cos(f*x+e)^2+10*cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e))^2*a^2","B"
63,1,395,124,1.627000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^4,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-21 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+63 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-63 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+80 \left(\cos^{4}\left(f x +e \right)\right)+21 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-154 \left(\cos^{3}\left(f x +e \right)\right)+140 \left(\cos^{2}\left(f x +e \right)\right)-42 \cos \left(f x +e \right)\right) a^{2}}{21 c^{4} f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"1/21/c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-21*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+63*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-63*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+80*cos(f*x+e)^4+21*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-154*cos(f*x+e)^3+140*cos(f*x+e)^2-42*cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e))^3*a^2","B"
64,1,492,152,1.899000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^5,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right) \left(-45 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+180 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-270 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+178 \left(\cos^{5}\left(f x +e \right)\right)+180 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-486 \left(\cos^{4}\left(f x +e \right)\right)-45 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+648 \left(\cos^{3}\left(f x +e \right)\right)-390 \left(\cos^{2}\left(f x +e \right)\right)+90 \cos \left(f x +e \right)\right) a^{2}}{45 c^{5} f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-1/45/c^5/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))*(-45*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+180*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-270*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+178*cos(f*x+e)^5+180*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-486*cos(f*x+e)^4-45*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+648*cos(f*x+e)^3-390*cos(f*x+e)^2+90*cos(f*x+e))/sin(f*x+e)^3/(-1+cos(f*x+e))^3*a^2","B"
65,1,544,162,1.974000," ","int((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(1/2),x)","-\frac{c^{4} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(5 \sin \left(f x +e \right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+10 \sin \left(f x +e \right) \sqrt{2}\, \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+80 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)+160 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+80 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)+328 \left(\cos^{3}\left(f x +e \right)\right)-384 \left(\cos^{2}\left(f x +e \right)\right)+64 \cos \left(f x +e \right)-8\right)}{20 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right) a}"," ",0,"-1/20*c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(5*sin(f*x+e)*2^(1/2)*cos(f*x+e)^2*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+10*sin(f*x+e)*2^(1/2)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+80*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2+5*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)+160*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)+80*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*sin(f*x+e)+328*cos(f*x+e)^3-384*cos(f*x+e)^2+64*cos(f*x+e)-8)/cos(f*x+e)^2/sin(f*x+e)/a","B"
66,1,372,131,1.921000," ","int((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x)","\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(3 \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)+24 \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+24 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)-40 \left(\cos^{2}\left(f x +e \right)\right)+44 \cos \left(f x +e \right)-4\right)}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right) a}"," ",0,"1/6*c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(3*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)+3*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)+24*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)+24*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)-40*cos(f*x+e)^2+44*cos(f*x+e)-4)/sin(f*x+e)/cos(f*x+e)/a","B"
67,1,329,102,1.897000," ","int((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x)","-\frac{c^{2} \left(\sqrt{2}\, \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}+4 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+4 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-2 \sin \left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \left(1+\cos \left(f x +e \right)\right) a}"," ",0,"-c^2/f*(2^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)+4*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)+4*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-2*sin(f*x+e))*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(1+cos(f*x+e))/a","B"
68,1,144,72,1.523000," ","int((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","-\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+2 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)\right)}{f a}"," ",0,"-c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+2*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e)))/a","A"
69,1,194,104,1.719000," ","int(1/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(2 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+\sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)\right)}{2 c f \sin \left(f x +e \right) a}"," ",0,"-1/2/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(2*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-2*cos(f*x+e))/sin(f*x+e)/a","A"
70,1,377,136,1.952000," ","int(1/(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(12 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-3 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-22 \left(\cos^{3}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right)+18 \cos \left(f x +e \right)\right)}{12 c^{2} f \sin \left(f x +e \right)^{3} a}"," ",0,"1/12/c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(12*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-12*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-22*cos(f*x+e)^3-4*cos(f*x+e)^2+18*cos(f*x+e))/sin(f*x+e)^3/a","B"
71,1,545,167,2.566000," ","int(1/(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(40 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-80 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+40 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-10 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-98 \left(\cos^{3}\left(f x +e \right)\right)+5 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+160 \left(\cos^{2}\left(f x +e \right)\right)-70 \cos \left(f x +e \right)\right)}{40 c^{3} f \sin \left(f x +e \right)^{5} a}"," ",0,"-1/40/c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(40*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-80*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+40*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-10*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-98*cos(f*x+e)^3+5*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+160*cos(f*x+e)^2-70*cos(f*x+e))/sin(f*x+e)^5/a","B"
72,1,552,179,1.970000," ","int((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(3/2),x)","-\frac{c^{4} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(3 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-36 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right)+6 \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}-72 \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)-36 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)+112 \left(\cos^{3}\left(f x +e \right)\right)-52 \left(\cos^{2}\left(f x +e \right)\right)-64 \cos \left(f x +e \right)+4\right)}{6 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"-1/6*c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(3*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)-36*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*sin(f*x+e)+6*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)-72*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)+3*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)-36*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)+112*cos(f*x+e)^3-52*cos(f*x+e)^2-64*cos(f*x+e)+4)/cos(f*x+e)/sin(f*x+e)^3/a^2","B"
73,1,377,149,1.992000," ","int((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x)","-\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+2 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+6 \left(\cos^{3}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-10 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)+2\right)}{f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"-c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+6*cos(f*x+e)^3-2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-10*cos(f*x+e)^2+2*cos(f*x+e)+2)/sin(f*x+e)^3/a^2","B"
74,1,369,102,1.762000," ","int((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x)","-\frac{c^{2} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+\sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+\cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+\sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-2 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)\right)}{f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}}"," ",0,"-c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-2*cos(f*x+e)^2+2*cos(f*x+e))/(1+cos(f*x+e))/sin(f*x+e)/a^2","B"
75,1,371,96,1.870000," ","int((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x)","\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-2 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-3 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-2 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-3 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+2 \left(\cos^{2}\left(f x +e \right)\right)-2 \cos \left(f x +e \right)\right)}{2 f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}}"," ",0,"1/2*c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-2*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-3*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-2*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+2*cos(f*x+e)^2-2*cos(f*x+e))/(1+cos(f*x+e))/sin(f*x+e)/a^2","B"
76,1,377,151,1.904000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(8 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+7 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-7 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)\right)}{8 c f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"1/8/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(8*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+7*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-8*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-7*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-6*cos(f*x+e)^3+4*cos(f*x+e)^2+2*cos(f*x+e))/sin(f*x+e)^3/a^2","B"
77,1,387,184,2.498000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(48 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+27 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-27 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-62 \left(\cos^{3}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right)+42 \cos \left(f x +e \right)\right) \left(-1+\cos^{2}\left(f x +e \right)\right)}{48 c^{2} f \sin \left(f x +e \right)^{5} a^{2}}"," ",0,"-1/48/c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(48*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+27*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-48*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-27*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-62*cos(f*x+e)^3+4*cos(f*x+e)^2+42*cos(f*x+e))/sin(f*x+e)^5*(-1+cos(f*x+e)^2)/a^2","B"
78,1,725,215,2.508000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(1+\cos \left(f x +e \right)\right)^{2} \left(480 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-480 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+165 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-480 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-165 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+480 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-165 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-898 \left(\cos^{4}\left(f x +e \right)\right)+165 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+702 \left(\cos^{3}\left(f x +e \right)\right)+730 \left(\cos^{2}\left(f x +e \right)\right)-630 \cos \left(f x +e \right)\right)}{480 c^{3} f \sin \left(f x +e \right)^{7} a^{2}}"," ",0,"1/480/c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(1+cos(f*x+e))^2*(480*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-480*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+165*sin(f*x+e)*cos(f*x+e)^3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-480*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-165*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+480*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-165*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-898*cos(f*x+e)^4+165*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+702*cos(f*x+e)^3+730*cos(f*x+e)^2-630*cos(f*x+e))/sin(f*x+e)^7/a^2","B"
79,1,726,229,2.549000," ","int((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^(5/2),x)","-\frac{c^{5} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)^{2} \left(-3 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}-69 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-9 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-207 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right)-9 \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}-207 \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)-69 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)+148 \left(\cos^{4}\left(f x +e \right)\right)+132 \left(\cos^{3}\left(f x +e \right)\right)-200 \left(\cos^{2}\left(f x +e \right)\right)-84 \cos \left(f x +e \right)+4\right)}{6 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/6*c^5/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^2*(-3*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-69*cos(f*x+e)^3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-9*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)-207*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*sin(f*x+e)-9*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)-207*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)-3*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)-69*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*sin(f*x+e)+148*cos(f*x+e)^4+132*cos(f*x+e)^3-200*cos(f*x+e)^2-84*cos(f*x+e)+4)/cos(f*x+e)/sin(f*x+e)^5/a^3","B"
80,1,550,200,2.058000," ","int((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(5/2),x)","-\frac{c^{4} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(2 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+11 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-22 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \left(\cos^{5}\left(f x +e \right)\right)+2 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+11 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-32 \left(\cos^{3}\left(f x +e \right)\right)+36 \left(\cos^{2}\left(f x +e \right)\right)-6 \cos \left(f x +e \right)-4\right)}{2 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/2*c^4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+11*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^4*sin(f*x+e)-4*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-22*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+6*cos(f*x+e)^5+2*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+11*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-32*cos(f*x+e)^3+36*cos(f*x+e)^2-6*cos(f*x+e)-4)/sin(f*x+e)^5/a^3","B"
81,1,553,164,2.112000," ","int((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x)","\frac{c^{3} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(4 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+8 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+7 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+14 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+7 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)-2 \cos \left(f x +e \right)\right)}{4 f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{3} a^{3}}"," ",0,"1/4*c^3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(4*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+8*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+7*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+4*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+14*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+7*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-6*cos(f*x+e)^3+8*cos(f*x+e)^2-2*cos(f*x+e))/(1+cos(f*x+e))/sin(f*x+e)^3/a^3","B"
82,1,545,162,1.879000," ","int((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x)","-\frac{c^{2} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(8 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+16 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+11 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+22 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+11 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-14 \left(\cos^{3}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)+6 \cos \left(f x +e \right)\right)}{8 f \left(1+\cos \left(f x +e \right)\right)^{2} \sin \left(f x +e \right) a^{3}}"," ",0,"-1/8*c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(8*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+16*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+11*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+8*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+22*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+11*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-14*cos(f*x+e)^3+8*cos(f*x+e)^2+6*cos(f*x+e))/(1+cos(f*x+e))^2/sin(f*x+e)/a^3","B"
83,1,543,123,1.618000," ","int((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x)","-\frac{c \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(16 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+32 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+23 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+16 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+46 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+23 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-22 \left(\cos^{3}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)+14 \cos \left(f x +e \right)\right)}{16 f \left(1+\cos \left(f x +e \right)\right)^{2} \sin \left(f x +e \right) a^{3}}"," ",0,"-1/16*c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(16*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+32*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+23*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+16*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+46*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+23*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-22*cos(f*x+e)^3+8*cos(f*x+e)^2+14*cos(f*x+e))/(1+cos(f*x+e))^2/sin(f*x+e)/a^3","B"
84,1,545,199,2.158000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)^{2} \left(64 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+128 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+71 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+64 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+142 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)+71 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-54 \left(\cos^{3}\left(f x +e \right)\right)-24 \left(\cos^{2}\left(f x +e \right)\right)+14 \cos \left(f x +e \right)\right)}{64 c f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/64/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^2*(64*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+128*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+71*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+64*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+142*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))+71*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-54*cos(f*x+e)^3-24*cos(f*x+e)^2+14*cos(f*x+e))/sin(f*x+e)^5/a^3","B"
85,1,725,234,2.328000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right) \left(-1+\cos \left(f x +e \right)\right)^{2} \left(384 \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+384 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+321 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-384 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+321 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-384 \sqrt{2}\, \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-321 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-410 \left(\cos^{4}\left(f x +e \right)\right)-321 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sin \left(f x +e \right)}\right)-142 \left(\cos^{3}\left(f x +e \right)\right)+298 \left(\cos^{2}\left(f x +e \right)\right)+126 \cos \left(f x +e \right)\right)}{384 c^{2} f \sin \left(f x +e \right)^{7} a^{3}}"," ",0,"1/384/c^2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))*(-1+cos(f*x+e))^2*(384*cos(f*x+e)^3*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+384*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+321*sin(f*x+e)*cos(f*x+e)^3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-384*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+321*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-384*2^(1/2)*sin(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-321*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-410*cos(f*x+e)^4-321*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-cos(f*x+e)+1)/sin(f*x+e))-142*cos(f*x+e)^3+298*cos(f*x+e)^2+126*cos(f*x+e))/sin(f*x+e)^7/a^3","B"
86,1,195,165,2.575000," ","int((c-c*sec(f*x+e))^(7/2)*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+29 \left(\cos^{3}\left(f x +e \right)\right)+18 \left(\cos^{2}\left(f x +e \right)\right)-9 \cos \left(f x +e \right)+2\right) \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{6 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-1/6/f*(6*cos(f*x+e)^3*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+6*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))+29*cos(f*x+e)^3+18*cos(f*x+e)^2-9*cos(f*x+e)+2)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))^3","A"
87,1,185,125,2.354000," ","int((c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-5 \left(\cos^{2}\left(f x +e \right)\right)-4 \cos \left(f x +e \right)+1\right) \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{2 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/2/f*(2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-2*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-5*cos(f*x+e)^2-4*cos(f*x+e)+1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))^2","A"
88,1,165,85,2.306000," ","int((c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(\cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)+1\right) \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/f*(cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)*ln(2/(1+cos(f*x+e)))+cos(f*x+e)+1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))","A"
89,1,128,44,2.398000," ","int((c-c*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)\right) \cos \left(f x +e \right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)}"," ",0,"-1/f*(ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-ln(2/(1+cos(f*x+e))))*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)","B"
90,1,100,47,2.120000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(2 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}{f \sin \left(f x +e \right) c}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-ln(2/(1+cos(f*x+e))))*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)/sin(f*x+e)/c","B"
91,1,164,88,2.548000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-\cos \left(f x +e \right)-4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{2 f \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(4*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-2*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-cos(f*x+e)-4*ln(-(-1+cos(f*x+e))/sin(f*x+e))+2*ln(2/(1+cos(f*x+e)))-1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)","A"
92,1,226,128,2.678000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(16 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-32 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-7 \left(\cos^{2}\left(f x +e \right)\right)+16 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)-8 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+5\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{8 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{2} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(16*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-8*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-32*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-7*cos(f*x+e)^2+16*cos(f*x+e)*ln(2/(1+cos(f*x+e)))+16*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)-8*ln(2/(1+cos(f*x+e)))+5)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)","A"
93,1,288,168,2.179000," ","int((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(7/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-36 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-7 \left(\cos^{3}\left(f x +e \right)\right)+18 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+36 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-18 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 \cos \left(f x +e \right)+6 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-4\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{3} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/6/f*(-1+cos(f*x+e))*(12*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3-6*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-36*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-7*cos(f*x+e)^3+18*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+36*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+3*cos(f*x+e)^2-18*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-12*ln(-(-1+cos(f*x+e))/sin(f*x+e))+6*cos(f*x+e)+6*ln(2/(1+cos(f*x+e)))-4)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)","A"
94,1,190,170,2.002000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x)","\frac{\left(6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\left(\cos^{3}\left(f x +e \right)\right)-6 \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right)+2\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{6 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/6/f*(6*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-6*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*cos(f*x+e)^3*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)^3-6*cos(f*x+e)^2-3*cos(f*x+e)+2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))^2*a","A"
95,1,172,93,2.084000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(2 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right)+1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{2 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/2/f*(2*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-cos(f*x+e)^2+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))*a","A"
96,1,152,85,2.031000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(1/2),x)","-\frac{\left(\cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-\cos \left(f x +e \right)-1\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{f \sin \left(f x +e \right)}"," ",0,"-1/f*(cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)*ln(2/(1+cos(f*x+e)))-cos(f*x+e)-1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)*a","A"
97,1,157,96,1.948000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) a}{f \sin \left(f x +e \right) c}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-ln(2/(1+cos(f*x+e))))*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)/sin(f*x+e)/c*a","A"
98,1,161,92,1.973000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{f \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"1/f*(-1+cos(f*x+e))*(cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+cos(f*x+e)-ln(2/(1+cos(f*x+e)))+2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)*a","A"
99,1,227,134,2.095000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-5 \left(\cos^{2}\left(f x +e \right)\right)-16 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+8 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+3\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{4 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{2} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/4/f*(-1+cos(f*x+e))*(8*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-4*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-5*cos(f*x+e)^2-16*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+8*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+8*ln(-(-1+cos(f*x+e))/sin(f*x+e))-4*ln(2/(1+cos(f*x+e)))+3)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*a","A"
100,1,289,176,2.295000," ","int((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(24 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-48 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)+35 \left(\cos^{3}\left(f x +e \right)\right)-72 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+144 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-9 \left(\cos^{2}\left(f x +e \right)\right)+72 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-144 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-27 \cos \left(f x +e \right)-24 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+17\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a}{24 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"1/24/f*(-1+cos(f*x+e))*(24*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-48*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+35*cos(f*x+e)^3-72*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+144*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-9*cos(f*x+e)^2+72*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-144*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-27*cos(f*x+e)-24*ln(2/(1+cos(f*x+e)))+48*ln(-(-1+cos(f*x+e))/sin(f*x+e))+17)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)/cos(f*x+e)^3*a","A"
101,1,192,137,2.104000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(4 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-3 \left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right)-1\right) a^{2}}{4 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2} \cos \left(f x +e \right)}"," ",0,"-1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*(4*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*cos(f*x+e)^4*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-4*cos(f*x+e)^4*ln(2/(1+cos(f*x+e)))-3*cos(f*x+e)^4+4*cos(f*x+e)^2-1)/sin(f*x+e)/(-1+cos(f*x+e))^2/cos(f*x+e)*a^2","A"
102,1,200,170,2.047000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+7 \left(\cos^{3}\left(f x +e \right)\right)+6 \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right)-2\right) a^{2}}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/6/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*(6*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-6*cos(f*x+e)^3*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-6*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+7*cos(f*x+e)^3+6*cos(f*x+e)^2-3*cos(f*x+e)-2)/sin(f*x+e)/cos(f*x+e)/(-1+cos(f*x+e))*a^2","A"
103,1,180,125,2.324000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(1/2),x)","\frac{\left(2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right)+4 \cos \left(f x +e \right)+1\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{2 f \cos \left(f x +e \right) \sin \left(f x +e \right)}"," ",0,"1/2/f*(2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-2*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+3*cos(f*x+e)^2+4*cos(f*x+e)+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)/sin(f*x+e)*a^2","A"
104,1,184,140,2.061000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\left(8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-3 \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 \cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)+1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{f \sin \left(f x +e \right) c}"," ",0,"-1/f*(8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-3*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)*ln(2/(1+cos(f*x+e)))+cos(f*x+e)+1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/c*a^2","A"
105,1,239,88,2.256000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{f \cos \left(f x +e \right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-1/f*(-1+cos(f*x+e))*(cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)*ln(2/(1+cos(f*x+e)))-ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)+ln(2/(1+cos(f*x+e)))-2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)*a^2","B"
106,1,229,92,2.251000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-3 \left(\cos^{2}\left(f x +e \right)\right)-8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+4 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{2 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{2}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(4*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-3*cos(f*x+e)^2-8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+4*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*ln(2/(1+cos(f*x+e)))+1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)/cos(f*x+e)^2*a^2","B"
107,1,281,134,2.369000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-6 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-9 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+5 \left(\cos^{3}\left(f x +e \right)\right)+18 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+9 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-18 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-3 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-3 \cos \left(f x +e \right)+6 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{3 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"1/3/f*(-1+cos(f*x+e))*(3*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-6*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3-9*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+5*cos(f*x+e)^3+18*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+9*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-18*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-3*ln(2/(1+cos(f*x+e)))-3*cos(f*x+e)+6*ln(-(-1+cos(f*x+e))/sin(f*x+e))+2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)/cos(f*x+e)^3*a^2","B"
108,1,353,176,2.352000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(32 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-29 \left(\cos^{4}\left(f x +e \right)\right)-128 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)+64 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+20 \left(\cos^{3}\left(f x +e \right)\right)+192 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+10 \left(\cos^{2}\left(f x +e \right)\right)-128 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+64 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-28 \cos \left(f x +e \right)+32 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+11\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{16 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{4} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{9}{2}}}"," ",0,"-1/16/f*(-1+cos(f*x+e))*(32*cos(f*x+e)^4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-16*cos(f*x+e)^4*ln(2/(1+cos(f*x+e)))-29*cos(f*x+e)^4-128*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+64*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))+20*cos(f*x+e)^3+192*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-96*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+10*cos(f*x+e)^2-128*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+64*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-28*cos(f*x+e)+32*ln(-(-1+cos(f*x+e))/sin(f*x+e))-16*ln(2/(1+cos(f*x+e)))+11)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/cos(f*x+e)^4/(c*(-1+cos(f*x+e))/cos(f*x+e))^(9/2)*a^2","A"
109,1,415,218,2.192000," ","int((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(240 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-120 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-1200 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-233 \left(\cos^{5}\left(f x +e \right)\right)+600 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+2400 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)+325 \left(\cos^{4}\left(f x +e \right)\right)-1200 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2400 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-110 \left(\cos^{3}\left(f x +e \right)\right)+1200 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+1200 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-290 \left(\cos^{2}\left(f x +e \right)\right)-600 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-240 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+295 \cos \left(f x +e \right)+120 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-83\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{120 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{11}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{5}}"," ",0,"-1/120/f*(-1+cos(f*x+e))*(240*cos(f*x+e)^5*ln(-(-1+cos(f*x+e))/sin(f*x+e))-120*cos(f*x+e)^5*ln(2/(1+cos(f*x+e)))-1200*cos(f*x+e)^4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-233*cos(f*x+e)^5+600*cos(f*x+e)^4*ln(2/(1+cos(f*x+e)))+2400*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+325*cos(f*x+e)^4-1200*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-2400*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-110*cos(f*x+e)^3+1200*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+1200*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-290*cos(f*x+e)^2-600*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-240*ln(-(-1+cos(f*x+e))/sin(f*x+e))+295*cos(f*x+e)+120*ln(2/(1+cos(f*x+e)))-83)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(11/2)/sin(f*x+e)/cos(f*x+e)^5*a^2","A"
110,1,190,186,2.216000," ","int((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+14 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+14 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+9 \left(\cos^{2}\left(f x +e \right)\right)+8 \cos \left(f x +e \right)-1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right)}{2 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{3} a}"," ",0,"1/2/f*(2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+14*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+14*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+9*cos(f*x+e)^2+8*cos(f*x+e)-1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2/sin(f*x+e)/(-1+cos(f*x+e))^3/a","A"
111,1,170,139,2.238000," ","int((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(3 \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 \cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)+1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right)}{f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2} a}"," ",0,"1/f*(3*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(2/(1+cos(f*x+e)))+cos(f*x+e)+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2/sin(f*x+e)/(-1+cos(f*x+e))^2/a","A"
112,1,93,94,2.396000," ","int((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x)","\frac{\ln \left(-\frac{4 \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right)^{2}}\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) a}"," ",0,"1/f*ln(-4*cos(f*x+e)/(1+cos(f*x+e))^2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*cos(f*x+e)^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-1+cos(f*x+e))/a","A"
113,1,75,45,2.411000," ","int((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)}{f \sin \left(f x +e \right) a}"," ",0,"1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)*ln(2/(1+cos(f*x+e)))/sin(f*x+e)/a","A"
114,1,101,42,2.376000," ","int(1/(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}{f \sin \left(f x +e \right) c a}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(ln(-(-1+cos(f*x+e))/sin(f*x+e))-ln(2/(1+cos(f*x+e))))*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)/sin(f*x+e)/c/a","B"
115,1,167,150,2.591000," ","int(1/(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(6 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-4 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-6 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right)+4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{4 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right) a}"," ",0,"-1/4/f*(-1+cos(f*x+e))*(6*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-4*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-6*ln(-(-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)+4*ln(2/(1+cos(f*x+e)))-1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/cos(f*x+e)/sin(f*x+e)/a","A"
116,1,229,246,2.587000," ","int(1/(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(16 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-28 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+56 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+9 \left(\cos^{2}\left(f x +e \right)\right)+16 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-28 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \cos \left(f x +e \right)-7\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{16 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right)^{2} a}"," ",0,"1/16/f*(-1+cos(f*x+e))*(16*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-28*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-32*cos(f*x+e)*ln(2/(1+cos(f*x+e)))+56*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+9*cos(f*x+e)^2+16*ln(2/(1+cos(f*x+e)))-28*ln(-(-1+cos(f*x+e))/sin(f*x+e))+2*cos(f*x+e)-7)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)/cos(f*x+e)^2/a","A"
117,1,278,199,2.271000," ","int((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(3/2),x)","\frac{\left(5 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+5 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+5 \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+5 \cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 \left(\cos^{2}\left(f x +e \right)\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+6 \cos \left(f x +e \right)+1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{2} a^{2}}"," ",0,"1/f*(5*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+5*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+5*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+5*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-3*cos(f*x+e)^2-cos(f*x+e)*ln(2/(1+cos(f*x+e)))+6*cos(f*x+e)+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*cos(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-1+cos(f*x+e))^2/a^2","A"
118,1,238,88,2.163000," ","int((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(3/2),x)","\frac{\left(\cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)-\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+2\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right) a^{2}}"," ",0,"1/f*(cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)*ln(2/(1+cos(f*x+e)))+ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)-ln(2/(1+cos(f*x+e)))+2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*cos(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-1+cos(f*x+e))/a^2","B"
119,1,106,90,2.191000," ","int((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(3/2),x)","-\frac{\left(\cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)+\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"-1/f*(cos(f*x+e)*ln(2/(1+cos(f*x+e)))+cos(f*x+e)+ln(2/(1+cos(f*x+e)))-1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*cos(f*x+e)^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/a^2","A"
120,1,119,86,2.302000," ","int((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x)","-\frac{\left(2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)-2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+1\right) \cos \left(f x +e \right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{2 f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"-1/2/f*(2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)-2*ln(2/(1+cos(f*x+e)))+1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/a^2","A"
121,1,159,193,2.433000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)^{2} \left(4 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-1\right)}{4 f \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"-1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^2*(4*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+4*ln(2/(1+cos(f*x+e)))+cos(f*x+e)-2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-1)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/a^2","A"
122,1,173,91,2.391000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\cos^{2}\left(f x +e \right)-4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+1\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{4 f \sin \left(f x +e \right)^{3} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right) a^{2}}"," ",0,"-1/4/f*(-1+cos(f*x+e))^2*(4*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-4*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+cos(f*x+e)^2-4*ln(2/(1+cos(f*x+e)))+4*ln(-(-1+cos(f*x+e))/sin(f*x+e))+1)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/cos(f*x+e)/a^2","A"
123,1,293,313,2.948000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(32 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-44 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-32 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+44 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+13 \left(\cos^{3}\left(f x +e \right)\right)-32 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+44 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+7 \left(\cos^{2}\left(f x +e \right)\right)+32 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-44 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \left(f x +e \right)-11\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{32 f \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{2} a^{2}}"," ",0,"-1/32/f*(-1+cos(f*x+e))^2*(32*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))-44*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3-32*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+44*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+13*cos(f*x+e)^3-32*cos(f*x+e)*ln(2/(1+cos(f*x+e)))+44*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+7*cos(f*x+e)^2+32*ln(2/(1+cos(f*x+e)))-44*ln(-(-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e)-11)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^3/cos(f*x+e)^2/a^2","A"
124,1,338,204,2.602000," ","int((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(5/2),x)","\frac{\left(\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \cos \left(f x +e \right) \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)^{5} \left(-1+\cos \left(f x +e \right)\right) a^{3}}"," ",0,"1/f*(ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+2*cos(f*x+e)*ln(2/(1+cos(f*x+e)))+cos(f*x+e)^2+2*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*cos(f*x+e)^4*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/(-1+cos(f*x+e))/a^3","A"
125,1,144,90,2.747000," ","int((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(5/2),x)","\frac{\left(2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right)+4 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+2 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-1\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{2 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"1/2/f*(2*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+3*cos(f*x+e)^2+4*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+2*ln(2/(1+cos(f*x+e)))-1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*cos(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/a^3","A"
126,1,152,132,2.653000," ","int((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+5 \left(\cos^{2}\left(f x +e \right)\right)+8 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+4 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-3\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{4 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"1/4/f*(-1+cos(f*x+e))*(4*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+5*cos(f*x+e)^2+8*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+4*ln(2/(1+cos(f*x+e)))-3)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)*cos(f*x+e)^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/a^3","A"
127,1,152,126,2.787000," ","int((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(8 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+7 \left(\cos^{2}\left(f x +e \right)\right)+16 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)+8 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-5\right) \cos \left(f x +e \right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{8 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"1/8/f*(-1+cos(f*x+e))^2*(8*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2+7*cos(f*x+e)^2+16*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-2*cos(f*x+e)+8*ln(2/(1+cos(f*x+e)))-5)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/a^3","A"
128,1,223,242,2.707000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)^{3} \left(16 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+32 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+9 \left(\cos^{2}\left(f x +e \right)\right)+16 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-4 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \cos \left(f x +e \right)-7\right)}{16 f \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"1/16/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^3*(16*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-4*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+32*cos(f*x+e)*ln(2/(1+cos(f*x+e)))-8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+9*cos(f*x+e)^2+16*ln(2/(1+cos(f*x+e)))-4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)-7)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/a^3","A"
129,1,284,311,2.604000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(20 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-32 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+20 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-13 \left(\cos^{3}\left(f x +e \right)\right)-20 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+32 \cos \left(f x +e \right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+7 \left(\cos^{2}\left(f x +e \right)\right)-20 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+32 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+\cos \left(f x +e \right)-11\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{32 f \,c^{3} \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/32/f*(20*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^3-32*cos(f*x+e)^3*ln(2/(1+cos(f*x+e)))+20*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-32*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-13*cos(f*x+e)^3-20*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+32*cos(f*x+e)*ln(2/(1+cos(f*x+e)))+7*cos(f*x+e)^2-20*ln(-(-1+cos(f*x+e))/sin(f*x+e))+32*ln(2/(1+cos(f*x+e)))+cos(f*x+e)-11)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/c^3/sin(f*x+e)^5/a^3","A"
130,1,237,135,2.480000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(32 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)-13 \left(\cos^{4}\left(f x +e \right)\right)-64 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+64 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)-6 \left(\cos^{2}\left(f x +e \right)\right)+32 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 \ln \left(\frac{2}{1+\cos \left(f x +e \right)}\right)+11\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{32 f \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)^{2} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} a^{3}}"," ",0,"-1/32/f*(-1+cos(f*x+e))^3*(32*cos(f*x+e)^4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-32*cos(f*x+e)^4*ln(2/(1+cos(f*x+e)))-13*cos(f*x+e)^4-64*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+64*ln(2/(1+cos(f*x+e)))*cos(f*x+e)^2-6*cos(f*x+e)^2+32*ln(-(-1+cos(f*x+e))/sin(f*x+e))-32*ln(2/(1+cos(f*x+e)))+11)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/a^3","A"
131,0,0,78,2.135000," ","int((1+sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","\int \left(1+\sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((1+sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","F"
132,0,0,97,2.389000," ","int((a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","F"
133,0,0,87,2.857000," ","int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{3} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^n,x)","F"
134,0,0,87,2.293000," ","int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{2} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^n,x)","F"
135,0,0,85,2.099000," ","int((a+a*sec(f*x+e))*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right) \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))*(c-c*sec(f*x+e))^n,x)","F"
136,0,0,87,2.274000," ","int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e)),x)","\int \frac{\left(c -c \sec \left(f x +e \right)\right)^{n}}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e)),x)","F"
137,0,0,87,1.752000," ","int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^2,x)","\int \frac{\left(c -c \sec \left(f x +e \right)\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^2,x)","F"
138,0,0,164,1.739000," ","int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{\frac{5}{2}} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^n,x)","F"
139,0,0,113,1.727000," ","int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^n,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}} \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^n,x)","F"
140,0,0,64,1.883000," ","int((a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^n,x)","\int \sqrt{a +a \sec \left(f x +e \right)}\, \left(c -c \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^n,x)","F"
141,0,0,127,1.928000," ","int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","\int \frac{\left(c -c \sec \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sec \left(f x +e \right)}}\, dx"," ",0,"int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","F"
142,0,0,187,2.005000," ","int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","\int \frac{\left(c -c \sec \left(f x +e \right)\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","F"
143,1,141,76,1.781000," ","int((a+a*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(\ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)\right)}{c f}"," ",0,"-1/c/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))+2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2)))","A"
144,1,295,217,1.923000," ","int((c+d*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x)","-\frac{\sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) c^{2}-2 c \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) d +\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) c^{2}-\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}-4 c^{2} \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{c -d}{c +d}}\right)\right)}{a f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-1/a/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(1+cos(f*x+e))^2*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(-1+cos(f*x+e))*(2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*c^2-2*c*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*d+EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*c^2-EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*d^2-4*c^2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((c-d)/(c+d))^(1/2)))/(d+c*cos(f*x+e))/sin(f*x+e)^2","A"
145,1,285,211,1.985000," ","int((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x)","-\frac{\sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) c -2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) d +c \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)+d \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)-4 c \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{c -d}{c +d}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{a f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-1/a/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(1+cos(f*x+e))^2*(2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*c-2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*d+c*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))+d*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))-4*c*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((c-d)/(c+d))^(1/2)))*(-1+cos(f*x+e))/(d+c*cos(f*x+e))/sin(f*x+e)^2","A"
146,1,327,296,2.100000," ","int(1/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) c -4 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) d +c \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)+d \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)-4 c \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{c -d}{c +d}}\right)+4 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{c -d}{c +d}}\right) d \right) \left(-1+\cos \left(f x +e \right)\right)}{a f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \left(c -d \right)}"," ",0,"-1/a/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(1+cos(f*x+e))^2*(2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*c-4*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*d+c*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))+d*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))-4*c*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((c-d)/(c+d))^(1/2))+4*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((c-d)/(c+d))^(1/2))*d)*(-1+cos(f*x+e))/(d+c*cos(f*x+e))/sin(f*x+e)^2/(c-d)","A"
147,1,546,247,2.134000," ","int((c+d*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \sqrt{2}\, \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{4}+315 \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{4}+315 \sqrt{2}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{4}+105 \sqrt{2}\, \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{4} \sin \left(f x +e \right)-6720 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d -6720 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{2}-3584 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{3}-768 \left(\cos^{4}\left(f x +e \right)\right) d^{4}+6720 \left(\cos^{3}\left(f x +e \right)\right) c^{3} d +3360 \left(\cos^{3}\left(f x +e \right)\right) c^{2} d^{2}+1792 \left(\cos^{3}\left(f x +e \right)\right) c \,d^{3}+384 \left(\cos^{3}\left(f x +e \right)\right) d^{4}+3360 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{2}+448 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{3}+96 \left(\cos^{2}\left(f x +e \right)\right) d^{4}+1344 \cos \left(f x +e \right) c \,d^{3}+48 \cos \left(f x +e \right) d^{4}+240 d^{4}\right)}{840 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"1/840/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*2^(1/2)*cos(f*x+e)^3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^4+315*2^(1/2)*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^4+315*2^(1/2)*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^4+105*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^4*sin(f*x+e)-6720*cos(f*x+e)^4*c^3*d-6720*cos(f*x+e)^4*c^2*d^2-3584*cos(f*x+e)^4*c*d^3-768*cos(f*x+e)^4*d^4+6720*cos(f*x+e)^3*c^3*d+3360*cos(f*x+e)^3*c^2*d^2+1792*cos(f*x+e)^3*c*d^3+384*cos(f*x+e)^3*d^4+3360*cos(f*x+e)^2*c^2*d^2+448*cos(f*x+e)^2*c*d^3+96*cos(f*x+e)^2*d^4+1344*cos(f*x+e)*c*d^3+48*cos(f*x+e)*d^4+240*d^4)/cos(f*x+e)^3/sin(f*x+e)","B"
148,1,389,185,1.955000," ","int((c+d*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(15 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} c^{3}+30 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} c^{3}+15 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}\, c^{3} \sin \left(f x +e \right)+360 \left(\cos^{3}\left(f x +e \right)\right) c^{2} d +240 \left(\cos^{3}\left(f x +e \right)\right) c \,d^{2}+64 \left(\cos^{3}\left(f x +e \right)\right) d^{3}-360 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d -120 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}-32 \left(\cos^{2}\left(f x +e \right)\right) d^{3}-120 \cos \left(f x +e \right) c \,d^{2}-8 \cos \left(f x +e \right) d^{3}-24 d^{3}\right)}{60 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"-1/60/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(15*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*c^3+30*cos(f*x+e)*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*c^3+15*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*2^(1/2)*c^3*sin(f*x+e)+360*cos(f*x+e)^3*c^2*d+240*cos(f*x+e)^3*c*d^2+64*cos(f*x+e)^3*d^3-360*cos(f*x+e)^2*c^2*d-120*cos(f*x+e)^2*c*d^2-32*cos(f*x+e)^2*d^3-120*cos(f*x+e)*c*d^2-8*cos(f*x+e)*d^3-24*d^3)/cos(f*x+e)^2/sin(f*x+e)","B"
149,1,248,128,1.735000," ","int((c+d*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(3 \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \cos \left(f x +e \right) \sqrt{2}\, c^{2}+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2} \sin \left(f x +e \right)-24 \left(\cos^{2}\left(f x +e \right)\right) c d -8 \left(\cos^{2}\left(f x +e \right)\right) d^{2}+24 \cos \left(f x +e \right) c d +4 \cos \left(f x +e \right) d^{2}+4 d^{2}\right)}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"1/6/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*cos(f*x+e)*2^(1/2)*c^2+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2*sin(f*x+e)-24*cos(f*x+e)^2*c*d-8*cos(f*x+e)^2*d^2+24*cos(f*x+e)*c*d+4*cos(f*x+e)*d^2+4*d^2)/sin(f*x+e)/cos(f*x+e)","A"
150,1,118,58,1.546000," ","int((c+d*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c \sin \left(f x +e \right)+2 d \cos \left(f x +e \right)-2 d \right)}{f \sin \left(f x +e \right)}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*sin(f*x+e)+2*d*cos(f*x+e)-2*d)/sin(f*x+e)","B"
151,1,502,85,1.750000," ","int((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x)","-\frac{\left(2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{\frac{d}{c -d}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)-d \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right)+d \ln \left(\frac{-2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)+2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right)\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2 f \sqrt{\frac{d}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, c}"," ",0,"-1/2/f*(2*((c+d)*(c-d))^(1/2)*(d/(c-d))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))-d*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))+d*ln(2*(-(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)+2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*2^(1/2)/(d/(c-d))^(1/2)/((c+d)*(c-d))^(1/2)/c","B"
152,1,97265,189,2.998000," ","int((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
153,1,330749,249,19.097000," ","int((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
154,1,539,216,1.853000," ","int((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^3,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \sqrt{2}\, \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3}+315 \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3}+315 \sqrt{2}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3}+105 \sqrt{2}\, \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)-1680 \left(\cos^{4}\left(f x +e \right)\right) c^{3}-8400 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d -6048 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{2}-1664 \left(\cos^{4}\left(f x +e \right)\right) d^{3}+1680 \left(\cos^{3}\left(f x +e \right)\right) c^{3}+6720 \left(\cos^{3}\left(f x +e \right)\right) c^{2} d +3024 \left(\cos^{3}\left(f x +e \right)\right) c \,d^{2}+832 \left(\cos^{3}\left(f x +e \right)\right) d^{3}+1680 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d +2016 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}+208 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+1008 \cos \left(f x +e \right) c \,d^{2}+384 \cos \left(f x +e \right) d^{3}+240 d^{3}\right) a}{840 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"1/840/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*2^(1/2)*cos(f*x+e)^3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3+315*2^(1/2)*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3+315*2^(1/2)*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3+105*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3*sin(f*x+e)-1680*cos(f*x+e)^4*c^3-8400*cos(f*x+e)^4*c^2*d-6048*cos(f*x+e)^4*c*d^2-1664*cos(f*x+e)^4*d^3+1680*cos(f*x+e)^3*c^3+6720*cos(f*x+e)^3*c^2*d+3024*cos(f*x+e)^3*c*d^2+832*cos(f*x+e)^3*d^3+1680*cos(f*x+e)^2*c^2*d+2016*cos(f*x+e)^2*c*d^2+208*cos(f*x+e)^2*d^3+1008*cos(f*x+e)*c*d^2+384*cos(f*x+e)*d^3+240*d^3)/cos(f*x+e)^3/sin(f*x+e)*a","B"
155,1,382,155,1.674000," ","int((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^2,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(15 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2}+30 \cos \left(f x +e \right) \sin \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2}+15 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{2} \sin \left(f x +e \right)+120 \left(\cos^{3}\left(f x +e \right)\right) c^{2}+400 \left(\cos^{3}\left(f x +e \right)\right) c d +144 \left(\cos^{3}\left(f x +e \right)\right) d^{2}-120 \left(\cos^{2}\left(f x +e \right)\right) c^{2}-320 \left(\cos^{2}\left(f x +e \right)\right) c d -72 \left(\cos^{2}\left(f x +e \right)\right) d^{2}-80 \cos \left(f x +e \right) c d -48 \cos \left(f x +e \right) d^{2}-24 d^{2}\right) a}{60 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"-1/60/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(15*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2+30*cos(f*x+e)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^2*sin(f*x+e)+120*cos(f*x+e)^3*c^2+400*cos(f*x+e)^3*c*d+144*cos(f*x+e)^3*d^2-120*cos(f*x+e)^2*c^2-320*cos(f*x+e)^2*c*d-72*cos(f*x+e)^2*d^2-80*cos(f*x+e)*c*d-48*cos(f*x+e)*d^2-24*d^2)/cos(f*x+e)^2/sin(f*x+e)*a","B"
156,1,237,91,1.536000," ","int((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(3 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} c +3 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} c \sin \left(f x +e \right)-12 \left(\cos^{2}\left(f x +e \right)\right) c -20 \left(\cos^{2}\left(f x +e \right)\right) d +12 c \cos \left(f x +e \right)+16 d \cos \left(f x +e \right)+4 d \right) a}{6 f \cos \left(f x +e \right) \sin \left(f x +e \right)}"," ",0,"1/6/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(3*sin(f*x+e)*cos(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*c+3*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*c*sin(f*x+e)-12*cos(f*x+e)^2*c-20*cos(f*x+e)^2*d+12*c*cos(f*x+e)+16*d*cos(f*x+e)+4*d)/cos(f*x+e)/sin(f*x+e)*a","B"
157,1,864,90,1.493000," ","int((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x)","-\frac{\left(2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{\frac{d}{c -d}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)+\ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) c -d \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right)-\ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) c +\ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) d \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{2}\, a}{2 f \sqrt{\left(c +d \right) \left(c -d \right)}\, c \sqrt{\frac{d}{c -d}}}"," ",0,"-1/2/f*(2*((c+d)*(c-d))^(1/2)*(d/(c-d))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))+ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*c-d*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))-ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*c+ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*d)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*2^(1/2)*a/((c+d)*(c-d))^(1/2)/c/(d/(c-d))^(1/2)","B"
158,1,62283,199,3.116000," ","int((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
159,1,234091,272,11.531000," ","int((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
160,1,677,308,1.908000," ","int((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^3,x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(315 \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} c^{3}+1260 \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} c^{3}+1890 \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} c^{3}+1260 \sqrt{2}\, \sin \left(f x +e \right) \cos \left(f x +e \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} c^{3}+315 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} c^{3} \sin \left(f x +e \right)+26880 \left(\cos^{5}\left(f x +e \right)\right) c^{3}+86688 \left(\cos^{5}\left(f x +e \right)\right) c^{2} d +66240 \left(\cos^{5}\left(f x +e \right)\right) c \,d^{2}+18688 \left(\cos^{5}\left(f x +e \right)\right) d^{3}-23520 \left(\cos^{4}\left(f x +e \right)\right) c^{3}-58464 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d -33120 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{2}-9344 \left(\cos^{4}\left(f x +e \right)\right) d^{3}-3360 \left(\cos^{3}\left(f x +e \right)\right) c^{3}-22176 \left(\cos^{3}\left(f x +e \right)\right) c^{2} d -15840 \left(\cos^{3}\left(f x +e \right)\right) c \,d^{2}-2336 \left(\cos^{3}\left(f x +e \right)\right) d^{3}-6048 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d -12960 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}-2848 \left(\cos^{2}\left(f x +e \right)\right) d^{3}-4320 \cos \left(f x +e \right) c \,d^{2}-3040 \cos \left(f x +e \right) d^{3}-1120 d^{3}\right) a^{2}}{5040 f \cos \left(f x +e \right)^{4} \sin \left(f x +e \right)}"," ",0,"-1/5040/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(315*2^(1/2)*sin(f*x+e)*cos(f*x+e)^4*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*c^3+1260*2^(1/2)*sin(f*x+e)*cos(f*x+e)^3*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*c^3+1890*2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*c^3+1260*2^(1/2)*sin(f*x+e)*cos(f*x+e)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*c^3+315*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*c^3*sin(f*x+e)+26880*cos(f*x+e)^5*c^3+86688*cos(f*x+e)^5*c^2*d+66240*cos(f*x+e)^5*c*d^2+18688*cos(f*x+e)^5*d^3-23520*cos(f*x+e)^4*c^3-58464*cos(f*x+e)^4*c^2*d-33120*cos(f*x+e)^4*c*d^2-9344*cos(f*x+e)^4*d^3-3360*cos(f*x+e)^3*c^3-22176*cos(f*x+e)^3*c^2*d-15840*cos(f*x+e)^3*c*d^2-2336*cos(f*x+e)^3*d^3-6048*cos(f*x+e)^2*c^2*d-12960*cos(f*x+e)^2*c*d^2-2848*cos(f*x+e)^2*d^3-4320*cos(f*x+e)*c*d^2-3040*cos(f*x+e)*d^3-1120*d^3)/cos(f*x+e)^4/sin(f*x+e)*a^2","B"
161,1,504,234,1.797000," ","int((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^2,x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(105 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} c^{2}+315 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} c^{2}+315 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} c^{2}+105 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \sqrt{2}\, c^{2} \sin \left(f x +e \right)-4480 \left(\cos^{4}\left(f x +e \right)\right) c^{2}-9632 \left(\cos^{4}\left(f x +e \right)\right) c d -3680 \left(\cos^{4}\left(f x +e \right)\right) d^{2}+3920 \left(\cos^{3}\left(f x +e \right)\right) c^{2}+6496 \left(\cos^{3}\left(f x +e \right)\right) c d +1840 \left(\cos^{3}\left(f x +e \right)\right) d^{2}+560 \left(\cos^{2}\left(f x +e \right)\right) c^{2}+2464 \left(\cos^{2}\left(f x +e \right)\right) c d +880 \left(\cos^{2}\left(f x +e \right)\right) d^{2}+672 \cos \left(f x +e \right) c d +720 \cos \left(f x +e \right) d^{2}+240 d^{2}\right) a^{2}}{840 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"1/840/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(105*sin(f*x+e)*cos(f*x+e)^3*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*c^2+315*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*c^2+315*sin(f*x+e)*cos(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*c^2+105*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*2^(1/2)*c^2*sin(f*x+e)-4480*cos(f*x+e)^4*c^2-9632*cos(f*x+e)^4*c*d-3680*cos(f*x+e)^4*d^2+3920*cos(f*x+e)^3*c^2+6496*cos(f*x+e)^3*c*d+1840*cos(f*x+e)^3*d^2+560*cos(f*x+e)^2*c^2+2464*cos(f*x+e)^2*c*d+880*cos(f*x+e)^2*d^2+672*cos(f*x+e)*c*d+720*cos(f*x+e)*d^2+240*d^2)/sin(f*x+e)/cos(f*x+e)^3*a^2","B"
162,1,341,124,1.481000," ","int((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(15 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} c +30 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} c +15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} c \sin \left(f x +e \right)+320 \left(\cos^{3}\left(f x +e \right)\right) c +344 \left(\cos^{3}\left(f x +e \right)\right) d -280 \left(\cos^{2}\left(f x +e \right)\right) c -232 \left(\cos^{2}\left(f x +e \right)\right) d -40 c \cos \left(f x +e \right)-88 d \cos \left(f x +e \right)-24 d \right) a^{2}}{60 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)}"," ",0,"-1/60/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(15*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*c+30*cos(f*x+e)*sin(f*x+e)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*c+15*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*c*sin(f*x+e)+320*cos(f*x+e)^3*c+344*cos(f*x+e)^3*d-280*cos(f*x+e)^2*c-232*cos(f*x+e)^2*d-40*c*cos(f*x+e)-88*d*cos(f*x+e)-24*d)/cos(f*x+e)^2/sin(f*x+e)*a^2","B"
163,1,1487,173,1.498000," ","int((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x)","-\frac{\left(2 \sqrt{\frac{d}{c -d}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-\ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c^{2} \sin \left(f x +e \right)+2 \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c d \sin \left(f x +e \right)-\ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d^{2} \sin \left(f x +e \right)+\ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c^{2} \sin \left(f x +e \right)-2 \ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c d \sin \left(f x +e \right)+\ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d^{2} \sin \left(f x +e \right)+4 \sqrt{\frac{d}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, c \cos \left(f x +e \right)-4 \sqrt{\frac{d}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, c \right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{2 f \sin \left(f x +e \right) c \sqrt{\left(c +d \right) \left(c -d \right)}\, d \sqrt{\frac{d}{c -d}}}"," ",0,"-1/2/f*(2*(d/(c-d))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*((c+d)*(c-d))^(1/2)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c^2*sin(f*x+e)+2*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c*d*sin(f*x+e)-ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d^2*sin(f*x+e)+ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c^2*sin(f*x+e)-2*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c*d*sin(f*x+e)+ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d^2*sin(f*x+e)+4*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*c*cos(f*x+e)-4*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*c)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)*a^2/c/((c+d)*(c-d))^(1/2)/d/(d/(c-d))^(1/2)","B"
164,1,46082,281,2.123000," ","int((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
165,1,209489,460,8.149000," ","int((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
166,1,907,227,1.913000," ","int((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, c^{3}+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) c^{3}-9 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) c^{2} d +9 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) c \,d^{2}-3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) d^{3}+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)-9 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} d \sin \left(f x +e \right)+9 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \,d^{2} \sin \left(f x +e \right)-3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{3} \sin \left(f x +e \right)-36 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}+4 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+36 \cos \left(f x +e \right) c \,d^{2}-8 \cos \left(f x +e \right) d^{3}+4 d^{3}\right)}{6 f \sin \left(f x +e \right) \cos \left(f x +e \right) a}"," ",0,"1/6/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*cos(f*x+e)*2^(1/2)*c^3+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3*sin(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*c^3-9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*c^2*d+9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*c*d^2-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*d^3+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3*sin(f*x+e)-9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d*sin(f*x+e)+9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2*sin(f*x+e)-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^3*sin(f*x+e)-36*cos(f*x+e)^2*c*d^2+4*cos(f*x+e)^2*d^3+36*cos(f*x+e)*c*d^2-8*cos(f*x+e)*d^3+4*d^3)/sin(f*x+e)/cos(f*x+e)/a","B"
167,1,358,158,1.692000," ","int((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2} \sin \left(f x +e \right)+\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} \sin \left(f x +e \right)-2 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c d \sin \left(f x +e \right)+\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{2} \sin \left(f x +e \right)+2 \cos \left(f x +e \right) d^{2}-2 d^{2}\right)}{f \sin \left(f x +e \right) a}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2*sin(f*x+e)+(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*sin(f*x+e)-2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d*sin(f*x+e)+(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^2*sin(f*x+e)+2*cos(f*x+e)*d^2-2*d^2)/sin(f*x+e)/a","B"
168,1,194,76,1.500000," ","int((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \left(c \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)-d \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right)+c \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right)\right)}{f a}"," ",0,"-1/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(c*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))-d*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))+c*2^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2)))/a","B"
169,1,662,137,2.051000," ","int(1/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c -2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) d +2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sqrt{\frac{d}{c -d}}\, c +\sqrt{2}\, \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) d^{2}-\sqrt{2}\, \ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) d^{2}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{2 f \sqrt{\frac{d}{c -d}}\, \left(c -d \right) c \sqrt{\left(c +d \right) \left(c -d \right)}\, a}"," ",0,"-1/2/f*(2*((c+d)*(c-d))^(1/2)*2^(1/2)*(d/(c-d))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c-2*((c+d)*(c-d))^(1/2)*2^(1/2)*(d/(c-d))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*d+2*((c+d)*(c-d))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*(d/(c-d))^(1/2)*c+2^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*d^2-2^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*d^2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(d/(c-d))^(1/2)/(c-d)/c/((c+d)*(c-d))^(1/2)/a","B"
170,1,117715,355,5.174000," ","int(1/(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
171,1,402966,564,24.788000," ","int(1/(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
172,1,957,280,1.882000," ","int((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(4 \sqrt{2}\, \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{3}+4 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)+5 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{3}-3 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{2} d -9 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c \,d^{2}+7 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) d^{3}+5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)-3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} d \sin \left(f x +e \right)-9 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \,d^{2} \sin \left(f x +e \right)+7 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{3} \sin \left(f x +e \right)-2 \left(\cos^{2}\left(f x +e \right)\right) c^{3}+6 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d -6 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}+10 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+2 c^{3} \cos \left(f x +e \right)-6 \cos \left(f x +e \right) c^{2} d +6 \cos \left(f x +e \right) c \,d^{2}-2 \cos \left(f x +e \right) d^{3}-8 d^{3}\right)}{4 f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(4*2^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*c^3+4*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3*sin(f*x+e)+5*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^3-3*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^2*d-9*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c*d^2+7*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*d^3+5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3*sin(f*x+e)-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d*sin(f*x+e)-9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2*sin(f*x+e)+7*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^3*sin(f*x+e)-2*cos(f*x+e)^2*c^3+6*cos(f*x+e)^2*c^2*d-6*cos(f*x+e)^2*c*d^2+10*cos(f*x+e)^2*d^3+2*c^3*cos(f*x+e)-6*cos(f*x+e)*c^2*d+6*cos(f*x+e)*c*d^2-2*cos(f*x+e)*d^3-8*d^3)/sin(f*x+e)^3/a^2","B"
173,1,756,248,1.548000," ","int((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-4 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) c^{2} \cos \left(f x +e \right)-5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{2} \cos \left(f x +e \right)+2 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c d \cos \left(f x +e \right)+3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) d^{2} \cos \left(f x +e \right)-4 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2} \sin \left(f x +e \right)-5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} \sin \left(f x +e \right)+2 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c d \sin \left(f x +e \right)+3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{2} \sin \left(f x +e \right)+2 \left(\cos^{2}\left(f x +e \right)\right) c^{2}-4 \left(\cos^{2}\left(f x +e \right)\right) c d +2 \left(\cos^{2}\left(f x +e \right)\right) d^{2}-2 \cos \left(f x +e \right) c^{2}+4 \cos \left(f x +e \right) c d -2 \cos \left(f x +e \right) d^{2}\right)}{4 f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}}"," ",0,"1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-4*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*sin(f*x+e)*c^2*cos(f*x+e)-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^2*cos(f*x+e)+2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c*d*cos(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*d^2*cos(f*x+e)-4*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2*sin(f*x+e)-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*sin(f*x+e)+2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d*sin(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^2*sin(f*x+e)+2*cos(f*x+e)^2*c^2-4*cos(f*x+e)^2*c*d+2*cos(f*x+e)^2*d^2-2*cos(f*x+e)*c^2+4*cos(f*x+e)*c*d-2*cos(f*x+e)*d^2)/(1+cos(f*x+e))/sin(f*x+e)/a^2","B"
174,1,552,106,1.380000," ","int((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-4 \sqrt{2}\, \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c \cos \left(f x +e \right)-5 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \cos \left(f x +e \right)+\sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d \cos \left(f x +e \right)-4 \sqrt{2}\, \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c -5 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c +\sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d +2 \left(\cos^{2}\left(f x +e \right)\right) c -2 \left(\cos^{2}\left(f x +e \right)\right) d -2 c \cos \left(f x +e \right)+2 d \cos \left(f x +e \right)\right)}{4 f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) a^{2}}"," ",0,"1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-4*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*cos(f*x+e)-5*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*cos(f*x+e)+sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d*cos(f*x+e)-4*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c-5*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c+sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d+2*cos(f*x+e)^2*c-2*cos(f*x+e)^2*d-2*c*cos(f*x+e)+2*d*cos(f*x+e))/(1+cos(f*x+e))/sin(f*x+e)/a^2","B"
175,1,2076,334,1.783000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c^{2}-8 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c d +4 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, d^{2}+4 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c^{2}-8 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c d +4 \sqrt{2}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, d^{2}-2 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) d^{3}+2 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) d^{3}+5 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c^{2}-9 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c d -2 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(\frac{2 \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-2 \sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)-2 c \sin \left(f x +e \right)+2 d \sin \left(f x +e \right)-2 \sqrt{\left(c +d \right) \left(c -d \right)}}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}\right) \sin \left(f x +e \right) d^{3}+2 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{2 \left(\sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}\, c \sin \left(f x +e \right)-\sqrt{2}\, \sqrt{\frac{d}{c -d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d}\right) \sin \left(f x +e \right) d^{3}+5 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c^{2}-9 \sqrt{\left(c +d \right) \left(c -d \right)}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c d -2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{d}{c -d}}\, c^{2}+2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{d}{c -d}}\, c d +2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c^{2}-2 \sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \left(f x +e \right) \sqrt{\frac{d}{c -d}}\, c d \right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{4 f \sin \left(f x +e \right)^{3} \sqrt{\frac{d}{c -d}}\, \left(c -d \right)^{2} c \sqrt{\left(c +d \right) \left(c -d \right)}\, a^{2}}"," ",0,"1/4/f*(-1+cos(f*x+e))*(4*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*cos(f*x+e)*(d/(c-d))^(1/2)*c^2-8*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*cos(f*x+e)*(d/(c-d))^(1/2)*c*d+4*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*cos(f*x+e)*(d/(c-d))^(1/2)*d^2+4*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*(d/(c-d))^(1/2)*c^2-8*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*(d/(c-d))^(1/2)*c*d+4*2^(1/2)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*(d/(c-d))^(1/2)*d^2-2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*sin(f*x+e)*cos(f*x+e)*d^3+2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*sin(f*x+e)*cos(f*x+e)*d^3+5*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*(d/(c-d))^(1/2)*c^2-9*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)*(d/(c-d))^(1/2)*c*d-2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*sin(f*x+e)*d^3+2*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*sin(f*x+e)*d^3+5*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*(d/(c-d))^(1/2)*c^2-9*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*(d/(c-d))^(1/2)*c*d-2*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(d/(c-d))^(1/2)*c^2+2*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(d/(c-d))^(1/2)*c*d+2*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(d/(c-d))^(1/2)*c^2-2*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(d/(c-d))^(1/2)*c*d)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(d/(c-d))^(1/2)/(c-d)^2/c/((c+d)*(c-d))^(1/2)/a^2","B"
176,1,164796,480,5.454000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
177,1,480553,694,31.938000," ","int(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
178,1,1444,415,1.898000," ","int((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(30 \cos \left(f x +e \right) c \,d^{2}+9 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} d +15 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \,d^{2}-32 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3}+18 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{2} d +30 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c \,d^{2}-64 \sqrt{2}\, \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{3}-42 \left(\cos^{3}\left(f x +e \right)\right) c^{2} d -43 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)+19 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{3} \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+18 \cos \left(f x +e \right) c^{2} d -6 \left(\cos^{3}\left(f x +e \right)\right) c \,d^{2}-24 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}-32 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c^{3} \sin \left(f x +e \right)-43 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{3}+19 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{3}+24 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d -86 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{3}+38 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) d^{3}+9 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} d \sin \left(f x +e \right)+15 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \,d^{2} \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right) c^{3}-26 \cos \left(f x +e \right) d^{3}-22 c^{3} \cos \left(f x +e \right)+30 \left(\cos^{3}\left(f x +e \right)\right) c^{3}+18 \left(\cos^{3}\left(f x +e \right)\right) d^{3}\right)}{32 f \left(1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{3} a^{3}}"," ",0,"-1/32/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(-6*cos(f*x+e)^3*c*d^2+24*cos(f*x+e)^2*c^2*d-24*cos(f*x+e)^2*c*d^2+30*cos(f*x+e)*c*d^2-64*2^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*sin(f*x+e)*c^3+18*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^2*d+30*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c*d^2-32*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3-42*cos(f*x+e)^3*c^2*d-43*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3*sin(f*x+e)+19*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^3*sin(f*x+e)+9*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d+15*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2+18*cos(f*x+e)*c^2*d-43*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3+19*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^3-32*2^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3*sin(f*x+e)-86*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^3+38*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*d^3+9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d*sin(f*x+e)+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2*sin(f*x+e)+18*cos(f*x+e)^3*d^3+8*cos(f*x+e)^2*d^3-26*cos(f*x+e)*d^3-8*cos(f*x+e)^2*c^3-22*c^3*cos(f*x+e)+30*cos(f*x+e)^3*c^3)/(1+cos(f*x+e))/sin(f*x+e)^3/a^3","B"
179,1,1133,403,1.636000," ","int((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(32 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c^{2}+64 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) c^{2} \cos \left(f x +e \right)+43 \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c^{2}-6 \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c d -5 \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, d^{2}+32 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, c^{2} \sin \left(f x +e \right)+86 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c^{2} \cos \left(f x +e \right)-12 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) c d \cos \left(f x +e \right)-10 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) d^{2} \cos \left(f x +e \right)+43 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c^{2} \sin \left(f x +e \right)-6 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c d \sin \left(f x +e \right)-5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d^{2} \sin \left(f x +e \right)-30 \left(\cos^{3}\left(f x +e \right)\right) c^{2}+28 \left(\cos^{3}\left(f x +e \right)\right) c d +2 \left(\cos^{3}\left(f x +e \right)\right) d^{2}+8 \left(\cos^{2}\left(f x +e \right)\right) c^{2}-16 \left(\cos^{2}\left(f x +e \right)\right) c d +8 \left(\cos^{2}\left(f x +e \right)\right) d^{2}+22 \cos \left(f x +e \right) c^{2}-12 \cos \left(f x +e \right) c d -10 \cos \left(f x +e \right) d^{2}\right)}{32 f \left(1+\cos \left(f x +e \right)\right)^{2} \sin \left(f x +e \right) a^{3}}"," ",0,"-1/32/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(32*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*cos(f*x+e)^2*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c^2+64*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*sin(f*x+e)*c^2*cos(f*x+e)+43*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c^2-6*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c*d-5*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d^2+32*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*c^2*sin(f*x+e)+86*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c^2*cos(f*x+e)-12*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*c*d*cos(f*x+e)-10*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*d^2*cos(f*x+e)+43*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*sin(f*x+e)-6*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d*sin(f*x+e)-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d^2*sin(f*x+e)-30*cos(f*x+e)^3*c^2+28*cos(f*x+e)^3*c*d+2*cos(f*x+e)^3*d^2+8*cos(f*x+e)^2*c^2-16*cos(f*x+e)^2*c*d+8*cos(f*x+e)^2*d^2+22*cos(f*x+e)*c^2-12*cos(f*x+e)*c*d-10*cos(f*x+e)*d^2)/(1+cos(f*x+e))^2/sin(f*x+e)/a^3","B"
180,1,824,139,1.727000," ","int((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(32 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c +64 \sqrt{2}\, \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c \cos \left(f x +e \right)+43 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c -3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d +32 \sqrt{2}\, \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{2 \cos \left(f x +e \right)}\right) c +86 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c \cos \left(f x +e \right)-6 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d \cos \left(f x +e \right)+43 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) c -3 \sin \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sin \left(f x +e \right)}\right) d -30 \left(\cos^{3}\left(f x +e \right)\right) c +14 \left(\cos^{3}\left(f x +e \right)\right) d +8 \left(\cos^{2}\left(f x +e \right)\right) c -8 \left(\cos^{2}\left(f x +e \right)\right) d +22 c \cos \left(f x +e \right)-6 d \cos \left(f x +e \right)\right)}{32 f \left(1+\cos \left(f x +e \right)\right)^{2} \sin \left(f x +e \right) a^{3}}"," ",0,"-1/32/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(32*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*c+64*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*cos(f*x+e)+43*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2*c-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2*d+32*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c+86*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*cos(f*x+e)-6*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d*cos(f*x+e)+43*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c-3*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*d-30*cos(f*x+e)^3*c+14*cos(f*x+e)^3*d+8*cos(f*x+e)^2*c-8*cos(f*x+e)^2*d+22*c*cos(f*x+e)-6*d*cos(f*x+e))/(1+cos(f*x+e))^2/sin(f*x+e)/a^3","B"
181,1,3860,509,2.046000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x)","\text{output too large to display}"," ",0,"-1/32/f*(-1+cos(f*x+e))^2*(115*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2-16*2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*d^4+32*2^(1/2)*sin(f*x+e)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*d^4+43*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3+16*2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*d^4-30*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^3*c^3+8*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*c^3+22*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*c^3-32*2^(1/2)*sin(f*x+e)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*d^4-16*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2)*cos(f*x+e)+((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d))*d^4-96*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^2*d+96*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*d^2-252*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d+230*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2+32*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3-32*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*d^3+64*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3-64*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*d^3-126*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d+76*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^3*c^2*d-46*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^3*c*d^2-16*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*c^2*d+8*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*c*d^2-60*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*c^2*d+38*(d/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*c*d^2+16*2^(1/2)*sin(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(2*((d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2)*c*sin(f*x+e)-2^(1/2)*(d/(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)+((c+d)*(c-d))^(1/2)*cos(f*x+e)-c*sin(f*x+e)+d*sin(f*x+e)-((c+d)*(c-d))^(1/2))/(((c+d)*(c-d))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d))*d^4-96*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^2*d+96*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*d^2-192*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^2*d+192*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c*d^2+43*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3+32*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*c^3-32*2^(1/2)*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*arctanh(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)*2^(1/2))*d^3+86*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^3-126*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c^2*d+115*(d/(c-d))^(1/2)*sin(f*x+e)*((c+d)*(c-d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*ln(-(-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+cos(f*x+e)-1)/sin(f*x+e))*c*d^2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/(d/(c-d))^(1/2)/(c-d)^3/c/((c+d)*(c-d))^(1/2)/a^3","B"
182,1,197500,653,7.791000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
183,1,556423,868,44.265000," ","int(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
184,1,1562,99,2.243000," ","int((c+d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c^{2} d -2 \sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c \,d^{2}+\sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d^{3}-\sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c +d \right)}{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}\right) c^{2} d +2 \sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c +d \right)}{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}\right) c \,d^{2}-\sqrt{c -d}\, \ln \left(-\frac{2 \left(\sqrt{2}\, \sqrt{-d}\, \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c +d \right)}{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}\right) d^{3}+\ln \left(\frac{\sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{c -d}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}{\sin \left(f x +e \right) \sqrt{c -d}}\right) \sqrt{2}\, \sqrt{-d}\, c^{3}-3 \ln \left(\frac{\sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{c -d}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}{\sin \left(f x +e \right) \sqrt{c -d}}\right) \sqrt{2}\, \sqrt{-d}\, c^{2} d +3 \ln \left(\frac{\sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{c -d}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}{\sin \left(f x +e \right) \sqrt{c -d}}\right) \sqrt{2}\, \sqrt{-d}\, c \,d^{2}-\ln \left(\frac{\sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{c -d}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d}{\sin \left(f x +e \right) \sqrt{c -d}}\right) \sqrt{2}\, \sqrt{-d}\, d^{3}-\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{-d}\, c^{3}+3 \ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{-d}\, c^{2} d -3 \ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{-d}\, c \,d^{2}+\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{-d}\, d^{3}-2 \sqrt{-\left(c -d \right)^{4} c}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{c -d}\, \sqrt{-d}\right) \sqrt{2}}{f \sin \left(f x +e \right)^{2} \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{c -d}\, \sqrt{-d}\, \left(c^{2}-2 c d +d^{2}\right)}"," ",0,"1/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*((c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(f*x+e)))*c^2*d-2*(c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(f*x+e)))*c*d^2+(c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(f*x+e)))*d^3-(c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)-c+d)/(-sin(f*x+e)-1+cos(f*x+e)))*c^2*d+2*(c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)-c+d)/(-sin(f*x+e)-1+cos(f*x+e)))*c*d^2-(c-d)^(1/2)*ln(-2*(2^(1/2)*(-d)^(1/2)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)-c+d)/(-sin(f*x+e)-1+cos(f*x+e)))*d^3+ln(((-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/sin(f*x+e)/(c-d)^(1/2))*2^(1/2)*(-d)^(1/2)*c^3-3*ln(((-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/sin(f*x+e)/(c-d)^(1/2))*2^(1/2)*(-d)^(1/2)*c^2*d+3*ln(((-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/sin(f*x+e)/(c-d)^(1/2))*2^(1/2)*(-d)^(1/2)*c*d^2-ln(((-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/sin(f*x+e)/(c-d)^(1/2))*2^(1/2)*(-d)^(1/2)*d^3-ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*2^(1/2)*(-d)^(1/2)*c^3+3*ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*2^(1/2)*(-d)^(1/2)*c^2*d-3*ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*2^(1/2)*(-d)^(1/2)*c*d^2+ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*2^(1/2)*(-d)^(1/2)*d^3-2*(-(c-d)^4*c)^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))*(c-d)^(1/2)*(-d)^(1/2))/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)/(c-d)^(1/2)*2^(1/2)/(-d)^(1/2)/(c^2-2*c*d+d^2)","B"
185,1,189,49,1.957000," ","int((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{2}\, \sqrt{-\left(c -d \right)^{4} c}}{f \sin \left(f x +e \right)^{2} \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \left(c^{2}-2 c d +d^{2}\right) c}"," ",0,"-2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*2^(1/2)*(-(c-d)^4*c)^(1/2)/(c^2-2*c*d+d^2)/c","B"
186,1,377,95,2.046000," ","int((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),x)","-\frac{\left(\sqrt{2}\, \sqrt{-\left(c -d \right)^{4} c}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)+\sqrt{2}\, \sqrt{-\left(c -d \right)^{4} c}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, d \sin \left(f x +e \right)-2 c^{3} d \cos \left(f x +e \right)+4 \cos \left(f x +e \right) c^{2} d^{2}-2 \cos \left(f x +e \right) c \,d^{3}+2 c^{3} d -4 c^{2} d^{2}+2 c \,d^{3}\right) \cos \left(f x +e \right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right) \left(c +d \right) c^{2} \left(c^{2}-2 c d +d^{2}\right)}"," ",0,"-1/f*(2^(1/2)*(-(c-d)^4*c)^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)+2^(1/2)*(-(c-d)^4*c)^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*d*sin(f*x+e)-2*c^3*d*cos(f*x+e)+4*cos(f*x+e)*c^2*d^2-2*cos(f*x+e)*c*d^3+2*c^3*d-4*c^2*d^2+2*c*d^3)*cos(f*x+e)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)/(d+c*cos(f*x+e))/sin(f*x+e)/(c+d)/c^2/(c^2-2*c*d+d^2)","B"
187,1,494,114,1.885000," ","int((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \left(\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c^{3}-3 \ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c^{2} d +3 \ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c \,d^{2}-\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) d^{3}+\sqrt{2}\, \sqrt{-\left(c -d \right)^{4} c}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{c -d}\right)}{f \sin \left(f x +e \right)^{2} \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, a \sqrt{c -d}\, \left(c^{2}-2 c d +d^{2}\right)}"," ",0,"-2/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*(ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c^3-3*ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c^2*d+3*ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c*d^2-ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*d^3+2^(1/2)*(-(c-d)^4*c)^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))*(c-d)^(1/2))/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)/a/(c-d)^(1/2)/(c^2-2*c*d+d^2)","B"
188,1,424,114,2.133000," ","int(1/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{2}\, \sqrt{-\left(c -d \right)^{4} c}\, \arctan \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \left(c -d \right)^{2} c \sqrt{2}}{\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-\left(c -d \right)^{4} c}}\right) \sqrt{c -d}+\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c^{3}-2 \ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c^{2} d +\ln \left(-\frac{\sqrt{c -d}\, \cos \left(f x +e \right)-\sin \left(f x +e \right) \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}-\sqrt{c -d}}{\sin \left(f x +e \right)}\right) c \,d^{2}\right)}{f \sin \left(f x +e \right)^{2} \sqrt{-\frac{2 \left(d +c \cos \left(f x +e \right)\right)}{1+\cos \left(f x +e \right)}}\, a \sqrt{c -d}\, \left(c^{2}-2 c d +d^{2}\right) c}"," ",0,"-2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)*(-1+cos(f*x+e))*(2^(1/2)*(-(c-d)^4*c)^(1/2)*arctan((-1+cos(f*x+e))/sin(f*x+e)/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*(c-d)^2*c*2^(1/2)/(-(c-d)^4*c)^(1/2))*(c-d)^(1/2)+ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c^3-2*ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c^2*d+ln(-((c-d)^(1/2)*cos(f*x+e)-sin(f*x+e)*(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)-(c-d)^(1/2))/sin(f*x+e))*c*d^2)/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)/a/(c-d)^(1/2)/(c^2-2*c*d+d^2)/c","B"
189,1,113,58,0.736000," ","int((a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x)","-\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) d a}{f c \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b}{f \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f c}"," ",0,"-2/f/c/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*d*a+2/f/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b+2/f*a/c*arctan(tan(1/2*e+1/2*f*x))","A"
190,1,328,114,0.769000," ","int((a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x)","-\frac{2 d^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a}{f c \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}+\frac{2 d \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b}{f \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}-\frac{4 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a d}{f \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a \,d^{3}}{f \,c^{2} \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b}{f \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{2}}"," ",0,"-2/f/c*d^2/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*a+2/f*d/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*b-4/f/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*d+2/f/c^2/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*d^3+2/f*c/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b+2/f*a/c^2*arctan(tan(1/2*e+1/2*f*x))","B"
191,1,1063,191,0.773000," ","int((a+b*sec(f*x+e))/(c+d*sec(f*x+e))^3,x)","-\frac{6 d^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{d^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 c d \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{d^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{6 d^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{d^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{2 d^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{4 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{d^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{5 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a \,d^{3}}{f c \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a \,d^{5}}{f \,c^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 c^{2} \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{\arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b \,d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{3}}"," ",0,"-6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^3/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a+2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^4/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a+4/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b+1/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^3/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a-2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^4/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a-4/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b+1/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2*d^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b-6/f*c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*d+5/f/c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*d^3-2/f/c^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*d^5+2/f*c^2/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b+1/f/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b*d^2+2/f*a/c^3*arctan(tan(1/2*e+1/2*f*x))","B"
192,1,462,124,0.782000," ","int((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x)","-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} d^{2}}{f c \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}+\frac{4 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b d}{f \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}-\frac{2 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2}}{f \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}-\frac{4 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} d}{f \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} d^{3}}{f \,c^{2} \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{4 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a b}{f \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{2} d}{f \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{2}}"," ",0,"-2/f/c/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*a^2*d^2+4/f/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*a*b*d-2/f*c/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*b^2-4/f/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d+2/f/c^2/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^3+4/f*c/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b-2/f/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^2*d+2/f*a^2/c^2*arctan(tan(1/2*e+1/2*f*x))","B"
193,1,1593,224,0.738000," ","int((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x)","-\frac{6 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} d^{3}}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} d^{4}}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{8 c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a b d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a b \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 c^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{2} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} d^{3}}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} d^{4}}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{8 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{2 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{5 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} d^{3}}{f c \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} d^{5}}{f \,c^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{4 c^{2} \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a b}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a b \,d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{3 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{2} d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{3}}"," ",0,"-6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^2-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^3+2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^4+8/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*d+2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*d^2-2/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2-1/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2*d-2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2*d^2+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*d^2-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*d^3-2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*d^4-8/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b*d+2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b*d^2+2/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^2-1/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^2*d+2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^2*d^2-6/f*c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d+5/f/c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^3-2/f/c^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^5+4/f*c^2/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b+2/f/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b*d^2-3/f*c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^2*d+2/f*a^2/c^3*arctan(tan(1/2*e+1/2*f*x))","B"
194,1,3293,362,0.802000," ","int((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^4,x)","\text{output too large to display}"," ",0,"2/f*a^2/c^4*arctan(tan(1/2*e+1/2*f*x))+6/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*d^4-1/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*d^5-8/3/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*d^3+4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b*d^3-2/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*d^6+2/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^2*d-6/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^2*d^2+6/f*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b*d^2-12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*d^2+6/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*d^4+1/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*d^5-2/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*d^6-2/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^2*d-6/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^2*d^2+24/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^2-44/3/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^4+4/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*d^6+28/3/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2*d^2-12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*d^2+4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b*d^3+6/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b*d^2+12/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b*d+12/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b*d+1/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^2*d^3-4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*d^3-1/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^2*d^3+4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*d^3-8/f*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d-4/f*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^2*d+2/f/c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^7+4/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2-2/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^2-7/f/c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^5+4/f*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b-2/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^2-24/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*d-6/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b*d^2+8/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*d^3-1/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^2*d^3","B"
195,1,2031,241,0.723000," ","int((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x)","\frac{6 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,b^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{4 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{3} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a \,b^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,b^{2} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} b \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{3 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} b \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{3} d^{3}}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{f \,c^{3}}-\frac{9 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a \,b^{2} d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{12 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} b d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{3 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,b^{2} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{3 c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a \,b^{2} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{12 c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} b d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{3} d^{4}}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{6 c^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a \,b^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{3} d}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} d^{3}}{f c \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} d^{4}}{f \,c^{2} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{c^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{3}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{3}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{3} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} d^{2}}{f \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 c \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{3} d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{3 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} b \,d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{5 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{3} d^{3}}{f c \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{3} d^{5}}{f \,c^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{6 c^{2} \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} b}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{c^{2} \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{3}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c -d \right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{3} d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}"," ",0,"2/f*a^3/c^3*arctan(tan(1/2*e+1/2*f*x))+12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*b*d-12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*b*d-3/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b^2*d+6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b^2-4/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^3*d-6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b^2*d^2+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b^2*d^2+3/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*b*d^2-3/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b^2*d+3/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*b*d^2-9/f*c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b^2*d-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^3+2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^4-6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b^2+4/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^3*d-1/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^3*d^3-2/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^3*d^4-6/f*c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d+1/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^3+1/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^3+3/f/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*b*d^2-6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^2+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^3*d^2+5/f/c/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d^3-2/f/c^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d^5+6/f*c^2/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*b+1/f*c^2/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^3+2/f/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^3*d^2","B"
196,1,4330,397,0.764000," ","int((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^4,x)","\text{output too large to display}"," ",0,"-12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^3*d^2-4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*b*d^3+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*b*d^3+24/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^2-44/3/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^4+4/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^3*d^6+3/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b^2*d^3-3/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b^2*d^3-6/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b^2+6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^3*d-2/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^3*d^2-12/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^3*d^2+6/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^3*d^4+1/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^3*d^5-2/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^3*d^6-6/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b^2-28/3/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^3*d+6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^3*d+2/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^3*d^2+9/f*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*b*d^2-12/f*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b^2*d+12/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b^2+6/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*b*d^3+6/f/c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^3*d^4-1/f/c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^3*d^5-2/f/c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^3*d^6+2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^3*d^3-4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^3*d^3+2/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^3*d^3-3/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a*b^2*d^3-8/f*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d+2/f/c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d^7+1/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*b^3-1/f*c^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*b^3-7/f/c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d^5+6/f*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^2*b+4/f*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^3*d^2-4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^3*d^3+4/f/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^3*d^3+2/f*a^3/c^4*arctan(tan(1/2*e+1/2*f*x))+18/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*b*d+28/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b^2*d^2+6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b^2*d-18/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a*b^2*d^2-6/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b^2*d-18/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a*b^2*d^2-36/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c^2-2*c*d+d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*b*d+8/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*a^3*d^3+1/f*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*b^3+9/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*b*d^2+18/f*c^2/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5*a^2*b*d-9/f*c/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)*a^2*b*d^2","B"
197,1,8573,603,0.795000," ","int((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
198,1,1372,293,1.944000," ","int((c+d*sec(f*x+e))*(a+b*sec(f*x+e))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a c -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a d -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b c -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b d +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a d +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b d -2 \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a c +\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a c -\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a d \sin \left(f x +e \right)-\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b c \sin \left(f x +e \right)-\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b d \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a d \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b d \sin \left(f x +e \right)-2 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a c \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) a d +\cos \left(f x +e \right) a d -\cos \left(f x +e \right) b d +b d \right)}{f \sin \left(f x +e \right)^{5} \left(b +a \cos \left(f x +e \right)\right)}"," ",0,"2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*c-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*d+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*d-2*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a*c+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*c-(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d*sin(f*x+e)-(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c*sin(f*x+e)-(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*d*sin(f*x+e)+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d*sin(f*x+e)+(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*d*sin(f*x+e)-2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a*c*sin(f*x+e)-cos(f*x+e)^2*a*d+cos(f*x+e)*a*d-cos(f*x+e)*b*d+b*d)/sin(f*x+e)^5/(b+a*cos(f*x+e))","B"
199,1,443,206,1.693000," ","int((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,c^{2}+\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a c d -\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \,c^{2}-\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b c d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) a \,d^{2}+2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) b c d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a \,c^{2}+2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a \,d^{2}\right) \left(-1+\cos \left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} c \left(c -d \right) \left(c +d \right)}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*c^2+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*c*d-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c^2-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*a*d^2+2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*b*c*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a*c^2+2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a*d^2)*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/c/(c-d)/(c+d)","B"
200,1,2337,345,1.884000," ","int((a+b*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-2/3/f*(-1+cos(f*x+e))^2*(4*cos(f*x+e)^3*a^2*d-4*cos(f*x+e)^2*a^2*d+3*cos(f*x+e)^3*a*b*c-b^2*d+cos(f*x+e)^3*a*b*d-3*cos(f*x+e)^2*a*b*c+4*cos(f*x+e)^2*a*b*d-5*cos(f*x+e)*a*b*d+3*cos(f*x+e)^2*b^2*c-3*cos(f*x+e)*b^2*c+cos(f*x+e)^2*b^2*d-3*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*c+6*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c-3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c+3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d+3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*c+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*d-4*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d-3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*c+6*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c+3*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d+3*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*c-3*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c+cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*d-4*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d+4*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d-3*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c-4*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d+6*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c+4*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d-3*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c-4*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d+6*cos(f*x+e)^2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2/(b+a*cos(f*x+e))/cos(f*x+e)/sin(f*x+e)^5","B"
201,1,581,303,1.704000," ","int((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} c^{2}+\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} c d -2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \,c^{2}-2 \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b c d +\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} c^{2}+\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} c d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} d^{2}+4 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) a b c d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} c^{2}-2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} c^{2}+2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} d^{2}\right) \left(-1+\cos \left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} c \left(c -d \right) \left(c +d \right)}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*c^2+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*c*d-2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b*c^2-2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b*c*d+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^2*c^2+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^2*c*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*a^2*d^2+4*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*a*b*c*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*b^2*c^2-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a^2*c^2+2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a^2*d^2)*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/c/(c-d)/(c+d)","A"
202,1,3285,403,2.199000," ","int((a+b*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x)","\text{output too large to display}"," ",0,"-2/15/f*(1+cos(f*x+e))^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))^2*(15*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*d+5*cos(f*x+e)^3*b^3*c+23*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*d+35*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*c+17*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*d-35*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*c-23*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*d-35*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*c-9*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*d+45*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*c+23*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*d+35*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*c+17*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*d-35*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*c-23*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*d-35*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*c-9*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*b^2*d+45*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^2*b*c-5*cos(f*x+e)*b^3*c+23*cos(f*x+e)^4*a^3*d-23*cos(f*x+e)^3*a^3*d+9*cos(f*x+e)^3*b^3*d-6*cos(f*x+e)^2*b^3*d-3*b^3*d-35*cos(f*x+e)^3*a^2*b*c+23*cos(f*x+e)^3*a^2*b*d+35*cos(f*x+e)^3*a*b^2*c+5*cos(f*x+e)^3*a*b^2*d-34*cos(f*x+e)^2*a^2*b*d-40*cos(f*x+e)^2*a*b^2*c-14*cos(f*x+e)*a*b^2*d+35*cos(f*x+e)^4*a^2*b*c+11*cos(f*x+e)^4*a^2*b*d+5*cos(f*x+e)^4*a*b^2*c+9*cos(f*x+e)^4*a*b^2*d-15*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*c-23*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*d+9*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*d+5*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*c+9*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*d-23*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*d-9*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*d+30*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a^3*c+30*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*a^3*c-15*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*c+15*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a^3*d+5*cos(f*x+e)^2*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*c-9*cos(f*x+e)^3*sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b^3*d)/(b+a*cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^5","B"
203,1,215,190,1.720000," ","int((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) c -\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) c \right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*c-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*c)/(b+a*cos(f*x+e))/sin(f*x+e)^2","A"
204,1,318,202,1.804000," ","int(1/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(c^{2} \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)+d \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) c -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \frac{c -d}{c +d}, \sqrt{\frac{a -b}{a +b}}\right) d^{2}-2 c^{2} \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)+2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) d^{2}\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} c \left(c -d \right) \left(c +d \right)}"," ",0,"-2/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(c^2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))+d*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*c-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*d^2-2*c^2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))+2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*d^2)/(b+a*cos(f*x+e))/sin(f*x+e)^2/c/(c-d)/(c+d)","A"
205,1,2010,347,1.804000," ","int((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(-\left(\cos^{2}\left(f x +e \right)\right) a b c -\left(\cos^{2}\left(f x +e \right)\right) a b d +\left(\cos^{2}\left(f x +e \right)\right) b^{2} c +\left(\cos^{2}\left(f x +e \right)\right) a^{2} d +\cos \left(f x +e \right) a b c -\cos \left(f x +e \right) a^{2} d +\cos \left(f x +e \right) a b d -\cos \left(f x +e \right) b^{2} c -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a^{2} d +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) b^{2} c +2 \cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a^{2} c -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a^{2} c +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a^{2} d -\sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a^{2} c +\sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a^{2} d -\sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a^{2} d +\sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, b^{2} c +2 \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a^{2} c -2 \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, b^{2} c -2 \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, b^{2} c -\sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a b c +\sin \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a b d +\sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a b c -\sin \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, a b d +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a b d +\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a b c -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a b d -\cos \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(f x +e \right) a b c \right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right) a \left(a +b \right) \left(a -b \right)}"," ",0,"-1/f*4^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)^2*a^2*d-sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*c+sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*d+cos(f*x+e)*a*b*c-cos(f*x+e)*a^2*d-cos(f*x+e)^2*a*b*c-cos(f*x+e)^2*a*b*d+cos(f*x+e)*a*b*d+cos(f*x+e)^2*b^2*c-cos(f*x+e)*b^2*c-2*cos(f*x+e)*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*c-sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a*b*c+sin(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a*b*d+sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a*b*c-sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a*b*d-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*d+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*b^2*c+2*cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*sin(f*x+e)*a^2*c-sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*d+sin(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*c+2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*a^2*c-2*sin(f*x+e)*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-1,((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*b^2*c-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d+cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*c-cos(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*b*d)/(b+a*cos(f*x+e))/sin(f*x+e)/a/(a+b)/(a-b)","B"
206,1,5710,456,1.806000," ","int((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
207,1,543,363,2.293000," ","int((a+b*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2),x)","\frac{2 \left(2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) b d +2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) a c -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) a c +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) a d +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) b c -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) b d \right) \cos \left(f x +e \right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/f*(2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*b*d+2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*c-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*d+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*d)*cos(f*x+e)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^2*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/((a-b)/(a+b))^(1/2)","A"
208,1,352,183,2.146000," ","int((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x)","\frac{2 \left(2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) a -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) a +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) b \right) \cos \left(f x +e \right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/f*(2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b)*cos(f*x+e)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/((a-b)/(a+b))^(1/2)","A"
209,1,2847,553,2.686000," ","int((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"2/f*(sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c*d-cos(f*x+e)^2*((a-b)/(a+b))^(1/2)*a*d^2+cos(f*x+e)*((a-b)/(a+b))^(1/2)*a*d^2-cos(f*x+e)*((a-b)/(a+b))^(1/2)*b*d^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c*d-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c*d+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c*d-b*c*d*((a-b)/(a+b))^(1/2)+b*d^2*((a-b)/(a+b))^(1/2)+2*sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*d^2+cos(f*x+e)^2*((a-b)/(a+b))^(1/2)*a*c*d-cos(f*x+e)*((a-b)/(a+b))^(1/2)*a*c*d+cos(f*x+e)*((a-b)/(a+b))^(1/2)*b*c*d+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*d^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*d^2-2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*c^2+2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*d^2+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c*d-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*c*d+sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c*d+sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*d^2-2*sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*c^2-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c^2-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*d^2)*cos(f*x+e)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/c/(c+d)/(c-d)/((a-b)/(a+b))^(1/2)","B"
210,1,15724,820,3.079000," ","int((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
211,1,4298,675,2.098000," ","int((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"2/f*(b^2*c^2*((a-b)/(a+b))^(1/2)-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c^2-2*sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a^2*c^2+2*sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a^2*d^2+((a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b*c*d-((a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2*c^2-((a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*d^2+((a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*d^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c*d+sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c^2-2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a^2*c^2+2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a^2*d^2+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-2*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c^2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+a*b*d^2*((a-b)/(a+b))^(1/2)-b^2*c*d*((a-b)/(a+b))^(1/2)-2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c*d+2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c*d-((a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a*b*c^2-((a-b)/(a+b))^(1/2)*cos(f*x+e)*a^2*c*d+((a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b*c^2-((a-b)/(a+b))^(1/2)*cos(f*x+e)*a*b*d^2+((a-b)/(a+b))^(1/2)*cos(f*x+e)*b^2*c*d+((a-b)/(a+b))^(1/2)*cos(f*x+e)^2*a^2*c*d-sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*d^2+2*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-2*sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c*d-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c*d+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*d^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c*d-2*sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c*d-a*b*c*d*((a-b)/(a+b))^(1/2)+sin(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c^2+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*c^2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a*b*d^2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*c^2+sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*a^2*d^2-sin(f*x+e)*cos(f*x+e)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b^2*c^2)*cos(f*x+e)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/c/(c-d)/((a-b)/(a+b))^(1/2)/(c+d)","B"
212,1,13060,840,2.234000," ","int((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
213,1,39420,1037,3.402000," ","int((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
214,1,15922,812,2.296000," ","int((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
215,1,32283,1065,2.977000," ","int((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
216,1,75468,1337,4.944000," ","int((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
217,1,491,623,2.103000," ","int((c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x)","\frac{2 \left(2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) d^{2}+2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) c^{2}-\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) c^{2}+2 \EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) c d -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) d^{2}\right) \cos \left(f x +e \right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/f*(2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*d^2+2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*c^2-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*c^2+2*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*c*d-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*d^2)*cos(f*x+e)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^2*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/((a-b)/(a+b))^(1/2)","A"
218,1,352,183,2.129000," ","int((c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x)","\frac{2 \left(2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right) c -\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) c +\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right) d \right) \cos \left(f x +e \right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/f*(2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*c-EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*c+EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*d)*cos(f*x+e)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)^2*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/((a-b)/(a+b))^(1/2)","A"
219,1,292,368,2.152000," ","int(1/(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(\EllipticF \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, \sqrt{\frac{\left(a +b \right) \left(c -d \right)}{\left(a -b \right) \left(c +d \right)}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(f x +e \right)}, -\frac{a +b}{a -b}, \frac{\sqrt{\frac{c -d}{c +d}}}{\sqrt{\frac{a -b}{a +b}}}\right)\right) \cos \left(f x +e \right) \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/f*(EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))-2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2)))*cos(f*x+e)*sin(f*x+e)^2*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/((a-b)/(a+b))^(1/2)","A"
220,1,3451,577,2.361000," ","int(1/(c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-2/f*(-EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*d^3*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*c*d^2+2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*c^2*d-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*c^2*d-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*c*d^2+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*c^2*d+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*c*d^2-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*c*d^2+cos(f*x+e)^2*((a-b)/(a+b))^(1/2)*a*d^3-cos(f*x+e)*((a-b)/(a+b))^(1/2)*a*d^3+cos(f*x+e)*((a-b)/(a+b))^(1/2)*b*d^3-2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*b*c^3+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*b*c^3+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*a*d^3-2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*a*d^3-b*d^3*((a-b)/(a+b))^(1/2)+b*c*d^2*((a-b)/(a+b))^(1/2)-2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*d^3-2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*c^3+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*c^3-cos(f*x+e)^2*((a-b)/(a+b))^(1/2)*a*c*d^2+cos(f*x+e)*((a-b)/(a+b))^(1/2)*a*c*d^2-cos(f*x+e)*((a-b)/(a+b))^(1/2)*b*c*d^2+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*a*d^3-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*cos(f*x+e)*b*d^3+2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*a*c^2*d*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)+2*EllipticPi((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),-(a+b)/(a-b),((c-d)/(c+d))^(1/2)/((a-b)/(a+b))^(1/2))*b*c*d^2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e)-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*a*c^2*d-((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*a*c*d^2+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticF((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*b*c^2*d+((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*sin(f*x+e)*a*c*d^2-EllipticE((-1+cos(f*x+e))*((a-b)/(a+b))^(1/2)/sin(f*x+e),((a+b)*(c-d)/(a-b)/(c+d))^(1/2))*b*c*d^2*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*sin(f*x+e))*cos(f*x+e)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(d+c*cos(f*x+e))/(b+a*cos(f*x+e))/c/(c-d)/((a-b)/(a+b))^(1/2)/(c+d)/(a*d-b*c)","B"
221,0,0,76,1.601000," ","int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(1/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(1/3),x)","F"
222,0,0,27,1.327000," ","int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(4/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(4/3),x)","F"
223,0,0,27,1.263000," ","int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(7/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{1}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{7}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(7/3),x)","F"
224,0,0,76,1.448000," ","int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(2/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(2/3),x)","F"
225,0,0,27,1.270000," ","int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(5/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(5/3),x)","F"
226,0,0,27,1.366000," ","int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(8/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{2}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{8}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(8/3),x)","F"
227,0,0,76,1.344000," ","int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(4/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{4}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(4/3),x)","F"
228,0,0,27,1.270000," ","int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(7/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{4}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{7}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(7/3),x)","F"
229,0,0,27,1.317000," ","int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(10/3),x)","\int \frac{\left(a +b \sec \left(f x +e \right)\right)^{\frac{4}{3}}}{\left(c +d \sec \left(f x +e \right)\right)^{\frac{10}{3}}}\, dx"," ",0,"int((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(10/3),x)","F"
230,0,0,98,2.509000," ","int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^m,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^m,x)","F"
231,0,0,257,1.273000," ","int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^3,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^3,x)","F"
232,0,0,187,1.178000," ","int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^2,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^2,x)","F"
233,0,0,138,1.224000," ","int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e)),x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sec \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e)),x)","F"
234,0,0,188,1.139000," ","int((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e)),x)","\int \frac{\left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n}}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e)),x)","F"
235,0,0,222,1.172000," ","int((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e))^2,x)","\int \frac{\left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e))^2,x)","F"
236,0,0,56,1.450000," ","int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^m,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^m,x)","F"
237,0,0,278,0.921000," ","int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^3,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^3,x)","F"
238,0,0,193,1.050000," ","int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^2,x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^2,x)","F"
239,0,0,138,1.049000," ","int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e)),x)","\int \left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sec \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e)),x)","F"
240,0,0,188,0.845000," ","int((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e)),x)","\int \frac{\left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e)),x)","F"
241,0,0,293,1.000000," ","int((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e))^2,x)","\int \frac{\left(c \left(d \sec \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e))^2,x)","F"