1,1,130,95,1.725000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^4,x)","-\frac{3 a \,c^{4} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{4 f}-\frac{a \,c^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{7 a \,c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}-\frac{17 a \,c^{4} \tan \left(f x +e \right)}{15 f}+\frac{14 a \,c^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{a \,c^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"-3/4*a*c^4*sec(f*x+e)^3*tan(f*x+e)/f-1/8*a*c^4*sec(f*x+e)*tan(f*x+e)/f+7/8/f*a*c^4*ln(sec(f*x+e)+tan(f*x+e))-17/15/f*a*c^4*tan(f*x+e)+14/15/f*a*c^4*tan(f*x+e)*sec(f*x+e)^2+1/5/f*a*c^4*tan(f*x+e)*sec(f*x+e)^4","A"
2,1,107,78,1.306000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^3,x)","-\frac{2 a \,c^{3} \tan \left(f x +e \right)}{3 f}+\frac{2 a \,c^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{5 a \,c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}-\frac{a \,c^{3} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{4 f}-\frac{3 a \,c^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}"," ",0,"-2/3/f*a*c^3*tan(f*x+e)+2/3/f*a*c^3*tan(f*x+e)*sec(f*x+e)^2+5/8/f*a*c^3*ln(sec(f*x+e)+tan(f*x+e))-1/4*a*c^3*sec(f*x+e)^3*tan(f*x+e)/f-3/8*a*c^3*sec(f*x+e)*tan(f*x+e)/f","A"
3,1,84,55,1.169000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^2,x)","-\frac{a \,c^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a \,c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}-\frac{a \,c^{2} \tan \left(f x +e \right)}{3 f}+\frac{a \,c^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"-1/2*a*c^2*sec(f*x+e)*tan(f*x+e)/f+1/2/f*a*c^2*ln(sec(f*x+e)+tan(f*x+e))-1/3*a*c^2*tan(f*x+e)/f+1/3/f*a*c^2*tan(f*x+e)*sec(f*x+e)^2","A"
4,1,42,34,0.662000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x)","\frac{c a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}-\frac{a c \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}"," ",0,"1/2/f*c*a*ln(sec(f*x+e)+tan(f*x+e))-1/2*a*c*sec(f*x+e)*tan(f*x+e)/f","A"
5,1,63,42,0.867000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x)","\frac{a \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f c}-\frac{a \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f c}+\frac{2 a}{f c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}"," ",0,"1/f*a/c*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a/c*ln(tan(1/2*e+1/2*f*x)+1)+2/f*a/c/tan(1/2*e+1/2*f*x)","A"
6,1,21,34,0.793000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x)","-\frac{a}{3 f \,c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}"," ",0,"-1/3/f*a/c^2/tan(1/2*e+1/2*f*x)^3","A"
7,1,37,72,0.720000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x)","\frac{a \left(-\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{2 f \,c^{3}}"," ",0,"1/2/f*a/c^3*(-1/3/tan(1/2*e+1/2*f*x)^3+1/5/tan(1/2*e+1/2*f*x)^5)","A"
8,1,50,110,0.759000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x)","\frac{a \left(-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}-\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{4 f \,c^{4}}"," ",0,"1/4/f*a/c^4*(-1/7/tan(1/2*e+1/2*f*x)^7-1/3/tan(1/2*e+1/2*f*x)^3+2/5/tan(1/2*e+1/2*f*x)^5)","A"
9,1,63,150,0.773000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^5,x)","\frac{a \left(-\frac{3}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{3}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{8 f \,c^{5}}"," ",0,"1/8/f*a/c^5*(-3/7/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9-1/3/tan(1/2*e+1/2*f*x)^3+3/5/tan(1/2*e+1/2*f*x)^5)","A"
10,1,192,157,1.936000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x)","-\frac{23 a^{2} c^{5} \tan \left(f x +e \right)}{35 f}-\frac{13 a^{2} c^{5} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{35 f}+\frac{41 a^{2} c^{5} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{35 f}-\frac{5 a^{2} c^{5} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{8 f}-\frac{7 a^{2} c^{5} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{9 a^{2} c^{5} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}+\frac{a^{2} c^{5} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{2 f}-\frac{a^{2} c^{5} \tan \left(f x +e \right) \left(\sec^{6}\left(f x +e \right)\right)}{7 f}"," ",0,"-23/35*a^2*c^5*tan(f*x+e)/f-13/35/f*a^2*c^5*tan(f*x+e)*sec(f*x+e)^4+41/35/f*a^2*c^5*tan(f*x+e)*sec(f*x+e)^2-5/8*a^2*c^5*sec(f*x+e)^3*tan(f*x+e)/f-7/16*a^2*c^5*sec(f*x+e)*tan(f*x+e)/f+9/16/f*a^2*c^5*ln(sec(f*x+e)+tan(f*x+e))+1/2/f*a^2*c^5*tan(f*x+e)*sec(f*x+e)^5-1/7/f*a^2*c^5*tan(f*x+e)*sec(f*x+e)^6","A"
11,1,167,138,1.658000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,x)","-\frac{a^{2} c^{4} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{24 f}-\frac{9 a^{2} c^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{7 a^{2} c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}-\frac{2 a^{2} c^{4} \tan \left(f x +e \right)}{5 f}+\frac{4 a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}-\frac{2 a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{a^{2} c^{4} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"-1/24*a^2*c^4*sec(f*x+e)^3*tan(f*x+e)/f-9/16*a^2*c^4*sec(f*x+e)*tan(f*x+e)/f+7/16/f*a^2*c^4*ln(sec(f*x+e)+tan(f*x+e))-2/5*a^2*c^4*tan(f*x+e)/f+4/5/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^2-2/5/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^4+1/6/f*a^2*c^4*tan(f*x+e)*sec(f*x+e)^5","A"
12,1,142,86,1.508000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,x)","-\frac{a^{2} c^{3} \tan \left(f x +e \right)}{5 f}+\frac{2 c^{3} a^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}-\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{c^{3} a^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}-\frac{a^{2} c^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"-1/5*a^2*c^3*tan(f*x+e)/f+2/5/f*a^2*c^3*tan(f*x+e)*sec(f*x+e)^2-5/8/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))+1/4/f*a^2*c^3*tan(f*x+e)*sec(f*x+e)^3-1/5/f*a^2*c^3*tan(f*x+e)*sec(f*x+e)^4","A"
13,1,75,67,0.874000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x)","-\frac{5 a^{2} c^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 a^{2} c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{a^{2} c^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"-5/8*a^2*c^2*sec(f*x+e)*tan(f*x+e)/f+3/8/f*a^2*c^2*ln(sec(f*x+e)+tan(f*x+e))+1/4/f*a^2*c^2*tan(f*x+e)*sec(f*x+e)^3","A"
14,1,84,55,1.104000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x)","\frac{a^{2} c \tan \left(f x +e \right)}{3 f}+\frac{a^{2} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}-\frac{a^{2} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}-\frac{a^{2} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"1/3*a^2*c*tan(f*x+e)/f+1/2/f*a^2*c*ln(sec(f*x+e)+tan(f*x+e))-1/2*a^2*c*sec(f*x+e)*tan(f*x+e)/f-1/3/f*a^2*c*tan(f*x+e)*sec(f*x+e)^2","A"
15,1,116,74,0.640000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x)","\frac{4 a^{2}}{f c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{a^{2}}{f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{3 a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f c}+\frac{a^{2}}{f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{3 a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f c}"," ",0,"4/f*a^2/c/tan(1/2*e+1/2*f*x)+1/f*a^2/c/(tan(1/2*e+1/2*f*x)-1)+3/f*a^2/c*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^2/c/(tan(1/2*e+1/2*f*x)+1)-3/f*a^2/c*ln(tan(1/2*e+1/2*f*x)+1)","A"
16,1,91,87,0.789000," ","int(sec(f*x+e)*(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{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,c^{2}}+\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\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)-1/f*a^2/c^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^2/c^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
17,1,23,36,0.806000," ","int(sec(f*x+e)*(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}}"," ",0,"1/5/f*a^2/c^3/tan(1/2*e+1/2*f*x)^5","A"
18,1,39,76,0.801000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x)","\frac{a^{2} \left(-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{2 f \,c^{4}}"," ",0,"1/2/f*a^2/c^4*(-1/7/tan(1/2*e+1/2*f*x)^7+1/5/tan(1/2*e+1/2*f*x)^5)","A"
19,1,52,115,0.831000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x)","\frac{a^{2} \left(-\frac{2}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{4 f \,c^{5}}"," ",0,"1/4/f*a^2/c^5*(-2/7/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9+1/5/tan(1/2*e+1/2*f*x)^5)","A"
20,1,65,155,0.899000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^6,x)","\frac{a^{2} \left(-\frac{1}{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}-\frac{3}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}\right)}{8 f \,c^{6}}"," ",0,"1/8/f*a^2/c^6*(-1/11/tan(1/2*e+1/2*f*x)^11-3/7/tan(1/2*e+1/2*f*x)^7+1/3/tan(1/2*e+1/2*f*x)^9+1/5/tan(1/2*e+1/2*f*x)^5)","A"
21,1,242,209,1.932000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^6,x)","-\frac{29 a^{3} c^{6} \tan \left(f x +e \right)}{63 f}+\frac{a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{8}\left(f x +e \right)\right)}{9 f}+\frac{8 a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{6}\left(f x +e \right)\right)}{63 f}-\frac{22 a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{21 f}+\frac{80 a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{63 f}+\frac{55 a^{3} c^{6} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{128 f}-\frac{73 a^{3} c^{6} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{192 f}-\frac{73 a^{3} c^{6} \sec \left(f x +e \right) \tan \left(f x +e \right)}{128 f}+\frac{43 a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{48 f}-\frac{3 a^{3} c^{6} \tan \left(f x +e \right) \left(\sec^{7}\left(f x +e \right)\right)}{8 f}"," ",0,"-29/63/f*a^3*c^6*tan(f*x+e)+1/9/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^8+8/63/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^6-22/21/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^4+80/63/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^2+55/128/f*a^3*c^6*ln(sec(f*x+e)+tan(f*x+e))-73/192*a^3*c^6*sec(f*x+e)^3*tan(f*x+e)/f-73/128*a^3*c^6*sec(f*x+e)*tan(f*x+e)/f+43/48/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^5-3/8/f*a^3*c^6*tan(f*x+e)*sec(f*x+e)^7","A"
22,1,217,190,1.911000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x)","-\frac{2 a^{3} c^{5} \tan \left(f x +e \right)}{7 f}-\frac{6 a^{3} c^{5} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{7 f}+\frac{6 a^{3} c^{5} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{7 f}-\frac{83 a^{3} c^{5} \sec \left(f x +e \right) \tan \left(f x +e \right)}{128 f}+\frac{45 a^{3} c^{5} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{128 f}+\frac{3 a^{3} c^{5} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{16 f}+\frac{15 a^{3} c^{5} \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{64 f}+\frac{2 a^{3} c^{5} \tan \left(f x +e \right) \left(\sec^{6}\left(f x +e \right)\right)}{7 f}-\frac{a^{3} c^{5} \tan \left(f x +e \right) \left(\sec^{7}\left(f x +e \right)\right)}{8 f}"," ",0,"-2/7*a^3*c^5*tan(f*x+e)/f-6/7/f*a^3*c^5*tan(f*x+e)*sec(f*x+e)^4+6/7/f*a^3*c^5*tan(f*x+e)*sec(f*x+e)^2-83/128*a^3*c^5*sec(f*x+e)*tan(f*x+e)/f+45/128/f*a^3*c^5*ln(sec(f*x+e)+tan(f*x+e))+3/16/f*a^3*c^5*tan(f*x+e)*sec(f*x+e)^5+15/64*a^3*c^5*sec(f*x+e)^3*tan(f*x+e)/f+2/7/f*a^3*c^5*tan(f*x+e)*sec(f*x+e)^6-1/8/f*a^3*c^5*tan(f*x+e)*sec(f*x+e)^7","A"
23,1,192,111,1.949000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x)","\frac{13 a^{3} c^{4} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}-\frac{11 a^{3} c^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{5 a^{3} c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}-\frac{a^{3} c^{4} \tan \left(f x +e \right)}{7 f}+\frac{3 a^{3} c^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{7 f}-\frac{3 a^{3} c^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{7 f}-\frac{a^{3} c^{4} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}+\frac{a^{3} c^{4} \tan \left(f x +e \right) \left(\sec^{6}\left(f x +e \right)\right)}{7 f}"," ",0,"13/24/f*a^3*c^4*tan(f*x+e)*sec(f*x+e)^3-11/16*a^3*c^4*sec(f*x+e)*tan(f*x+e)/f+5/16/f*a^3*c^4*ln(sec(f*x+e)+tan(f*x+e))-1/7*a^3*c^4*tan(f*x+e)/f+3/7/f*a^3*c^4*tan(f*x+e)*sec(f*x+e)^2-3/7/f*a^3*c^4*tan(f*x+e)*sec(f*x+e)^4-1/6/f*a^3*c^4*tan(f*x+e)*sec(f*x+e)^5+1/7/f*a^3*c^4*tan(f*x+e)*sec(f*x+e)^6","A"
24,1,100,92,1.141000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x)","-\frac{11 a^{3} c^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{5 a^{3} c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}+\frac{13 a^{3} c^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}-\frac{a^{3} c^{3} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"-11/16*a^3*c^3*sec(f*x+e)*tan(f*x+e)/f+5/16/f*a^3*c^3*ln(sec(f*x+e)+tan(f*x+e))+13/24/f*a^3*c^3*tan(f*x+e)*sec(f*x+e)^3-1/6/f*a^3*c^3*tan(f*x+e)*sec(f*x+e)^5","A"
25,1,142,86,1.559000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x)","-\frac{5 a^{3} c^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 a^{3} c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{a^{3} c^{2} \tan \left(f x +e \right)}{5 f}-\frac{2 a^{3} c^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}+\frac{a^{3} c^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{a^{3} c^{2} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"-5/8*a^3*c^2*sec(f*x+e)*tan(f*x+e)/f+3/8/f*a^3*c^2*ln(sec(f*x+e)+tan(f*x+e))+1/5*a^3*c^2*tan(f*x+e)/f-2/5/f*a^3*c^2*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a^3*c^2*tan(f*x+e)*sec(f*x+e)^3+1/5/f*a^3*c^2*tan(f*x+e)*sec(f*x+e)^4","A"
26,1,107,78,1.118000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x)","\frac{2 a^{3} c \tan \left(f x +e \right)}{3 f}+\frac{5 a^{3} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}-\frac{2 a^{3} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}-\frac{a^{3} c \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{4 f}-\frac{3 a^{3} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}"," ",0,"2/3*a^3*c*tan(f*x+e)/f+5/8/f*a^3*c*ln(sec(f*x+e)+tan(f*x+e))-2/3/f*a^3*c*tan(f*x+e)*sec(f*x+e)^2-1/4*a^3*c*sec(f*x+e)^3*tan(f*x+e)/f-3/8*a^3*c*sec(f*x+e)*tan(f*x+e)/f","A"
27,1,166,96,0.698000," ","int(sec(f*x+e)*(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}}{2 f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{7 a^{3}}{2 f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{15 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f c}+\frac{a^{3}}{2 f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{7 a^{3}}{2 f c \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{15 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f c}"," ",0,"8/f*a^3/c/tan(1/2*e+1/2*f*x)-1/2/f*a^3/c/(tan(1/2*e+1/2*f*x)-1)^2+7/2/f*a^3/c/(tan(1/2*e+1/2*f*x)-1)+15/2/f*a^3/c*ln(tan(1/2*e+1/2*f*x)-1)+1/2/f*a^3/c/(tan(1/2*e+1/2*f*x)+1)^2+7/2/f*a^3/c/(tan(1/2*e+1/2*f*x)+1)-15/2/f*a^3/c*ln(tan(1/2*e+1/2*f*x)+1)","A"
28,1,140,115,0.688000," ","int(sec(f*x+e)*(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{8 a^{3}}{f \,c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}-\frac{a^{3}}{f \,c^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{5 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,c^{2}}-\frac{a^{3}}{f \,c^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,c^{2}}"," ",0,"-4/3/f*a^3/c^2/tan(1/2*e+1/2*f*x)^3-8/f*a^3/c^2/tan(1/2*e+1/2*f*x)-1/f*a^3/c^2/(tan(1/2*e+1/2*f*x)-1)-5/f*a^3/c^2*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a^3/c^2/(tan(1/2*e+1/2*f*x)+1)+5/f*a^3/c^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
29,1,113,128,0.917000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","\frac{2 a^{3}}{5 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{2 a^{3}}{3 f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2 a^{3}}{f \,c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}+\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,c^{3}}-\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,c^{3}}"," ",0,"2/5/f*a^3/c^3/tan(1/2*e+1/2*f*x)^5+2/3/f*a^3/c^3/tan(1/2*e+1/2*f*x)^3+2/f*a^3/c^3/tan(1/2*e+1/2*f*x)+1/f*a^3/c^3*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a^3/c^3*ln(tan(1/2*e+1/2*f*x)+1)","A"
30,1,23,36,0.923000," ","int(sec(f*x+e)*(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}}"," ",0,"-1/7/f*a^3/c^4/tan(1/2*e+1/2*f*x)^7","A"
31,1,39,76,0.953000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x)","\frac{a^{3} \left(-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}\right)}{2 f \,c^{5}}"," ",0,"1/2/f*a^3/c^5*(-1/7/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9)","A"
32,1,52,115,0.960000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x)","\frac{a^{3} \left(-\frac{1}{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{2}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}\right)}{4 f \,c^{6}}"," ",0,"1/4/f*a^3/c^6*(-1/11/tan(1/2*e+1/2*f*x)^11-1/7/tan(1/2*e+1/2*f*x)^7+2/9/tan(1/2*e+1/2*f*x)^9)","A"
33,1,65,154,0.962000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^7,x)","\frac{a^{3} \left(-\frac{3}{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}+\frac{1}{13 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{13}}-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}\right)}{8 f \,c^{7}}"," ",0,"1/8/f*a^3/c^7*(-3/11/tan(1/2*e+1/2*f*x)^11+1/13/tan(1/2*e+1/2*f*x)^13-1/7/tan(1/2*e+1/2*f*x)^7+1/3/tan(1/2*e+1/2*f*x)^9)","A"
34,1,212,115,0.746000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^4/(a+a*sec(f*x+e)),x)","\frac{16 c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}-\frac{c^{4}}{3 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{3 c^{4}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{29 c^{4}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{35 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f a}-\frac{c^{4}}{3 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}+\frac{3 c^{4}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{29 c^{4}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{35 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f a}"," ",0,"16/f*c^4/a*tan(1/2*e+1/2*f*x)-1/3/f*c^4/a/(tan(1/2*e+1/2*f*x)-1)^3-3/f*c^4/a/(tan(1/2*e+1/2*f*x)-1)^2-29/2/f*c^4/a/(tan(1/2*e+1/2*f*x)-1)+35/2/f*c^4/a*ln(tan(1/2*e+1/2*f*x)-1)-1/3/f*c^4/a/(tan(1/2*e+1/2*f*x)+1)^3+3/f*c^4/a/(tan(1/2*e+1/2*f*x)+1)^2-29/2/f*c^4/a/(tan(1/2*e+1/2*f*x)+1)-35/2/f*c^4/a*ln(tan(1/2*e+1/2*f*x)+1)","A"
35,1,164,96,0.705000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e)),x)","\frac{8 c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}-\frac{c^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{9 c^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{15 c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f a}+\frac{c^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{9 c^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{15 c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f a}"," ",0,"8/f*c^3/a*tan(1/2*e+1/2*f*x)-1/2/f*c^3/a/(tan(1/2*e+1/2*f*x)-1)^2-9/2/f*c^3/a/(tan(1/2*e+1/2*f*x)-1)+15/2/f*c^3/a*ln(tan(1/2*e+1/2*f*x)-1)+1/2/f*c^3/a/(tan(1/2*e+1/2*f*x)+1)^2-9/2/f*c^3/a/(tan(1/2*e+1/2*f*x)+1)-15/2/f*c^3/a*ln(tan(1/2*e+1/2*f*x)+1)","A"
36,1,116,74,0.705000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e)),x)","\frac{4 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}-\frac{c^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{3 c^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f a}-\frac{c^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{3 c^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f a}"," ",0,"4/f*c^2/a*tan(1/2*e+1/2*f*x)-1/f*c^2/a/(tan(1/2*e+1/2*f*x)-1)+3/f*c^2/a*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c^2/a/(tan(1/2*e+1/2*f*x)+1)-3/f*c^2/a*ln(tan(1/2*e+1/2*f*x)+1)","A"
37,1,61,41,0.776000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x)","\frac{2 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}+\frac{c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f a}-\frac{c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f a}"," ",0,"2/f/a*c*tan(1/2*e+1/2*f*x)+1/f/a*c*ln(tan(1/2*e+1/2*f*x)-1)-1/f/a*c*ln(tan(1/2*e+1/2*f*x)+1)","A"
38,-2,0,16,180.000000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x)","\int \frac{\sec \left(f x +e \right)}{\left(a +a \sec \left(f x +e \right)\right) \left(c -c \sec \left(f x +e \right)\right)}\, dx"," ",0,"int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e)),x)","F"
39,1,48,55,0.784000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^2,x)","\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{2}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{4 f a \,c^{2}}"," ",0,"1/4/f/a/c^2*(tan(1/2*e+1/2*f*x)-1/3/tan(1/2*e+1/2*f*x)^3+2/tan(1/2*e+1/2*f*x))","A"
40,1,61,74,1.029000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^3,x)","\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{3}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{8 f a \,c^{3}}"," ",0,"1/8/f/a/c^3*(tan(1/2*e+1/2*f*x)-1/tan(1/2*e+1/2*f*x)^3+1/5/tan(1/2*e+1/2*f*x)^5+3/tan(1/2*e+1/2*f*x))","A"
41,1,74,112,0.964000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^4,x)","\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}-\frac{2}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{4}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{4}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{16 f a \,c^{4}}"," ",0,"1/16/f/a/c^4*(tan(1/2*e+1/2*f*x)-1/7/tan(1/2*e+1/2*f*x)^7-2/tan(1/2*e+1/2*f*x)^3+4/5/tan(1/2*e+1/2*f*x)^5+4/tan(1/2*e+1/2*f*x))","A"
42,1,234,158,0.795000," ","int(sec(f*x+e)*(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{64 c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{c^{5}}{3 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}+\frac{4 c^{5}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{55 c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{105 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,a^{2}}+\frac{c^{5}}{3 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{4 c^{5}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{55 c^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{105 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,a^{2}}"," ",0,"-16/3/f*c^5/a^2*tan(1/2*e+1/2*f*x)^3-64/f*c^5/a^2*tan(1/2*e+1/2*f*x)+1/3/f*c^5/a^2/(tan(1/2*e+1/2*f*x)-1)^3+4/f*c^5/a^2/(tan(1/2*e+1/2*f*x)-1)^2+55/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)-1)-105/2/f*c^5/a^2*ln(tan(1/2*e+1/2*f*x)-1)+1/3/f*c^5/a^2/(tan(1/2*e+1/2*f*x)+1)^3-4/f*c^5/a^2/(tan(1/2*e+1/2*f*x)+1)^2+55/2/f*c^5/a^2/(tan(1/2*e+1/2*f*x)+1)+105/2/f*c^5/a^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
43,1,186,140,0.743000," ","int(sec(f*x+e)*(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{24 c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{c^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{13 c^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{35 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,a^{2}}-\frac{c^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{13 c^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{35 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,a^{2}}"," ",0,"-8/3/f*c^4/a^2*tan(1/2*e+1/2*f*x)^3-24/f*c^4/a^2*tan(1/2*e+1/2*f*x)+1/2/f*c^4/a^2/(tan(1/2*e+1/2*f*x)-1)^2+13/2/f*c^4/a^2/(tan(1/2*e+1/2*f*x)-1)-35/2/f*c^4/a^2*ln(tan(1/2*e+1/2*f*x)-1)-1/2/f*c^4/a^2/(tan(1/2*e+1/2*f*x)+1)^2+13/2/f*c^4/a^2/(tan(1/2*e+1/2*f*x)+1)+35/2/f*c^4/a^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
44,1,136,115,0.678000," ","int(sec(f*x+e)*(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{8 c^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{c^{3}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{5 c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}+\frac{c^{3}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{2}}"," ",0,"-4/3/f*c^3/a^2*tan(1/2*e+1/2*f*x)^3-8/f*c^3/a^2*tan(1/2*e+1/2*f*x)+1/f*c^3/a^2/(tan(1/2*e+1/2*f*x)-1)-5/f*c^3/a^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*c^3/a^2/(tan(1/2*e+1/2*f*x)+1)+5/f*c^3/a^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
45,1,89,86,0.823000," ","int(sec(f*x+e)*(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{c^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}+\frac{c^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\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)-1/f*c^2/a^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*c^2/a^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
46,1,21,34,0.800000," ","int(sec(f*x+e)*(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}}"," ",0,"-1/3/f*c/a^2*tan(1/2*e+1/2*f*x)^3","A"
47,1,48,55,0.645000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x)","\frac{-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+\frac{1}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{4 f \,a^{2} c}"," ",0,"1/4/f/a^2/c*(-1/3*tan(1/2*e+1/2*f*x)^3+2*tan(1/2*e+1/2*f*x)+1/tan(1/2*e+1/2*f*x))","A"
48,-2,0,36,180.000000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x)","\int \frac{\sec \left(f x +e \right)}{\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(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x)","F"
49,1,76,74,0.857000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+4 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{4}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{6}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{16 f \,a^{2} c^{3}}"," ",0,"1/16/f/a^2/c^3*(-1/3*tan(1/2*e+1/2*f*x)^3+4*tan(1/2*e+1/2*f*x)-4/3/tan(1/2*e+1/2*f*x)^3+1/5/tan(1/2*e+1/2*f*x)^5+6/tan(1/2*e+1/2*f*x))","A"
50,1,87,92,0.845000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}-\frac{10}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{1}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{10}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{32 f \,a^{2} c^{4}}"," ",0,"1/32/f/a^2/c^4*(-1/3*tan(1/2*e+1/2*f*x)^3+5*tan(1/2*e+1/2*f*x)-1/7/tan(1/2*e+1/2*f*x)^7-10/3/tan(1/2*e+1/2*f*x)^3+1/tan(1/2*e+1/2*f*x)^5+10/tan(1/2*e+1/2*f*x))","A"
51,1,102,131,0.979000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{6}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{20}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{3}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{15}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{64 f \,a^{2} c^{5}}"," ",0,"1/64/f/a^2/c^5*(-1/3*tan(1/2*e+1/2*f*x)^3+6*tan(1/2*e+1/2*f*x)-6/7/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9-20/3/tan(1/2*e+1/2*f*x)^3+3/tan(1/2*e+1/2*f*x)^5+15/tan(1/2*e+1/2*f*x))","A"
52,1,256,201,0.822000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x)","\frac{16 c^{6} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5 f \,a^{3}}+\frac{64 c^{6} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{3}}+\frac{160 c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}-\frac{c^{6}}{3 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{5 c^{6}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{89 c^{6}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{231 c^{6} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,a^{3}}-\frac{c^{6}}{3 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}+\frac{5 c^{6}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{89 c^{6}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{231 c^{6} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,a^{3}}"," ",0,"16/5/f*c^6/a^3*tan(1/2*e+1/2*f*x)^5+64/3/f*c^6/a^3*tan(1/2*e+1/2*f*x)^3+160/f*c^6/a^3*tan(1/2*e+1/2*f*x)-1/3/f*c^6/a^3/(tan(1/2*e+1/2*f*x)-1)^3-5/f*c^6/a^3/(tan(1/2*e+1/2*f*x)-1)^2-89/2/f*c^6/a^3/(tan(1/2*e+1/2*f*x)-1)+231/2/f*c^6/a^3*ln(tan(1/2*e+1/2*f*x)-1)-1/3/f*c^6/a^3/(tan(1/2*e+1/2*f*x)+1)^3+5/f*c^6/a^3/(tan(1/2*e+1/2*f*x)+1)^2-89/2/f*c^6/a^3/(tan(1/2*e+1/2*f*x)+1)-231/2/f*c^6/a^3*ln(tan(1/2*e+1/2*f*x)+1)","A"
53,1,208,183,0.800000," ","int(sec(f*x+e)*(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)}{f \,a^{3}}+\frac{48 c^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}-\frac{c^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{17 c^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{63 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,a^{3}}+\frac{c^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{17 c^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{63 c^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,a^{3}}"," ",0,"8/5/f*c^5/a^3*tan(1/2*e+1/2*f*x)^5+8/f*c^5/a^3*tan(1/2*e+1/2*f*x)^3+48/f*c^5/a^3*tan(1/2*e+1/2*f*x)-1/2/f*c^5/a^3/(tan(1/2*e+1/2*f*x)-1)^2-17/2/f*c^5/a^3/(tan(1/2*e+1/2*f*x)-1)+63/2/f*c^5/a^3*ln(tan(1/2*e+1/2*f*x)-1)+1/2/f*c^5/a^3/(tan(1/2*e+1/2*f*x)+1)^2-17/2/f*c^5/a^3/(tan(1/2*e+1/2*f*x)+1)-63/2/f*c^5/a^3*ln(tan(1/2*e+1/2*f*x)+1)","A"
54,1,160,158,0.685000," ","int(sec(f*x+e)*(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{8 c^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 f \,a^{3}}+\frac{12 c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}-\frac{c^{4}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{7 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}-\frac{c^{4}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{7 c^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{3}}"," ",0,"4/5/f*c^4/a^3*tan(1/2*e+1/2*f*x)^5+8/3/f*c^4/a^3*tan(1/2*e+1/2*f*x)^3+12/f*c^4/a^3*tan(1/2*e+1/2*f*x)-1/f*c^4/a^3/(tan(1/2*e+1/2*f*x)-1)+7/f*c^4/a^3*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c^4/a^3/(tan(1/2*e+1/2*f*x)+1)-7/f*c^4/a^3*ln(tan(1/2*e+1/2*f*x)+1)","A"
55,1,111,127,0.830000," ","int(sec(f*x+e)*(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{c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}-\frac{c^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\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)+1/f*c^3/a^3*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c^3/a^3*ln(tan(1/2*e+1/2*f*x)+1)","A"
56,1,23,36,0.836000," ","int(sec(f*x+e)*(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}}"," ",0,"1/5/f*c^2/a^3*tan(1/2*e+1/2*f*x)^5","A"
57,1,37,72,0.800000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x)","\frac{c \left(\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}\right)}{2 f \,a^{3}}"," ",0,"1/2/f*c/a^3*(1/5*tan(1/2*e+1/2*f*x)^5-1/3*tan(1/2*e+1/2*f*x)^3)","A"
58,1,61,74,0.705000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)+3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+\frac{1}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{8 f \,a^{3} c}"," ",0,"1/8/f/a^3/c*(1/5*tan(1/2*e+1/2*f*x)^5-tan(1/2*e+1/2*f*x)^3+3*tan(1/2*e+1/2*f*x)+1/tan(1/2*e+1/2*f*x))","A"
59,1,76,74,0.868000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{4 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{4}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{16 f \,a^{3} c^{2}}"," ",0,"1/16/f/a^3/c^2*(1/5*tan(1/2*e+1/2*f*x)^5-4/3*tan(1/2*e+1/2*f*x)^3+6*tan(1/2*e+1/2*f*x)-1/3/tan(1/2*e+1/2*f*x)^3+4/tan(1/2*e+1/2*f*x))","A"
60,-2,0,55,180.000000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","\int \frac{\sec \left(f x +e \right)}{\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(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x)","F"
61,1,102,93,0.926000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)+15 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}-\frac{5}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{6}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{20}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{64 f \,a^{3} c^{4}}"," ",0,"1/64/f/a^3/c^4*(1/5*tan(1/2*e+1/2*f*x)^5-2*tan(1/2*e+1/2*f*x)^3+15*tan(1/2*e+1/2*f*x)-1/7/tan(1/2*e+1/2*f*x)^7-5/tan(1/2*e+1/2*f*x)^3+6/5/tan(1/2*e+1/2*f*x)^5+20/tan(1/2*e+1/2*f*x))","A"
62,1,115,112,0.972000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{7 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+21 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{35}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{21}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{35}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{128 f \,a^{3} c^{5}}"," ",0,"1/128/f/a^3/c^5*(1/5*tan(1/2*e+1/2*f*x)^5-7/3*tan(1/2*e+1/2*f*x)^3+21*tan(1/2*e+1/2*f*x)-1/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9-35/3/tan(1/2*e+1/2*f*x)^3+21/5/tan(1/2*e+1/2*f*x)^5+35/tan(1/2*e+1/2*f*x))","A"
63,1,128,150,0.998000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{8 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}+28 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)-\frac{1}{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}-\frac{4}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{8}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}-\frac{70}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{3}}+\frac{56}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}+\frac{56}{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}}{256 f \,a^{3} c^{6}}"," ",0,"1/256/f/a^3/c^6*(1/5*tan(1/2*e+1/2*f*x)^5-8/3*tan(1/2*e+1/2*f*x)^3+28*tan(1/2*e+1/2*f*x)-1/11/tan(1/2*e+1/2*f*x)^11-4/tan(1/2*e+1/2*f*x)^7+8/9/tan(1/2*e+1/2*f*x)^9-70/3/tan(1/2*e+1/2*f*x)^3+56/5/tan(1/2*e+1/2*f*x)^5+56/tan(1/2*e+1/2*f*x))","A"
64,1,83,147,1.223000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(7/2),x)","\frac{2 a \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right) \left(319 \left(\cos^{3}\left(f x +e \right)\right)-321 \left(\cos^{2}\left(f x +e \right)\right)+165 \cos \left(f x +e \right)-35\right)}{315 f \left(-1+\cos \left(f x +e \right)\right)^{5} \cos \left(f x +e \right)}"," ",0,"2/315*a/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*sin(f*x+e)^3*(319*cos(f*x+e)^3-321*cos(f*x+e)^2+165*cos(f*x+e)-35)/(-1+cos(f*x+e))^5/cos(f*x+e)","A"
65,1,73,110,1.177000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(5/2),x)","\frac{2 a \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\sin^{3}\left(f x +e \right)\right) \left(71 \left(\cos^{2}\left(f x +e \right)\right)-54 \cos \left(f x +e \right)+15\right)}{105 f \left(-1+\cos \left(f x +e \right)\right)^{4} \cos \left(f x +e \right)}"," ",0,"2/105*a/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*sin(f*x+e)^3*(71*cos(f*x+e)^2-54*cos(f*x+e)+15)/(-1+cos(f*x+e))^4/cos(f*x+e)","A"
66,1,63,73,1.211000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(3/2),x)","\frac{2 a \left(7 \cos \left(f x +e \right)-3\right) \left(\sin^{3}\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}}}{15 f \left(-1+\cos \left(f x +e \right)\right)^{3} \cos \left(f x +e \right)}"," ",0,"2/15*a/f*(7*cos(f*x+e)-3)*sin(f*x+e)^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))^3/cos(f*x+e)","A"
67,1,53,35,1.340000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c-c*sec(f*x+e))^(1/2),x)","\frac{2 a \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sin^{3}\left(f x +e \right)\right)}{3 f \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"2/3*a/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^3/cos(f*x+e)/(-1+cos(f*x+e))^2","A"
68,1,85,66,1.595000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x)","-\frac{2 a \left(\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-1\right) \sin \left(f x +e \right)}{f \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}"," ",0,"-2*a/f*(arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-1)*sin(f*x+e)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)","A"
69,1,164,66,1.375000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x)","\frac{2 a \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+\cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{f \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)^{3} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2*a/f*(-1+cos(f*x+e))^2*(cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^3/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)","B"
70,1,308,94,1.422000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x)","-\frac{a \left(-1+\cos \left(f x +e \right)\right)^{3} \left(\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}}+4 \cos \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}}-\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)}}-\left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+2 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+2 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{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)^{5} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/2*a/f*(-1+cos(f*x+e))^3*(cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+4*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+2*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+2*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)","B"
71,1,85,155,1.654000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(7/2),x)","-\frac{2 a^{2} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{7}{2}} \left(\sin^{5}\left(f x +e \right)\right) \left(533 \left(\cos^{3}\left(f x +e \right)\right)-755 \left(\cos^{2}\left(f x +e \right)\right)+455 \cos \left(f x +e \right)-105\right)}{1155 f \left(-1+\cos \left(f x +e \right)\right)^{6} \cos \left(f x +e \right)^{2}}"," ",0,"-2/1155*a^2/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*sin(f*x+e)^5*(533*cos(f*x+e)^3-755*cos(f*x+e)^2+455*cos(f*x+e)-105)/(-1+cos(f*x+e))^6/cos(f*x+e)^2","A"
72,1,75,116,1.639000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(5/2),x)","-\frac{2 a^{2} \left(107 \left(\cos^{2}\left(f x +e \right)\right)-110 \cos \left(f x +e \right)+35\right) \left(\sin^{5}\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{5}{2}}}{315 f \left(-1+\cos \left(f x +e \right)\right)^{5} \cos \left(f x +e \right)^{2}}"," ",0,"-2/315*a^2/f*(107*cos(f*x+e)^2-110*cos(f*x+e)+35)*sin(f*x+e)^5*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/(-1+cos(f*x+e))^5/cos(f*x+e)^2","A"
73,1,65,77,1.576000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(3/2),x)","-\frac{2 a^{2} \left(9 \cos \left(f x +e \right)-5\right) \left(\sin^{5}\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}}}{35 f \left(-1+\cos \left(f x +e \right)\right)^{4} \cos \left(f x +e \right)^{2}}"," ",0,"-2/35*a^2/f*(9*cos(f*x+e)-5)*sin(f*x+e)^5*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))^4/cos(f*x+e)^2","A"
74,1,55,37,1.805000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^(1/2),x)","-\frac{2 a^{2} \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sin^{5}\left(f x +e \right)\right)}{5 f \cos \left(f x +e \right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-2/5*a^2/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^5/cos(f*x+e)^2/(-1+cos(f*x+e))^3","A"
75,1,145,100,1.751000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x)","\frac{2 a^{2} \left(3 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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}}+3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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}}+7 \cos \left(f x +e \right)+1\right) \sin \left(f x +e \right)}{3 f \cos \left(f x +e \right)^{2} \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}"," ",0,"2/3*a^2/f*(3*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+7*cos(f*x+e)+1)*sin(f*x+e)/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)","A"
76,1,144,100,1.701000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x)","\frac{a^{2} \left(3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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)-3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-4 \cos \left(f x +e \right)+2\right) \sin \left(f x +e \right)}{f \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{3}{2}}}"," ",0,"a^2/f*(3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)-3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-4*cos(f*x+e)+2)*sin(f*x+e)/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)","A"
77,1,230,100,1.898000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x)","-\frac{a^{2} \left(-1+\cos \left(f x +e \right)\right)^{3} \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)}}+3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-4 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-6 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-5 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{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)^{5} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-a^2/f*(-1+cos(f*x+e))^3*(cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+3*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-4*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-6*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)","B"
78,1,402,141,2.463000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(7/2),x)","-\frac{a^{2} \left(-1+\cos \left(f x +e \right)\right)^{4} \left(5 \left(\cos^{3}\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}}+15 \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}}+3 \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)}}+3 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+27 \cos \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}}-9 \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)}}-9 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+17 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+9 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+9 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{6 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)^{7} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}}"," ",0,"-1/6*a^2/f*(-1+cos(f*x+e))^4*(5*cos(f*x+e)^3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+15*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+3*cos(f*x+e)^3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+3*cos(f*x+e)^3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+27*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-9*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-9*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+17*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+9*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+9*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)^7/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)","B"
79,1,85,155,1.955000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(7/2),x)","\frac{2 a^{3} \left(835 \left(\cos^{3}\left(f x +e \right)\right)-1421 \left(\cos^{2}\left(f x +e \right)\right)+945 \cos \left(f x +e \right)-231\right) \left(\sin^{7}\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{7}{2}}}{3003 f \left(-1+\cos \left(f x +e \right)\right)^{7} \cos \left(f x +e \right)^{3}}"," ",0,"2/3003*a^3/f*(835*cos(f*x+e)^3-1421*cos(f*x+e)^2+945*cos(f*x+e)-231)*sin(f*x+e)^7*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/(-1+cos(f*x+e))^7/cos(f*x+e)^3","A"
80,1,75,116,1.835000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(5/2),x)","\frac{2 a^{3} \left(151 \left(\cos^{2}\left(f x +e \right)\right)-182 \cos \left(f x +e \right)+63\right) \left(\sin^{7}\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{5}{2}}}{693 f \left(-1+\cos \left(f x +e \right)\right)^{6} \cos \left(f x +e \right)^{3}}"," ",0,"2/693*a^3/f*(151*cos(f*x+e)^2-182*cos(f*x+e)+63)*sin(f*x+e)^7*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/(-1+cos(f*x+e))^6/cos(f*x+e)^3","A"
81,1,65,77,1.805000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(3/2),x)","\frac{2 a^{3} \left(11 \cos \left(f x +e \right)-7\right) \left(\sin^{7}\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}}}{63 f \left(-1+\cos \left(f x +e \right)\right)^{5} \cos \left(f x +e \right)^{3}}"," ",0,"2/63*a^3/f*(11*cos(f*x+e)-7)*sin(f*x+e)^7*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))^5/cos(f*x+e)^3","A"
82,1,55,37,1.980000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^(1/2),x)","\frac{2 a^{3} \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sin^{7}\left(f x +e \right)\right)}{7 f \cos \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{4}}"," ",0,"2/7*a^3/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^7/cos(f*x+e)^3/(-1+cos(f*x+e))^4","A"
83,1,206,145,1.908000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x)","-\frac{2 a^{3} \left(15 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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}}-73 \left(\cos^{2}\left(f x +e \right)\right)-16 \cos \left(f x +e \right)-3\right) \sin \left(f x +e \right)}{15 f \cos \left(f x +e \right)^{3} \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}"," ",0,"-2/15*a^3/f*(15*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+30*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-73*cos(f*x+e)^2-16*cos(f*x+e)-3)*sin(f*x+e)/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)","A"
84,1,157,151,1.731000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x)","-\frac{a^{3} \left(15 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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}}-15 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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}}+38 \left(\cos^{2}\left(f x +e \right)\right)-24 \cos \left(f x +e \right)-2\right) \sin \left(f x +e \right)}{3 f \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{3}{2}}}"," ",0,"-1/3*a^3/f*(15*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+38*cos(f*x+e)^2-24*cos(f*x+e)-2)*sin(f*x+e)/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)","A"
85,1,206,151,1.884000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x)","-\frac{a^{3} \left(15 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-30 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\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)-18 \left(\cos^{2}\left(f x +e \right)\right)+15 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+34 \cos \left(f x +e \right)-8\right) \sin \left(f x +e \right)}{4 f \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{5}{2}}}"," ",0,"-1/4*a^3/f*(15*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-30*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*cos(f*x+e)-18*cos(f*x+e)^2+15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+34*cos(f*x+e)-8)*sin(f*x+e)/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)","A"
86,1,83,128,1.759000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e)),x)","-\frac{2 \left(91 \left(\cos^{3}\left(f x +e \right)\right)+43 \left(\cos^{2}\left(f x +e \right)\right)-7 \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{7}{2}}}{5 a f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-2/5/a/f*(91*cos(f*x+e)^3+43*cos(f*x+e)^2-7*cos(f*x+e)+1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)/(-1+cos(f*x+e))^3","A"
87,1,73,98,1.886000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e)),x)","-\frac{2 \left(23 \left(\cos^{2}\left(f x +e \right)\right)+10 \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}}}{3 a f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"-2/3/a/f*(23*cos(f*x+e)^2+10*cos(f*x+e)-1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)/(-1+cos(f*x+e))^2","A"
88,1,63,68,1.851000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x)","-\frac{2 \left(3 \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}}}{a f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-2/a/f*(3*cos(f*x+e)+1)*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)/(-1+cos(f*x+e))","A"
89,1,43,37,2.123000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x)","-\frac{2 \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)}"," ",0,"-2/a/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)/sin(f*x+e)","A"
90,1,107,78,2.161000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{a 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) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}"," ",0,"-1/a/f*(-1+cos(f*x+e))*((-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)","A"
91,1,266,105,2.135000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(\left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \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}}+\cos \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}}-\left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}-3 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-3 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{2 a f \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)^{3} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/2/a/f*(-1+cos(f*x+e))^2*((-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)+(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-3*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-3*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^3/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)","B"
92,1,471,135,2.317000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(5 \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)+4 \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)-\left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)\right)-6 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}-5 \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}}+10 \cos \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}}-5 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+15 \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)}}+15 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-30 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-30 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+15 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+15 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{8 a 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)^{5} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/8/a/f*(-1+cos(f*x+e))^3*(5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^2+4*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)-(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)^2-6*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-5*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+10*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+15*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+15*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-30*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-30*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)","B"
93,1,85,141,1.633000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^2,x)","-\frac{2 \left(3 \cos \left(f x +e \right)+1\right) \left(15 \left(\cos^{2}\left(f x +e \right)\right)+18 \cos \left(f x +e \right)-1\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{7}{2}}}{3 a^{2} f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"-2/3/a^2/f*(3*cos(f*x+e)+1)*(15*cos(f*x+e)^2+18*cos(f*x+e)-1)*cos(f*x+e)^2*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)^3/(-1+cos(f*x+e))^2","A"
94,1,75,111,1.667000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^2,x)","-\frac{2 \left(11 \left(\cos^{2}\left(f x +e \right)\right)+18 \cos \left(f x +e \right)+3\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{5}{2}}}{3 a^{2} f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-2/3/a^2/f*(11*cos(f*x+e)^2+18*cos(f*x+e)+3)*cos(f*x+e)^2*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^3/(-1+cos(f*x+e))","A"
95,1,53,81,1.658000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^2,x)","-\frac{2 \left(\cos \left(f x +e \right)+3\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}}}{3 a^{2} f \sin \left(f x +e \right)^{3}}"," ",0,"-2/3/a^2/f*(cos(f*x+e)+3)*cos(f*x+e)^2*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^3","A"
96,1,53,37,1.848000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^2,x)","\frac{2 \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right)}{3 a^{2} f \sin \left(f x +e \right)^{3}}"," ",0,"2/3/a^2/f*(-1+cos(f*x+e))*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2/sin(f*x+e)^3","A"
97,1,131,119,1.825000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(\left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}-3 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{6 a^{2} 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) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}"," ",0,"1/6/a^2/f*(-1+cos(f*x+e))*((-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-3*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)","A"
98,1,320,146,1.990000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 \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)+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}+3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)-3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}-5 \cos \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}}+5 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+15 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+15 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-15 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-15 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{12 a^{2} f \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)^{3} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/12/a^2/f*(-1+cos(f*x+e))^2*(3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)+3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)-3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-5*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+15*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+15*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^3/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)","B"
99,1,551,176,2.027000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(21 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \left(\cos^{2}\left(f x +e \right)\right)+12 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \cos \left(f x +e \right)+15 \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)-9 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}-30 \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)-21 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)\right)+15 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}+42 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)+35 \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}}-21 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}-70 \cos \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}}-105 \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)}}-105 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+35 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+210 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+210 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-105 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-105 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{48 a^{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)^{5} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"1/48/a^2/f*(-1+cos(f*x+e))^3*(21*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*cos(f*x+e)^2+12*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*cos(f*x+e)+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^2-9*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)-30*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)-21*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)^2+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)+42*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)+35*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-21*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-70*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-105*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-105*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+35*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+210*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+210*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-105*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-105*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)","B"
100,1,85,153,1.812000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^3,x)","-\frac{2 \left(23 \left(\cos^{3}\left(f x +e \right)\right)+55 \left(\cos^{2}\left(f x +e \right)\right)+45 \cos \left(f x +e \right)+5\right) \left(\cos^{3}\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{7}{2}}}{5 a^{3} f \sin \left(f x +e \right)^{5} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-2/5/a^3/f*(23*cos(f*x+e)^3+55*cos(f*x+e)^2+45*cos(f*x+e)+5)*cos(f*x+e)^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)/sin(f*x+e)^5/(-1+cos(f*x+e))","A"
101,1,65,123,1.820000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^3,x)","-\frac{2 \left(7 \left(\cos^{2}\left(f x +e \right)\right)+10 \cos \left(f x +e \right)+15\right) \left(\cos^{3}\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{5}{2}}}{15 a^{3} f \sin \left(f x +e \right)^{5}}"," ",0,"-2/15/a^3/f*(7*cos(f*x+e)^2+10*cos(f*x+e)+15)*cos(f*x+e)^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5","A"
102,1,63,80,1.815000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^3,x)","-\frac{2 \left(5+\cos^{2}\left(f x +e \right)-6 \cos \left(f x +e \right)\right) \left(\cos^{3}\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}}}{15 a^{3} f \sin \left(f x +e \right)^{5}}"," ",0,"-2/15/a^3/f*(5+cos(f*x+e)^2-6*cos(f*x+e))*cos(f*x+e)^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^5","A"
103,1,55,37,1.906000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^3,x)","-\frac{2 \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{5 a^{3} f \sin \left(f x +e \right)^{5}}"," ",0,"-2/5/a^3/f*(-1+cos(f*x+e))^2*cos(f*x+e)^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5","A"
104,1,155,158,2.054000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}-5 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}+15 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+15 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\right)}{60 a^{3} 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) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}"," ",0,"-1/60/a^3/f*(-1+cos(f*x+e))*(3*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)-5*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+15*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)","A"
105,1,370,185,2.016000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(15 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \cos \left(f x +e \right)+15 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}+15 \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)-15 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}-21 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)+21 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+35 \cos \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}}-35 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}-105 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}-105 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+105 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+105 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)\right)}{120 a^{3} f \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)^{3} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/120/a^3/f*(-1+cos(f*x+e))^2*(15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*cos(f*x+e)+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)+15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)-15*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)-21*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)+21*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+35*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-35*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-105*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-105*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+105*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+105*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^3/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)","A"
106,1,631,215,2.198000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(45 \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{11}{2}}+20 \cos \left(f x +e \right) \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{11}{2}}+35 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \left(\cos^{2}\left(f x +e \right)\right)-25 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{11}{2}}-70 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}} \cos \left(f x +e \right)-45 \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)+35 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{9}{2}}+90 \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)+63 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)\right)-45 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{7}{2}}-126 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)-105 \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}}+63 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}+210 \cos \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}}+315 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+315 \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)}}-105 \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}}-630 \cos \left(f x +e \right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)-630 \cos \left(f x +e \right) \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}+315 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}\right)+315 \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\right)}{160 a^{3} 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)^{5} \left(-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/160/a^3/f*(-1+cos(f*x+e))^3*(45*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(11/2)+20*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(11/2)+35*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*cos(f*x+e)^2-25*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(11/2)-70*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)*cos(f*x+e)-45*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)^2+35*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(9/2)+90*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)*cos(f*x+e)+63*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)^2-45*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(7/2)-126*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)*cos(f*x+e)-105*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+63*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)+210*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)+315*cos(f*x+e)^2*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+315*cos(f*x+e)^2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)-105*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(3/2)-630*cos(f*x+e)*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))-630*cos(f*x+e)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)+315*arctan(1/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))+315*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/sin(f*x+e)^5/(-2*cos(f*x+e)/(1+cos(f*x+e)))^(5/2)","B"
107,1,82,37,1.965000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(7 \left(\cos^{2}\left(f x +e \right)\right)-4 \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)}}}{3 f \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-1/3/f*sin(f*x+e)*(7*cos(f*x+e)^2-4*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)/(-1+cos(f*x+e))^3","B"
108,1,72,37,1.976000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x)","-\frac{\sin \left(f x +e \right) \left(3 \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)}}\, \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{2 f \left(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"-1/2/f*sin(f*x+e)*(3*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)/(-1+cos(f*x+e))^2","A"
109,1,62,37,1.949000," ","int(sec(f*x+e)*(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)}}\, \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{f \left(-1+\cos \left(f x +e \right)\right)}"," ",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)*sin(f*x+e)/(-1+cos(f*x+e))","A"
110,1,141,47,2.019000," ","int(sec(f*x+e)*(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{-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)\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)}}}{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(-(-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)))*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/c","B"
111,1,60,36,2.050000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(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)}}\, \sin \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}}}"," ",0,"-1/2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)/cos(f*x+e)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)","A"
112,1,70,37,2.117000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(3 \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)}}\, \sin \left(f x +e \right)}{8 f \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*(3*cos(f*x+e)-1)*(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"
113,1,103,77,1.955000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(7/2),x)","\frac{\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(13 \left(\cos^{3}\left(f x +e \right)\right)-16 \left(\cos^{2}\left(f x +e \right)\right)+9 \cos \left(f x +e \right)-2\right) \left(\sin^{3}\left(f x +e \right)\right) a}{10 f \left(-1+\cos \left(f x +e \right)\right)^{5} \cos \left(f x +e \right)}"," ",0,"1/10/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(13*cos(f*x+e)^3-16*cos(f*x+e)^2+9*cos(f*x+e)-2)*sin(f*x+e)^3/(-1+cos(f*x+e))^5/cos(f*x+e)*a","A"
114,1,93,77,2.441000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x)","\frac{\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(11 \left(\cos^{2}\left(f x +e \right)\right)-10 \cos \left(f x +e \right)+3\right) \left(\sin^{3}\left(f x +e \right)\right) a}{12 f \left(-1+\cos \left(f x +e \right)\right)^{4} \cos \left(f x +e \right)}"," ",0,"1/12/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(11*cos(f*x+e)^2-10*cos(f*x+e)+3)*sin(f*x+e)^3/(-1+cos(f*x+e))^4/cos(f*x+e)*a","A"
115,1,83,77,2.172000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x)","\frac{\left(\sin^{3}\left(f x +e \right)\right) \left(2 \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)}}\, \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} a}{3 f \left(-1+\cos \left(f x +e \right)\right)^{3} \cos \left(f x +e \right)}"," ",0,"1/3/f*sin(f*x+e)^3*(2*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)/(-1+cos(f*x+e))^3/cos(f*x+e)*a","A"
116,1,73,37,2.072000," ","int(sec(f*x+e)*(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(\sin^{3}\left(f x +e \right)\right) \sqrt{\frac{c \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(-1+\cos \left(f x +e \right)\right)^{2}}"," ",0,"1/2/f*(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))^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))^2*a","A"
117,1,161,87,2.061000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x)","-\frac{\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{-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)+\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}{f \sin \left(f x +e \right) c}"," ",0,"-1/f*(4*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-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))+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","A"
118,1,246,91,1.894000," ","int(sec(f*x+e)*(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(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{-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)-2 \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)+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))*(2*ln(-(-1+cos(f*x+e))/sin(f*x+e))*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)-2*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))+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","B"
119,1,73,36,1.936000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(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(\sin^{3}\left(f x +e \right)\right) a}{4 f \left(-1+\cos \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{5}{2}} \cos \left(f x +e \right)^{2}}"," ",0,"1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^3/(-1+cos(f*x+e))/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/cos(f*x+e)^2*a","A"
120,1,83,76,2.182000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x)","\frac{\left(5 \cos \left(f x +e \right)-1\right) \left(\sin^{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)}}\, a}{24 f \left(-1+\cos \left(f x +e \right)\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,"1/24/f*(5*cos(f*x+e)-1)*sin(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*a","A"
121,1,93,80,2.130000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(9/2),x)","\frac{\left(17 \left(\cos^{2}\left(f x +e \right)\right)-6 \cos \left(f x +e \right)+1\right) \left(\sin^{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)}}\, a}{96 f \left(-1+\cos \left(f x +e \right)\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,"1/96/f*(17*cos(f*x+e)^2-6*cos(f*x+e)+1)*sin(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/cos(f*x+e)^4/(c*(-1+cos(f*x+e))/cos(f*x+e))^(9/2)*a","A"
122,1,103,80,2.174000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(11/2),x)","\frac{\left(49 \left(\cos^{3}\left(f x +e \right)\right)-23 \left(\cos^{2}\left(f x +e \right)\right)+7 \cos \left(f x +e \right)-1\right) \left(\sin^{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)}}\, a}{320 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{5} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{11}{2}}}"," ",0,"1/320/f*(49*cos(f*x+e)^3-23*cos(f*x+e)^2+7*cos(f*x+e)-1)*sin(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/cos(f*x+e)^5/(c*(-1+cos(f*x+e))/cos(f*x+e))^(11/2)*a","A"
123,1,105,116,2.427000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(7/2),x)","-\frac{\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(21 \left(\cos^{3}\left(f x +e \right)\right)-33 \left(\cos^{2}\left(f x +e \right)\right)+21 \cos \left(f x +e \right)-5\right) \left(\sin^{5}\left(f x +e \right)\right) a^{2}}{30 f \left(-1+\cos \left(f x +e \right)\right)^{6} \cos \left(f x +e \right)^{2}}"," ",0,"-1/30/f*(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(21*cos(f*x+e)^3-33*cos(f*x+e)^2+21*cos(f*x+e)-5)*sin(f*x+e)^5/(-1+cos(f*x+e))^6/cos(f*x+e)^2*a^2","A"
124,1,95,116,2.320000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x)","-\frac{\left(\sin^{5}\left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right)-9 \cos \left(f x +e \right)+3\right) \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}} a^{2}}{15 f \left(-1+\cos \left(f x +e \right)\right)^{5} \cos \left(f x +e \right)^{2}}"," ",0,"-1/15/f*sin(f*x+e)^5*(8*cos(f*x+e)^2-9*cos(f*x+e)+3)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/(-1+cos(f*x+e))^5/cos(f*x+e)^2*a^2","A"
125,1,85,77,2.184000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(\sin^{5}\left(f x +e \right)\right) \left(5 \cos \left(f x +e \right)-3\right) \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}} a^{2}}{12 f \left(-1+\cos \left(f x +e \right)\right)^{4} \cos \left(f x +e \right)^{2}}"," ",0,"-1/12/f*sin(f*x+e)^5*(5*cos(f*x+e)-3)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/(-1+cos(f*x+e))^4/cos(f*x+e)^2*a^2","A"
126,1,75,37,2.299000," ","int(sec(f*x+e)*(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(\sin^{5}\left(f x +e \right)\right) \sqrt{\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{3 f \cos \left(f x +e \right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{3}}"," ",0,"-1/3/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^5*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/cos(f*x+e)^2/(-1+cos(f*x+e))^3*a^2","A"
127,1,189,127,2.470000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x)","\frac{\left(8 \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)+8 \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)-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)-5 \left(\cos^{2}\left(f x +e \right)\right)-6 \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}}{2 f \sin \left(f x +e \right) \cos \left(f x +e \right) c}"," ",0,"1/2/f*(8*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+8*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-16*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-5*cos(f*x+e)^2-6*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)/cos(f*x+e)/c*a^2","A"
128,1,289,133,2.196000," ","int(sec(f*x+e)*(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(4 \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)+4 \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)-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)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \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)-4 \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)+8 \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)+1\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)^{2} \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))*(4*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-8*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-3*cos(f*x+e)^2-4*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-2*cos(f*x+e)+1)*(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)/sin(f*x+e)*a^2","B"
129,1,364,131,2.293000," ","int(sec(f*x+e)*(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{-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)-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{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 \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^{2}\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{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \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)-2 \cos \left(f x +e \right)-3\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)^{2} \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)}"," ",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(-(-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)^2-8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+cos(f*x+e)^2+4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)-3)*(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))^(5/2)/sin(f*x+e)*a^2","B"
130,1,75,36,1.956000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x)","-\frac{\left(\sin^{5}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{6 f \left(-1+\cos \left(f x +e \right)\right)^{2} \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*sin(f*x+e)^5*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))^2/cos(f*x+e)^3/(c*(-1+cos(f*x+e))/cos(f*x+e))^(7/2)*a^2","B"
131,1,85,76,1.990000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x)","-\frac{\left(7 \cos \left(f x +e \right)-1\right) \left(\sin^{5}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{48 f \left(-1+\cos \left(f x +e \right)\right)^{2} \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,"-1/48/f*(7*cos(f*x+e)-1)*sin(f*x+e)^5*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))^2/cos(f*x+e)^4/(c*(-1+cos(f*x+e))/cos(f*x+e))^(9/2)*a^2","A"
132,1,95,115,2.034000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x)","-\frac{\left(31 \left(\cos^{2}\left(f x +e \right)\right)-8 \cos \left(f x +e \right)+1\right) \left(\sin^{5}\left(f x +e \right)\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, a^{2}}{240 f \left(-1+\cos \left(f x +e \right)\right)^{2} \cos \left(f x +e \right)^{5} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{11}{2}}}"," ",0,"-1/240/f*(31*cos(f*x+e)^2-8*cos(f*x+e)+1)*sin(f*x+e)^5*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))^2/cos(f*x+e)^5/(c*(-1+cos(f*x+e))/cos(f*x+e))^(11/2)*a^2","A"
133,1,165,125,2.062000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*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)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+8 \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)+7 \left(\cos^{2}\left(f x +e \right)\right)+6 \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} a}"," ",0,"-1/2/f*(8*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+8*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+7*cos(f*x+e)^2+6*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","A"
134,1,149,86,1.893000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x)","-\frac{\left(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)+\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) a}"," ",0,"-1/f*(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))+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","A"
135,1,116,46,1.985000," ","int(sec(f*x+e)*(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)\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) a}"," ",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)))*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)/a","B"
136,1,85,43,1.899000," ","int(sec(f*x+e)/(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)}}\, \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \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))*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)/sin(f*x+e)/c/a","A"
137,1,131,83,1.981000," ","int(sec(f*x+e)/(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(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)-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)}}}{4 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) a}"," ",0,"-1/4/f*(-1+cos(f*x+e))*(2*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-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"
138,1,170,122,2.284000," ","int(sec(f*x+e)/(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(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)-8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-5 \left(\cos^{2}\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)+3\right) \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}}{16 f \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}} \sin \left(f x +e \right) a}"," ",0,"-1/16/f*(-1+cos(f*x+e))*(4*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-5*cos(f*x+e)^2+4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)+3)*(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))^(5/2)/sin(f*x+e)/a","A"
139,1,235,130,1.873000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(3/2),x)","-\frac{\left(4 \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)+4 \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)-\left(\cos^{2}\left(f x +e \right)\right)+4 \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)+4 \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)+4 \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}} \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} \left(-1+\cos \left(f x +e \right)\right) a^{2}}"," ",0,"-1/f*(4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2+4*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)^2-cos(f*x+e)^2+4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+4*cos(f*x+e)+1)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)*cos(f*x+e)^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-1+cos(f*x+e))/a^2","A"
140,1,193,87,1.931000," ","int(sec(f*x+e)*(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{-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{-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{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(-(-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(-(-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))^(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","B"
141,1,73,36,2.069000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x)","\frac{\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)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}{2 f \sin \left(f x +e \right)^{3} a^{2}}"," ",0,"1/2/f*(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)*(-1+cos(f*x+e))^2/sin(f*x+e)^3/a^2","A"
142,1,123,83,2.104000," ","int(sec(f*x+e)/(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(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)+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*(2*ln(-(-1+cos(f*x+e))/sin(f*x+e))*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"
143,1,133,92,2.045000," ","int(sec(f*x+e)/(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(\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)-\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\cos \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)^{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,"1/2/f*(-1+cos(f*x+e))^2*(cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e))/sin(f*x+e))-cos(f*x+e))*(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"
144,1,211,128,2.166000," ","int(sec(f*x+e)/(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(12 \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)}\right)-12 \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)-5 \left(\cos^{3}\left(f x +e \right)\right)-12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-15 \left(\cos^{2}\left(f x +e \right)\right)+12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+9 \cos \left(f x +e \right)+3\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)^{3} \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^{2}}"," ",0,"1/32/f*(-1+cos(f*x+e))^2*(12*cos(f*x+e)^3*ln(-(-1+cos(f*x+e))/sin(f*x+e))-12*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-5*cos(f*x+e)^3-12*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-15*cos(f*x+e)^2+12*ln(-(-1+cos(f*x+e))/sin(f*x+e))+9*cos(f*x+e)+3)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^3/cos(f*x+e)^2/(c*(-1+cos(f*x+e))/cos(f*x+e))^(5/2)/a^2","A"
145,1,281,131,2.075000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(5/2),x)","-\frac{\left(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)-\left(\cos^{2}\left(f x +e \right)\right)+4 \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)+4 \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)-2 \cos \left(f x +e \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)+2 \ln \left(-\frac{-\sin \left(f x +e \right)-1+\cos \left(f x +e \right)}{\sin \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{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(-(-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-cos(f*x+e)^2+4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*cos(f*x+e)*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)+2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*ln(-(-sin(f*x+e)-1+cos(f*x+e))/sin(f*x+e))+3)*(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","B"
146,1,75,36,2.059000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(3/2)/(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(\cos^{2}\left(f x +e \right)\right) \left(-1+\cos \left(f x +e \right)\right)^{3} \left(\frac{c \left(-1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{4 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/4/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2*(-1+cos(f*x+e))^3*(c*(-1+cos(f*x+e))/cos(f*x+e))^(3/2)/sin(f*x+e)^5/a^3","B"
147,1,83,37,2.169000," ","int(sec(f*x+e)*(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x)","-\frac{\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)}}\, \cos \left(f x +e \right) \left(3 \cos \left(f x +e \right)+1\right) \left(-1+\cos \left(f x +e \right)\right)^{3}}{8 f \sin \left(f x +e \right)^{5} a^{3}}"," ",0,"-1/8/f*(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)*(3*cos(f*x+e)+1)*(-1+cos(f*x+e))^3/sin(f*x+e)^5/a^3","B"
148,1,164,122,2.261000," ","int(sec(f*x+e)/(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(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)+8 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)+5 \left(\cos^{2}\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)-3\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*(4*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))+8*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)+5*cos(f*x+e)^2+4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*cos(f*x+e)-3)/(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)^5/a^3","A"
149,1,204,128,2.211000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x)","-\frac{\left(12 \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)}\right)+5 \left(\cos^{3}\left(f x +e \right)\right)+12 \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)-15 \left(\cos^{2}\left(f x +e \right)\right)-12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \cos \left(f x +e \right)-9 \cos \left(f x +e \right)-12 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \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)}}\, \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*(12*cos(f*x+e)^3*ln(-(-1+cos(f*x+e))/sin(f*x+e))+5*cos(f*x+e)^3+12*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-15*cos(f*x+e)^2-12*ln(-(-1+cos(f*x+e))/sin(f*x+e))*cos(f*x+e)-9*cos(f*x+e)-12*ln(-(-1+cos(f*x+e))/sin(f*x+e))+3)*(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"
150,1,173,142,2.569000," ","int(sec(f*x+e)/(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(3 \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)-6 \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)-5 \left(\cos^{3}\left(f x +e \right)\right)+3 \ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 \cos \left(f x +e \right)\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} \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,"-1/8/f*(-1+cos(f*x+e))^3*(3*cos(f*x+e)^4*ln(-(-1+cos(f*x+e))/sin(f*x+e))-6*cos(f*x+e)^2*ln(-(-1+cos(f*x+e))/sin(f*x+e))-5*cos(f*x+e)^3+3*ln(-(-1+cos(f*x+e))/sin(f*x+e))+3*cos(f*x+e))*(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"
151,0,0,91,2.956000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","\int \sec \left(f x +e \right) \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(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x)","F"
152,0,0,78,2.340000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^2,x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^2,x)","F"
153,0,0,76,1.759000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e)),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e)),x)","F"
154,0,0,78,1.677000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e)),x)","\int \frac{\sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}}{c -c \sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e)),x)","F"
155,0,0,78,1.974000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^2,x)","\int \frac{\sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}}{\left(c -c \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^2,x)","F"
156,0,0,154,1.766000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(5/2),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(5/2),x)","F"
157,0,0,96,1.634000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(3/2),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(3/2),x)","F"
158,0,0,44,1.861000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1/2),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \sqrt{c -c \sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1/2),x)","F"
159,0,0,63,1.676000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(1/2),x)","\int \frac{\sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sec \left(f x +e \right)}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(1/2),x)","F"
160,0,0,66,1.588000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(3/2),x)","\int \frac{\sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}}{\left(c -c \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(3/2),x)","F"
161,0,0,66,1.657000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(5/2),x)","\int \frac{\sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}}{\left(c -c \sec \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/(c-c*sec(f*x+e))^(5/2),x)","F"
162,0,0,169,3.883000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-3-m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{-3-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-3-m),x)","F"
163,0,0,104,3.806000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-2-m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{-2-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-2-m),x)","F"
164,0,0,47,3.817000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-1-m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(-1-m),x)","F"
165,0,0,91,2.547000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m/((c-c*sec(f*x+e))^m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m/((c-c*sec(f*x+e))^m),x)","F"
166,0,0,89,3.685000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1-m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{1-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(1-m),x)","F"
167,0,0,91,3.990000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(2-m),x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m} \left(c -c \sec \left(f x +e \right)\right)^{2-m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^(2-m),x)","F"
168,1,130,95,1.400000," ","int(sec(f*x+e)^2*(a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x)","\frac{a^{3} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{4 f}+\frac{a^{3} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+\frac{7 a^{3} c \tan \left(f x +e \right)}{15 f}-\frac{a^{3} c \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{2 f}-\frac{a^{3} c \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}-\frac{4 a^{3} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}"," ",0,"1/4*a^3*c*sec(f*x+e)*tan(f*x+e)/f+1/4/f*a^3*c*ln(sec(f*x+e)+tan(f*x+e))+7/15*a^3*c*tan(f*x+e)/f-1/2*a^3*c*sec(f*x+e)^3*tan(f*x+e)/f-1/5/f*a^3*c*tan(f*x+e)*sec(f*x+e)^4-4/15/f*a^3*c*tan(f*x+e)*sec(f*x+e)^2","A"
169,1,107,78,1.369000," ","int(sec(f*x+e)^2*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x)","\frac{a^{2} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{a^{2} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{a^{2} c \tan \left(f x +e \right)}{3 f}-\frac{a^{2} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}-\frac{a^{2} c \left(\sec^{3}\left(f x +e \right)\right) \tan \left(f x +e \right)}{4 f}"," ",0,"1/8*a^2*c*sec(f*x+e)*tan(f*x+e)/f+1/8/f*a^2*c*ln(sec(f*x+e)+tan(f*x+e))+1/3*a^2*c*tan(f*x+e)/f-1/3/f*a^2*c*tan(f*x+e)*sec(f*x+e)^2-1/4*a^2*c*sec(f*x+e)^3*tan(f*x+e)/f","A"
170,1,36,15,0.937000," ","int(sec(f*x+e)^2*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x)","\frac{c a \tan \left(f x +e \right)+c a \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*(c*a*tan(f*x+e)+c*a*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","B"
171,1,104,56,0.583000," ","int(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x)","-\frac{2 c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}+\frac{c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{2 c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f a}+\frac{2 c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f a}+\frac{c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}"," ",0,"-2/f/a*c*tan(1/2*e+1/2*f*x)+1/f/a*c/(tan(1/2*e+1/2*f*x)-1)-2/f/a*c*ln(tan(1/2*e+1/2*f*x)-1)+2/f/a*c*ln(tan(1/2*e+1/2*f*x)+1)+1/f/a*c/(tan(1/2*e+1/2*f*x)+1)","A"
172,1,81,66,0.712000," ","int(sec(f*x+e)^2*(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{c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}-\frac{c \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\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)+1/f*c/a^2*ln(tan(1/2*e+1/2*f*x)-1)-1/f*c/a^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
173,1,37,80,0.757000," ","int(sec(f*x+e)^2*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x)","\frac{c \left(-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3}\right)}{2 f \,a^{3}}"," ",0,"1/2/f*c/a^3*(-1/5*tan(1/2*e+1/2*f*x)^5-1/3*tan(1/2*e+1/2*f*x)^3)","A"
174,0,0,124,3.000000," ","int((g*sec(f*x+e))^p*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x)","\int \left(g \sec \left(f x +e \right)\right)^{p} \left(a +a \sec \left(f x +e \right)\right)^{2} \left(c -c \sec \left(f x +e \right)\right)\, dx"," ",0,"int((g*sec(f*x+e))^p*(a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x)","F"
175,0,0,57,2.615000," ","int((g*sec(f*x+e))^p*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x)","\int \left(g \sec \left(f x +e \right)\right)^{p} \left(a +a \sec \left(f x +e \right)\right) \left(c -c \sec \left(f x +e \right)\right)\, dx"," ",0,"int((g*sec(f*x+e))^p*(a+a*sec(f*x+e))*(c-c*sec(f*x+e)),x)","F"
176,0,0,162,4.055000," ","int((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x)","\int \frac{\left(g \sec \left(f x +e \right)\right)^{p} \left(c -c \sec \left(f x +e \right)\right)}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e)),x)","F"
177,0,0,200,2.516000," ","int((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x)","\int \frac{\left(g \sec \left(f x +e \right)\right)^{p} \left(c -c \sec \left(f x +e \right)\right)}{\left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*sec(f*x+e))^p*(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x)","F"
178,1,236,88,2.293000," ","int((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x)","-\frac{\left(2 \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right) \cos \left(f x +e \right)+\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right) \cos \left(f x +e \right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right)-\arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right)\right) \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(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{c f \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{4}}"," ",0,"-1/c/f*(2*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)+arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))*cos(f*x+e)+arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e)))*cos(f*x+e)-arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))-arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e))))*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2/(1/(1+cos(f*x+e)))^(3/2)/sin(f*x+e)^4","B"
179,1,204,70,1.684000," ","int(sec(f*x+e)^2/(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(\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)}}\, \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) \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)\right)}{2 c f \left(-1+\cos^{2}\left(f x +e \right)\right) a}"," ",0,"-1/2/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)*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)*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)))/(-1+cos(f*x+e)^2)/a","B"
180,1,317,120,2.876000," ","int(sec(f*x+e)^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(\frac{1}{\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)}}\, \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right) \sqrt{2}}{4}\right) \cos \left(f x +e \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1-\sin \left(f x +e \right)\right) \sqrt{2}}{4}\right) \cos \left(f x +e \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right) \sqrt{2}}{4}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1-\sin \left(f x +e \right)\right) \sqrt{2}}{4}\right)-\arctan \left(\frac{\sin \left(f x +e \right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}}{2}\right) \cos \left(f x +e \right)+\sin \left(f x +e \right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}+\arctan \left(\frac{\sin \left(f x +e \right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}}{2}\right)\right)}{c f \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)^{2} a}"," ",0,"1/c/f*(1/cos(f*x+e))^(5/2)*cos(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(2^(1/2)*arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e))*2^(1/2))*cos(f*x+e)-2^(1/2)*arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1-sin(f*x+e))*2^(1/2))*cos(f*x+e)-2^(1/2)*arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e))*2^(1/2))+2^(1/2)*arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1-sin(f*x+e))*2^(1/2))-arctan(1/2*sin(f*x+e)*(-2/(1+cos(f*x+e)))^(1/2))*cos(f*x+e)+sin(f*x+e)*(-2/(1+cos(f*x+e)))^(1/2)+arctan(1/2*sin(f*x+e)*(-2/(1+cos(f*x+e)))^(1/2)))/(-2/(1+cos(f*x+e)))^(1/2)/sin(f*x+e)^2/a","B"
181,1,152,97,2.698000," ","int((g*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(\cos \left(f x +e \right) \sqrt{2}\, \arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sqrt{2}\, \arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\right) \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right) \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)}}}{2 c f \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{4} a}"," ",0,"1/2/c/f*(cos(f*x+e)*2^(1/2)*arcsinh((-1+cos(f*x+e))/sin(f*x+e))-2^(1/2)*arcsinh((-1+cos(f*x+e))/sin(f*x+e))-2*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2))*(g/cos(f*x+e))^(3/2)*(-1+cos(f*x+e))*cos(f*x+e)^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(1/(1+cos(f*x+e)))^(3/2)/sin(f*x+e)^4/a","A"
182,1,294,149,2.954000," ","int((g*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(\cos \left(f x +e \right) \sqrt{2}\, \arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sqrt{2}\, \arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}+2 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right) \cos \left(f x +e \right)+2 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right) \cos \left(f x +e \right)-2 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right)-2 \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right)\right) \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(f x +e \right)\right)^{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 c f \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sin \left(f x +e \right)^{6} a}"," ",0,"1/2/c/f*(cos(f*x+e)*2^(1/2)*arcsinh((-1+cos(f*x+e))/sin(f*x+e))-2^(1/2)*arcsinh((-1+cos(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*(1/(1+cos(f*x+e)))^(1/2)+2*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))*cos(f*x+e)+2*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e)))*cos(f*x+e)-2*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))-2*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e))))*(g/cos(f*x+e))^(5/2)*(-1+cos(f*x+e))^2*cos(f*x+e)^3*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)/(1/(1+cos(f*x+e)))^(5/2)/sin(f*x+e)^6/a","A"
183,1,142,42,1.977000," ","int(sec(f*x+e)^2/(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(\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)\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)}}}{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(-(-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)))*cos(f*x+e)*(c*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/c/a","B"
184,1,414,51,1.664000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c-d*sec(f*x+e)),x)","-\frac{\left(\ln \left(-\frac{2 \left(\sqrt{-\frac{2 d}{c +d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)+\sqrt{-\frac{2 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)+\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \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)}\right)}{c \cos \left(f x +e \right)+d \cos \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c -d}\right)-\ln \left(-\frac{2 \left(\sqrt{-\frac{2 d}{c +d}}\, \sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)+\sqrt{-\frac{2 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)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \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)}\right)}{c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \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)}}}{f \sqrt{-\frac{2 d}{c +d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}}"," ",0,"-1/f*(ln(-2*((-2*d/(c+d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)+(-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*cos(f*x+e)+d*cos(f*x+e)-((c+d)*(c-d))^(1/2)*sin(f*x+e)-c-d))-ln(-2*((-2*d/(c+d))^(1/2)*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)+(-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*cos(f*x+e)+d*cos(f*x+e)+((c+d)*(c-d))^(1/2)*sin(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*d/(c+d))^(1/2)/((c+d)*(c-d))^(1/2)","B"
185,1,431,224,1.614000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^4,x)","\frac{a \,c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 a \,c^{3} d \tan \left(f x +e \right)}{f}+\frac{3 a \,c^{2} d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{3 a \,c^{2} d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{8 a c \,d^{3} \tan \left(f x +e \right)}{3 f}+\frac{4 a c \,d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a \,d^{4} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 a \,d^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 a \,d^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{a \,c^{4} \tan \left(f x +e \right)}{f}+\frac{2 a \,c^{3} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{2 a \,c^{3} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 a \,c^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{2 a \,c^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{a c \,d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{f}+\frac{3 a c \,d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 a c \,d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{8 a \,d^{4} \tan \left(f x +e \right)}{15 f}+\frac{a \,d^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{4 a \,d^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}"," ",0,"1/f*a*c^4*ln(sec(f*x+e)+tan(f*x+e))+4/f*a*c^3*d*tan(f*x+e)+3/f*a*c^2*d^2*sec(f*x+e)*tan(f*x+e)+3/f*a*c^2*d^2*ln(sec(f*x+e)+tan(f*x+e))+8/3/f*a*c*d^3*tan(f*x+e)+4/3/f*a*c*d^3*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a*d^4*tan(f*x+e)*sec(f*x+e)^3+3/8/f*a*d^4*sec(f*x+e)*tan(f*x+e)+3/8/f*a*d^4*ln(sec(f*x+e)+tan(f*x+e))+1/f*a*c^4*tan(f*x+e)+2/f*a*c^3*d*sec(f*x+e)*tan(f*x+e)+2/f*a*c^3*d*ln(sec(f*x+e)+tan(f*x+e))+4/f*a*c^2*d^2*tan(f*x+e)+2/f*a*c^2*d^2*tan(f*x+e)*sec(f*x+e)^2+1/f*a*c*d^3*tan(f*x+e)*sec(f*x+e)^3+3/2/f*a*c*d^3*sec(f*x+e)*tan(f*x+e)+3/2/f*a*c*d^3*ln(sec(f*x+e)+tan(f*x+e))+8/15/f*a*d^4*tan(f*x+e)+1/5/f*a*d^4*tan(f*x+e)*sec(f*x+e)^4+4/15/f*a*d^4*tan(f*x+e)*sec(f*x+e)^2","A"
186,1,290,161,1.329000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^3,x)","\frac{a \,c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{3 a \,c^{2} d \tan \left(f x +e \right)}{f}+\frac{3 a c \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 a c \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{2 a \,d^{3} \tan \left(f x +e \right)}{3 f}+\frac{a \,d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a \,c^{3} \tan \left(f x +e \right)}{f}+\frac{3 a \,c^{2} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 a \,c^{2} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{2 a c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{a c \,d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{a \,d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 a \,d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 a \,d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}"," ",0,"1/f*a*c^3*ln(sec(f*x+e)+tan(f*x+e))+3/f*a*c^2*d*tan(f*x+e)+3/2/f*a*c*d^2*sec(f*x+e)*tan(f*x+e)+3/2/f*a*c*d^2*ln(sec(f*x+e)+tan(f*x+e))+2/3/f*a*d^3*tan(f*x+e)+1/3/f*a*d^3*tan(f*x+e)*sec(f*x+e)^2+1/f*a*c^3*tan(f*x+e)+3/2/f*a*c^2*d*sec(f*x+e)*tan(f*x+e)+3/2/f*a*c^2*d*ln(sec(f*x+e)+tan(f*x+e))+2/f*a*c*d^2*tan(f*x+e)+1/f*a*c*d^2*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a*d^3*tan(f*x+e)*sec(f*x+e)^3+3/8/f*a*d^3*sec(f*x+e)*tan(f*x+e)+3/8/f*a*d^3*ln(sec(f*x+e)+tan(f*x+e))","A"
187,1,174,100,1.111000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e))^2,x)","\frac{a \,c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{2 a c d \tan \left(f x +e \right)}{f}+\frac{a \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{a \,c^{2} \tan \left(f x +e \right)}{f}+\frac{a c d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{a c d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{2 a \,d^{2} \tan \left(f x +e \right)}{3 f}+\frac{a \,d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"1/f*a*c^2*ln(sec(f*x+e)+tan(f*x+e))+2/f*a*c*d*tan(f*x+e)+1/2/f*a*d^2*sec(f*x+e)*tan(f*x+e)+1/2/f*a*d^2*ln(sec(f*x+e)+tan(f*x+e))+a*c^2*tan(f*x+e)/f+1/f*a*c*d*sec(f*x+e)*tan(f*x+e)+1/f*a*c*d*ln(sec(f*x+e)+tan(f*x+e))+2/3/f*a*d^2*tan(f*x+e)+1/3/f*a*d^2*tan(f*x+e)*sec(f*x+e)^2","A"
188,1,86,52,0.961000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))*(c+d*sec(f*x+e)),x)","\frac{c a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{d a \tan \left(f x +e \right)}{f}+\frac{a c \tan \left(f x +e \right)}{f}+\frac{a d \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{d a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}"," ",0,"1/f*c*a*ln(sec(f*x+e)+tan(f*x+e))+1/f*d*a*tan(f*x+e)+a*c*tan(f*x+e)/f+1/2*a*d*sec(f*x+e)*tan(f*x+e)/f+1/2/f*d*a*ln(sec(f*x+e)+tan(f*x+e))","A"
189,1,135,60,0.703000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x)","-\frac{2 a \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) c}{f d \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a \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)}{f \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f d}+\frac{a \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f d}"," ",0,"-2/f*a/d/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c+2/f*a/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))-1/f*a/d*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a/d*ln(tan(1/2*e+1/2*f*x)+1)","B"
190,1,105,70,0.717000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x)","\frac{4 a \left(-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \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{\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)}{2 \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"4/f*a*(-1/2*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)+1/2/(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"
191,1,178,118,0.745000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x)","\frac{4 a \left(\frac{-\frac{\left(2 c -d \right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{4 \left(c^{2}+2 c d +d^{2}\right)}+\frac{\left(2 c -3 d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 \left(c +d \right) \left(c -d \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)^{2}}+\frac{\left(2 c -d \right) \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)}{4 \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"4/f*a*((-1/4*(2*c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/4*(2*c-3*d)/(c+d)/(c-d)*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)^2+1/4*(2*c-d)/(c^3+c^2*d-c*d^2-d^3)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2)))","A"
192,1,271,174,0.779000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^4,x)","\frac{4 a \left(\frac{-\frac{\left(2 c^{2}-2 c d +d^{2}\right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{4 \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{\left(3 c^{2}-6 c d +d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{\left(2 c^{2}-6 c d +3 d^{2}\right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 \left(c +d \right) \left(c^{2}-2 c d +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)^{3}}+\frac{\left(2 c^{2}-2 c d +d^{2}\right) \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)}{4 \left(c^{5}+c^{4} d -2 c^{3} d^{2}-2 c^{2} d^{3}+c \,d^{4}+d^{5}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"4/f*a*((-1/4*(2*c^2-2*c*d+d^2)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5+1/3*(3*c^2-6*c*d+d^2)/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3-1/4*(2*c^2-6*c*d+3*d^2)/(c+d)/(c^2-2*c*d+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)^3+1/4*(2*c^2-2*c*d+d^2)/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2)))","A"
193,1,602,313,1.964000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^4,x)","\frac{20 a^{2} c^{3} d \tan \left(f x +e \right)}{3 f}+\frac{2 a^{2} c \,d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{f}+\frac{12 a^{2} c \,d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}+\frac{3 a^{2} c \,d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{a^{2} c^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{4 a^{2} c^{3} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{21 a^{2} c^{2} d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{4 f}+\frac{4 a^{2} c^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{4 a^{2} c \,d^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{3 a^{2} c^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{2 f}+\frac{4 a^{2} c^{3} d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{2 a^{2} c^{4} \tan \left(f x +e \right)}{f}+\frac{3 a^{2} c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{11 a^{2} d^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}+\frac{16 a^{2} d^{4} \tan \left(f x +e \right)}{15 f}+\frac{11 a^{2} d^{4} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}+\frac{2 a^{2} d^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{8 a^{2} d^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{21 a^{2} c^{2} d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+\frac{11 a^{2} d^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{4 a^{2} c^{3} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{3 a^{2} c \,d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{24 a^{2} c \,d^{3} \tan \left(f x +e \right)}{5 f}+\frac{8 a^{2} c^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{a^{2} d^{4} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"20/3/f*a^2*c^3*d*tan(f*x+e)+4/f*a^2*c^2*d^2*tan(f*x+e)*sec(f*x+e)^2+2/f*a^2*c*d^3*tan(f*x+e)*sec(f*x+e)^3+3/f*a^2*c*d^3*sec(f*x+e)*tan(f*x+e)+12/5/f*a^2*c*d^3*tan(f*x+e)*sec(f*x+e)^2+1/2*a^2*c^4*sec(f*x+e)*tan(f*x+e)/f+4/f*a^2*c^3*d*sec(f*x+e)*tan(f*x+e)+21/4/f*a^2*c^2*d^2*sec(f*x+e)*tan(f*x+e)+4/5/f*a^2*c*d^3*tan(f*x+e)*sec(f*x+e)^4+3/2/f*a^2*c^2*d^2*tan(f*x+e)*sec(f*x+e)^3+4/3/f*a^2*c^3*d*tan(f*x+e)*sec(f*x+e)^2+2*a^2*c^4*tan(f*x+e)/f+3/2/f*a^2*c^4*ln(sec(f*x+e)+tan(f*x+e))+11/16/f*a^2*d^4*ln(sec(f*x+e)+tan(f*x+e))+16/15/f*a^2*d^4*tan(f*x+e)+21/4/f*a^2*c^2*d^2*ln(sec(f*x+e)+tan(f*x+e))+11/24/f*a^2*d^4*tan(f*x+e)*sec(f*x+e)^3+11/16/f*a^2*d^4*sec(f*x+e)*tan(f*x+e)+4/f*a^2*c^3*d*ln(sec(f*x+e)+tan(f*x+e))+3/f*a^2*c*d^3*ln(sec(f*x+e)+tan(f*x+e))+2/5/f*a^2*d^4*tan(f*x+e)*sec(f*x+e)^4+8/15/f*a^2*d^4*tan(f*x+e)*sec(f*x+e)^2+24/5/f*a^2*c*d^3*tan(f*x+e)+8/f*a^2*c^2*d^2*tan(f*x+e)+1/6/f*a^2*d^4*tan(f*x+e)*sec(f*x+e)^5","A"
194,1,420,230,1.624000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^3,x)","\frac{3 a^{2} c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{5 a^{2} c^{2} d \tan \left(f x +e \right)}{f}+\frac{21 a^{2} c \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{21 a^{2} c \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{6 a^{2} d^{3} \tan \left(f x +e \right)}{5 f}+\frac{3 a^{2} d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}+\frac{2 a^{2} c^{3} \tan \left(f x +e \right)}{f}+\frac{3 a^{2} c^{2} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{3 a^{2} c^{2} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 a^{2} c \,d^{2} \tan \left(f x +e \right)}{f}+\frac{2 a^{2} c \,d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{a^{2} d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{2 f}+\frac{3 a^{2} d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{4 f}+\frac{3 a^{2} d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+\frac{c^{3} a^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a^{2} c^{2} d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{3 a^{2} c \,d^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{a^{2} d^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"3/2/f*a^2*c^3*ln(sec(f*x+e)+tan(f*x+e))+5/f*a^2*c^2*d*tan(f*x+e)+21/8/f*a^2*c*d^2*sec(f*x+e)*tan(f*x+e)+21/8/f*a^2*c*d^2*ln(sec(f*x+e)+tan(f*x+e))+6/5/f*a^2*d^3*tan(f*x+e)+3/5/f*a^2*d^3*tan(f*x+e)*sec(f*x+e)^2+2*a^2*c^3*tan(f*x+e)/f+3/f*a^2*c^2*d*sec(f*x+e)*tan(f*x+e)+3/f*a^2*c^2*d*ln(sec(f*x+e)+tan(f*x+e))+4/f*a^2*c*d^2*tan(f*x+e)+2/f*a^2*c*d^2*tan(f*x+e)*sec(f*x+e)^2+1/2/f*a^2*d^3*tan(f*x+e)*sec(f*x+e)^3+3/4/f*a^2*d^3*sec(f*x+e)*tan(f*x+e)+3/4/f*a^2*d^3*ln(sec(f*x+e)+tan(f*x+e))+1/2/f*c^3*a^2*sec(f*x+e)*tan(f*x+e)+1/f*a^2*c^2*d*tan(f*x+e)*sec(f*x+e)^2+3/4/f*a^2*c*d^2*tan(f*x+e)*sec(f*x+e)^3+1/5/f*a^2*d^3*tan(f*x+e)*sec(f*x+e)^4","A"
195,1,268,166,1.420000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e))^2,x)","\frac{3 a^{2} c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{10 a^{2} c d \tan \left(f x +e \right)}{3 f}+\frac{7 a^{2} d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{7 a^{2} d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{2 a^{2} c^{2} \tan \left(f x +e \right)}{f}+\frac{2 a^{2} c d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{2 a^{2} c d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 a^{2} d^{2} \tan \left(f x +e \right)}{3 f}+\frac{2 a^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a^{2} c^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{2 a^{2} c d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"3/2/f*a^2*c^2*ln(sec(f*x+e)+tan(f*x+e))+10/3/f*a^2*c*d*tan(f*x+e)+7/8/f*a^2*d^2*sec(f*x+e)*tan(f*x+e)+7/8/f*a^2*d^2*ln(sec(f*x+e)+tan(f*x+e))+2*a^2*c^2*tan(f*x+e)/f+2/f*a^2*c*d*sec(f*x+e)*tan(f*x+e)+2/f*a^2*c*d*ln(sec(f*x+e)+tan(f*x+e))+4/3/f*a^2*d^2*tan(f*x+e)+2/3/f*a^2*d^2*tan(f*x+e)*sec(f*x+e)^2+1/2*a^2*c^2*sec(f*x+e)*tan(f*x+e)/f+2/3/f*a^2*c*d*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a^2*d^2*tan(f*x+e)*sec(f*x+e)^3","A"
196,1,141,95,1.156000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2*(c+d*sec(f*x+e)),x)","\frac{3 a^{2} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{5 a^{2} d \tan \left(f x +e \right)}{3 f}+\frac{2 a^{2} c \tan \left(f x +e \right)}{f}+\frac{a^{2} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{a^{2} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{a^{2} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a^{2} d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"3/2/f*a^2*c*ln(sec(f*x+e)+tan(f*x+e))+5/3/f*a^2*d*tan(f*x+e)+2*a^2*c*tan(f*x+e)/f+1/f*a^2*d*sec(f*x+e)*tan(f*x+e)+1/f*a^2*d*ln(sec(f*x+e)+tan(f*x+e))+1/2*a^2*c*sec(f*x+e)*tan(f*x+e)/f+1/3/f*a^2*d*tan(f*x+e)*sec(f*x+e)^2","A"
197,1,291,86,0.622000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x)","\frac{2 a^{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) c^{2}}{f \,d^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{4 a^{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) c}{f d \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{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)}{f \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a^{2}}{f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,d^{2}}-\frac{2 a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f d}-\frac{a^{2}}{f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,d^{2}}+\frac{2 a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f d}"," ",0,"2/f*a^2/d^2/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c^2-4/f*a^2/d/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c+2/f*a^2/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))-1/f*a^2/d/(tan(1/2*e+1/2*f*x)-1)+1/f*a^2/d^2*ln(tan(1/2*e+1/2*f*x)-1)*c-2/f*a^2/d*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a^2/d/(tan(1/2*e+1/2*f*x)+1)-1/f*a^2/d^2*ln(tan(1/2*e+1/2*f*x)+1)*c+2/f*a^2/d*ln(tan(1/2*e+1/2*f*x)+1)","B"
198,1,330,108,0.821000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x)","\frac{2 a^{2} c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f d \left(c +d \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 a^{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) c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 a^{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)}{f d \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 a^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \left(c +d \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 a^{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)}{f \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,d^{2}}+\frac{a^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,d^{2}}"," ",0,"2/f*a^2/d*c/(c+d)*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)-2/f*a^2/d^2/(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))*c^2-2/f*a^2/d*c/(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))-2/f*a^2/(c+d)*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)+4/f*a^2/(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))-1/f*a^2/d^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^2/d^2*ln(tan(1/2*e+1/2*f*x)+1)","B"
199,1,167,117,0.772000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x)","\frac{8 a^{2} \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 \left(c +d \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)^{2}}+\frac{-\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{8 \left(c +d \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{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)}{8 \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}}{c +d}\right)}{f}"," ",0,"8/f*a^2*(1/4*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2+3/4/(c+d)*(-1/2*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)+1/2/(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"
200,1,228,198,0.826000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^4,x)","\frac{8 a^{2} \left(-\frac{\frac{\left(3 c -2 d \right) \left(c -d \right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{8 c^{3}+24 c^{2} d +24 c \,d^{2}+8 d^{3}}-\frac{\left(3 c -2 d \right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 \left(c^{2}+2 c d +d^{2}\right)}+\frac{\left(5 c -6 d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{8 \left(c +d \right) \left(c -d \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)^{3}}+\frac{\left(3 c -2 d \right) \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)}{8 \left(c^{4}+2 c^{3} d -2 c \,d^{3}-d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"8/f*a^2*(-(1/8*(3*c-2*d)*(c-d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5-1/3*(3*c-2*d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/8*(5*c-6*d)/(c+d)/(c-d)*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)^3+1/8*(3*c-2*d)/(c^4+2*c^3*d-2*c*d^3-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"
201,1,352,257,0.921000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^5,x)","\frac{8 a^{2} \left(-\frac{\frac{\left(12 c^{2}-16 c d +7 d^{2}\right) \left(c -d \right) \left(\tan^{7}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{32 c^{4}+128 c^{3} d +192 c^{2} d^{2}+128 c \,d^{3}+32 d^{4}}-\frac{11 \left(12 c^{2}-16 c d +7 d^{2}\right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{96 \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{\left(156 c^{2}-272 c d +83 d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{96 \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{\left(20 c^{2}-48 c d +25 d^{2}\right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{32 \left(c +d \right) \left(c^{2}-2 c d +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)^{4}}+\frac{\left(12 c^{2}-16 c d +7 d^{2}\right) \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)}{32 \left(c^{6}+2 c^{5} d -c^{4} d^{2}-4 c^{3} d^{3}-c^{2} d^{4}+2 c \,d^{5}+d^{6}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"8/f*a^2*(-(1/32*(12*c^2-16*c*d+7*d^2)*(c-d)/(c^4+4*c^3*d+6*c^2*d^2+4*c*d^3+d^4)*tan(1/2*e+1/2*f*x)^7-11/96*(12*c^2-16*c*d+7*d^2)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5+1/96*(156*c^2-272*c*d+83*d^2)/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3-1/32*(20*c^2-48*c*d+25*d^2)/(c+d)/(c^2-2*c*d+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)^4+1/32*(12*c^2-16*c*d+7*d^2)/(c^6+2*c^5*d-c^4*d^2-4*c^3*d^3-c^2*d^4+2*c*d^5+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"
202,1,523,273,1.950000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^3,x)","\frac{23 a^{3} d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{24 f}+\frac{23 a^{3} d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{16 f}+\frac{3 a^{3} c^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a^{3} d^{3} \tan \left(f x +e \right) \left(\sec^{5}\left(f x +e \right)\right)}{6 f}+\frac{45 a^{3} c^{2} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{9 a^{3} c \,d^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{34 a^{3} d^{3} \tan \left(f x +e \right)}{15 f}+\frac{17 a^{3} d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{3 a^{3} d^{3} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{a^{3} c^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{3 a^{3} c^{2} d \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{38 a^{3} c \,d^{2} \tan \left(f x +e \right)}{5 f}+\frac{19 a^{3} c \,d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{5 f}+\frac{3 a^{3} c^{2} d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{3 a^{3} c \,d^{2} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{9 a^{3} c^{2} d \tan \left(f x +e \right)}{f}+\frac{39 a^{3} c \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{45 a^{3} c^{2} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{39 a^{3} c \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{5 a^{3} c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{11 a^{3} c^{3} \tan \left(f x +e \right)}{3 f}+\frac{23 a^{3} d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{16 f}"," ",0,"23/24/f*a^3*d^3*tan(f*x+e)*sec(f*x+e)^3+23/16/f*a^3*d^3*sec(f*x+e)*tan(f*x+e)+3/2*a^3*c^3*sec(f*x+e)*tan(f*x+e)/f+1/6/f*a^3*d^3*tan(f*x+e)*sec(f*x+e)^5+45/8/f*a^3*c^2*d*sec(f*x+e)*tan(f*x+e)+9/4/f*a^3*c*d^2*tan(f*x+e)*sec(f*x+e)^3+34/15/f*a^3*d^3*tan(f*x+e)+17/15/f*a^3*d^3*tan(f*x+e)*sec(f*x+e)^2+3/5/f*a^3*d^3*tan(f*x+e)*sec(f*x+e)^4+1/3/f*a^3*c^3*tan(f*x+e)*sec(f*x+e)^2+3/4/f*a^3*c^2*d*tan(f*x+e)*sec(f*x+e)^3+38/5/f*a^3*c*d^2*tan(f*x+e)+19/5/f*a^3*c*d^2*tan(f*x+e)*sec(f*x+e)^2+3/f*a^3*c^2*d*tan(f*x+e)*sec(f*x+e)^2+3/5/f*a^3*c*d^2*tan(f*x+e)*sec(f*x+e)^4+9/f*a^3*c^2*d*tan(f*x+e)+39/8/f*a^3*c*d^2*ln(sec(f*x+e)+tan(f*x+e))+45/8/f*a^3*c^2*d*ln(sec(f*x+e)+tan(f*x+e))+39/8/f*a^3*c*d^2*sec(f*x+e)*tan(f*x+e)+5/2/f*a^3*c^3*ln(sec(f*x+e)+tan(f*x+e))+11/3*a^3*c^3*tan(f*x+e)/f+23/16/f*a^3*d^3*ln(sec(f*x+e)+tan(f*x+e))","A"
203,1,342,245,1.721000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e))^2,x)","\frac{5 a^{3} c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{6 a^{3} c d \tan \left(f x +e \right)}{f}+\frac{13 a^{3} d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{13 a^{3} d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{11 a^{3} c^{2} \tan \left(f x +e \right)}{3 f}+\frac{15 a^{3} c d \sec \left(f x +e \right) \tan \left(f x +e \right)}{4 f}+\frac{15 a^{3} c d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{4 f}+\frac{38 a^{3} d^{2} \tan \left(f x +e \right)}{15 f}+\frac{19 a^{3} d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}+\frac{3 a^{3} c^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{2 a^{3} c d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{3 a^{3} d^{2} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{a^{3} c^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a^{3} c d \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{2 f}+\frac{a^{3} d^{2} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"5/2/f*a^3*c^2*ln(sec(f*x+e)+tan(f*x+e))+6/f*a^3*c*d*tan(f*x+e)+13/8/f*a^3*d^2*sec(f*x+e)*tan(f*x+e)+13/8/f*a^3*d^2*ln(sec(f*x+e)+tan(f*x+e))+11/3*a^3*c^2*tan(f*x+e)/f+15/4/f*a^3*c*d*sec(f*x+e)*tan(f*x+e)+15/4/f*a^3*c*d*ln(sec(f*x+e)+tan(f*x+e))+38/15/f*a^3*d^2*tan(f*x+e)+19/15/f*a^3*d^2*tan(f*x+e)*sec(f*x+e)^2+3/2*a^3*c^2*sec(f*x+e)*tan(f*x+e)/f+2/f*a^3*c*d*tan(f*x+e)*sec(f*x+e)^2+3/4/f*a^3*d^2*tan(f*x+e)*sec(f*x+e)^3+1/3/f*a^3*c^2*tan(f*x+e)*sec(f*x+e)^2+1/2/f*a^3*c*d*tan(f*x+e)*sec(f*x+e)^3+1/5/f*a^3*d^2*tan(f*x+e)*sec(f*x+e)^4","A"
204,1,188,117,1.390000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3*(c+d*sec(f*x+e)),x)","\frac{5 a^{3} c \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{3 a^{3} d \tan \left(f x +e \right)}{f}+\frac{11 a^{3} c \tan \left(f x +e \right)}{3 f}+\frac{15 a^{3} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{15 a^{3} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{3 a^{3} c \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a^{3} d \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{a^{3} c \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a^{3} d \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"5/2/f*a^3*c*ln(sec(f*x+e)+tan(f*x+e))+3/f*a^3*d*tan(f*x+e)+11/3*a^3*c*tan(f*x+e)/f+15/8/f*a^3*d*sec(f*x+e)*tan(f*x+e)+15/8/f*a^3*d*ln(sec(f*x+e)+tan(f*x+e))+3/2*a^3*c*sec(f*x+e)*tan(f*x+e)/f+1/f*a^3*d*tan(f*x+e)*sec(f*x+e)^2+1/3/f*a^3*c*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a^3*d*tan(f*x+e)*sec(f*x+e)^3","A"
205,1,491,140,0.666000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x)","-\frac{2 a^{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) c^{3}}{f \,d^{3} \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{6 a^{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) c^{2}}{f \,d^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{6 a^{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) c}{f d \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{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)}{f \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{a^{3}}{2 f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{a^{3} c}{f \,d^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{5 a^{3}}{2 f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2}}{f \,d^{3}}+\frac{3 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,d^{2}}-\frac{7 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f d}-\frac{a^{3}}{2 f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{a^{3} c}{f \,d^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{5 a^{3}}{2 f d \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2}}{f \,d^{3}}-\frac{3 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,d^{2}}+\frac{7 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f d}"," ",0,"-2/f*a^3/d^3/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c^3+6/f*a^3/d^2/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c^2-6/f*a^3/d/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c+2/f*a^3/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))+1/2/f*a^3/d/(tan(1/2*e+1/2*f*x)-1)^2+1/f*a^3/d^2/(tan(1/2*e+1/2*f*x)-1)*c-5/2/f*a^3/d/(tan(1/2*e+1/2*f*x)-1)-1/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)-1)*c^2+3/f*a^3/d^2*ln(tan(1/2*e+1/2*f*x)-1)*c-7/2/f*a^3/d*ln(tan(1/2*e+1/2*f*x)-1)-1/2/f*a^3/d/(tan(1/2*e+1/2*f*x)+1)^2+1/f*a^3/d^2/(tan(1/2*e+1/2*f*x)+1)*c-5/2/f*a^3/d/(tan(1/2*e+1/2*f*x)+1)+1/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)+1)*c^2-3/f*a^3/d^2*ln(tan(1/2*e+1/2*f*x)+1)*c+7/2/f*a^3/d*ln(tan(1/2*e+1/2*f*x)+1)","B"
206,1,548,152,0.695000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x)","-\frac{2 a^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}}{f \,d^{2} \left(c +d \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 a^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c}{f d \left(c +d \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 a^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \left(c +d \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 a^{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) c^{3}}{f \,d^{3} \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 a^{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) c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{8 a^{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) c}{f d \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{6 a^{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)}{f \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a^{3}}{f \,d^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{2 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,d^{3}}-\frac{3 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,d^{2}}-\frac{a^{3}}{f \,d^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{2 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,d^{3}}+\frac{3 a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,d^{2}}"," ",0,"-2/f*a^3/d^2/(c+d)*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)*c^2+4/f*a^3/d/(c+d)*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)*c-2/f*a^3/(c+d)*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)+4/f*a^3/d^3/(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))*c^3-2/f*a^3/d^2/(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))*c^2-8/f*a^3/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))*c+6/f*a^3/(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))-1/f*a^3/d^2/(tan(1/2*e+1/2*f*x)-1)+2/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)-1)*c-3/f*a^3/d^2*ln(tan(1/2*e+1/2*f*x)-1)-1/f*a^3/d^2/(tan(1/2*e+1/2*f*x)+1)-2/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)+1)*c+3/f*a^3/d^2*ln(tan(1/2*e+1/2*f*x)+1)","B"
207,1,768,175,0.872000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x)","\frac{2 a^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3}}{f \,d^{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^{2}+2 c d +d^{2}\right)}+\frac{a^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{f d \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^{2}+2 c d +d^{2}\right)}-\frac{8 a^{3} c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{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^{2}+2 c d +d^{2}\right)}-\frac{2 a^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}}{f \,d^{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)}-\frac{5 a^{3} c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f d \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)}-\frac{2 a^{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) c^{3}}{f \,d^{3} \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{4 a^{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) c^{2}}{f \,d^{2} \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a^{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)}{f d \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{5 a^{3} d \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{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^{2}+2 c d +d^{2}\right)}+\frac{7 a^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{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)}+\frac{7 a^{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)}{f \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,d^{3}}+\frac{a^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,d^{3}}"," ",0,"2/f*a^3/d^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^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*c^3+1/f*a^3/d/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*c^2-8/f*a^3*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^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3-2/f*a^3/d^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)*tan(1/2*e+1/2*f*x)*c^2-5/f*a^3/d*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)*tan(1/2*e+1/2*f*x)-2/f*a^3/d^3/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c^3-4/f*a^3/d^2/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c^2-1/f*a^3/d*c/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))+5/f*a^3*d/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+7/f*a^3/(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)*tan(1/2*e+1/2*f*x)+7/f*a^3/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))-1/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)-1)+1/f*a^3/d^3*ln(tan(1/2*e+1/2*f*x)+1)","B"
208,1,227,163,0.960000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^4,x)","\frac{16 a^{3} \left(-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{6 \left(c +d \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)^{3}}-\frac{5 \left(-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 \left(c +d \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)^{2}}-\frac{3 \left(-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \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{\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)}{2 \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{4 \left(c +d \right)}\right)}{6 \left(c +d \right)}\right)}{f}"," ",0,"16/f*a^3*(-1/6*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^3-5/6/(c+d)*(-1/4*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2-3/4/(c+d)*(-1/2*tan(1/2*e+1/2*f*x)/(c+d)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)+1/2/(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"
209,1,303,247,1.005000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^5,x)","\frac{16 a^{3} \left(\frac{-\frac{5 \left(4 c -3 d \right) \left(c^{2}-2 c d +d^{2}\right) \left(\tan^{7}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{64 \left(c^{4}+4 c^{3} d +6 c^{2} d^{2}+4 c \,d^{3}+d^{4}\right)}+\frac{55 \left(c -d \right) \left(4 c -3 d \right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{192 \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{73 \left(4 c -3 d \right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{192 \left(c^{2}+2 c d +d^{2}\right)}+\frac{\left(44 c -49 d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{64 \left(c +d \right) \left(c -d \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)^{4}}+\frac{5 \left(4 c -3 d \right) \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)}{64 \left(c^{5}+3 c^{4} d +2 c^{3} d^{2}-2 c^{2} d^{3}-3 c \,d^{4}-d^{5}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f}"," ",0,"16/f*a^3*((-5/64*(4*c-3*d)*(c^2-2*c*d+d^2)/(c^4+4*c^3*d+6*c^2*d^2+4*c*d^3+d^4)*tan(1/2*e+1/2*f*x)^7+55/192*(c-d)*(4*c-3*d)/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*e+1/2*f*x)^5-73/192*(4*c-3*d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/64*(44*c-49*d)/(c+d)/(c-d)*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)^4+5/64*(4*c-3*d)/(c^5+3*c^4*d+2*c^3*d^2-2*c^2*d^3-3*c*d^4-d^5)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2)))","A"
210,1,596,174,0.672000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e)),x)","-\frac{d^{4}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{4}}{3 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{4}}{a f}-\frac{d^{4}}{3 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{4}}{2 a f}-\frac{5 d^{4}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{4}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{4}}{2 a f}-\frac{5 d^{4}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f a}+\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{3}}{a f}-\frac{2 d^{3} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{6 d^{3} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{4 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3} d}{a f}-\frac{4 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3} d}{a f}+\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d^{2}}{a f}-\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{3}}{a f}-\frac{6 d^{2} c^{2}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{4 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3} d}{a f}-\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d^{2}}{a f}+\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{2}}{a f}-\frac{4 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{3}}{a f}-\frac{6 d^{2} c^{2}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{6 d^{3} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{2 d^{3} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}"," ",0,"-1/a/f*d^4/(tan(1/2*e+1/2*f*x)-1)^2-1/3/a/f*d^4/(tan(1/2*e+1/2*f*x)+1)^3+1/a/f*tan(1/2*e+1/2*f*x)*d^4-1/3/a/f*d^4/(tan(1/2*e+1/2*f*x)-1)^3-3/2/a/f*ln(tan(1/2*e+1/2*f*x)+1)*d^4-5/2/a/f*d^4/(tan(1/2*e+1/2*f*x)+1)+1/a/f*d^4/(tan(1/2*e+1/2*f*x)+1)^2+3/2/a/f*ln(tan(1/2*e+1/2*f*x)-1)*d^4-5/2/a/f*d^4/(tan(1/2*e+1/2*f*x)-1)+1/f*c^4/a*tan(1/2*e+1/2*f*x)+6/a/f*ln(tan(1/2*e+1/2*f*x)+1)*c*d^3-2/a/f*d^3/(tan(1/2*e+1/2*f*x)+1)^2*c+6/a/f*d^3/(tan(1/2*e+1/2*f*x)+1)*c-4/a/f*tan(1/2*e+1/2*f*x)*c^3*d-4/a/f*ln(tan(1/2*e+1/2*f*x)-1)*c^3*d+6/a/f*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d^2-6/a/f*ln(tan(1/2*e+1/2*f*x)-1)*c*d^3-6/a/f*d^2/(tan(1/2*e+1/2*f*x)+1)*c^2+4/a/f*ln(tan(1/2*e+1/2*f*x)+1)*c^3*d-6/a/f*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d^2+6/a/f*tan(1/2*e+1/2*f*x)*c^2*d^2-4/a/f*tan(1/2*e+1/2*f*x)*c*d^3-6/a/f*d^2/(tan(1/2*e+1/2*f*x)-1)*c^2+6/a/f*d^3/(tan(1/2*e+1/2*f*x)-1)*c+2/a/f*d^3/(tan(1/2*e+1/2*f*x)-1)^2*c","B"
211,1,371,114,0.680000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e)),x)","\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3}}{a f}-\frac{3 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{a f}+\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{2}}{a f}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{3}}{a f}+\frac{d^{3}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d}{a f}+\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{2}}{a f}-\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{3}}{2 a f}-\frac{3 d^{2} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{3 d^{3}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{3}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d}{a f}-\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{2}}{a f}+\frac{3 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{3}}{2 a f}-\frac{3 d^{2} c}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{3 d^{3}}{2 a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}"," ",0,"1/a/f*tan(1/2*e+1/2*f*x)*c^3-3/a/f*c^2*tan(1/2*e+1/2*f*x)*d+3/a/f*tan(1/2*e+1/2*f*x)*c*d^2-1/a/f*tan(1/2*e+1/2*f*x)*d^3+1/2/a/f*d^3/(tan(1/2*e+1/2*f*x)-1)^2-3/a/f*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d+3/a/f*ln(tan(1/2*e+1/2*f*x)-1)*c*d^2-3/2/a/f*ln(tan(1/2*e+1/2*f*x)-1)*d^3-3/a/f*d^2/(tan(1/2*e+1/2*f*x)-1)*c+3/2/a/f*d^3/(tan(1/2*e+1/2*f*x)-1)-1/2/a/f*d^3/(tan(1/2*e+1/2*f*x)+1)^2+3/a/f*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d-3/a/f*ln(tan(1/2*e+1/2*f*x)+1)*c*d^2+3/2/a/f*ln(tan(1/2*e+1/2*f*x)+1)*d^3-3/a/f*d^2/(tan(1/2*e+1/2*f*x)+1)*c+3/2/a/f*d^3/(tan(1/2*e+1/2*f*x)+1)","B"
212,1,196,68,0.639000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e)),x)","\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}}{a f}-\frac{2 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{a f}-\frac{d^{2}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{a f}+\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{a f}-\frac{d^{2}}{a f \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{a f}-\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{a f}"," ",0,"1/a/f*tan(1/2*e+1/2*f*x)*c^2-2/a/f*c*d*tan(1/2*e+1/2*f*x)+1/a/f*tan(1/2*e+1/2*f*x)*d^2-1/a/f*d^2/(tan(1/2*e+1/2*f*x)-1)-2/a/f*d*ln(tan(1/2*e+1/2*f*x)-1)*c+1/a/f*d^2*ln(tan(1/2*e+1/2*f*x)-1)-1/a/f*d^2/(tan(1/2*e+1/2*f*x)+1)+2/a/f*d*ln(tan(1/2*e+1/2*f*x)+1)*c-1/a/f*d^2*ln(tan(1/2*e+1/2*f*x)+1)","B"
213,1,78,43,0.744000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e)),x)","-\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{a f}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c}{a f}-\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{a f}+\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{a f}"," ",0,"-1/a/f*d*ln(tan(1/2*e+1/2*f*x)-1)+1/a/f*tan(1/2*e+1/2*f*x)*c-1/a/f*tan(1/2*e+1/2*f*x)*d+1/a/f*d*ln(tan(1/2*e+1/2*f*x)+1)","A"
214,1,74,74,0.686000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e)),x)","\frac{\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{c -d}-\frac{2 d \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)}{\left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}}{f a}"," ",0,"1/f/a*(1/(c-d)*tan(1/2*e+1/2*f*x)-2*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"
215,1,146,136,0.787000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^2,x)","\frac{\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{c^{2}-2 c d +d^{2}}+\frac{4 d \left(-\frac{d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \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{\left(2 c +d \right) \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)}{2 \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{2}}}{f a}"," ",0,"1/f/a*(1/(c^2-2*c*d+d^2)*tan(1/2*e+1/2*f*x)+4*d/(c-d)^2*(-1/2*d/(c+d)*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)-1/2*(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"
216,1,221,194,1.006000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^3,x)","\frac{\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}}+\frac{2 d \left(\frac{-\frac{3 d \left(2 c^{2}-c d -d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{2 \left(c^{2}+2 c d +d^{2}\right)}+\frac{d \left(6 c +d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 c +2 d}}{\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}}-\frac{3 \left(2 c^{2}+2 c d +d^{2}\right) \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)}{2 \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{3}}}{f a}"," ",0,"1/f/a*(1/(c^3-3*c^2*d+3*c*d^2-d^3)*tan(1/2*e+1/2*f*x)+2*d/(c-d)^3*((-3/2*d*(2*c^2-c*d-d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/2*d*(6*c+d)/(c+d)*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)^2-3/2*(2*c^2+2*c*d+d^2)/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))))","A"
217,1,766,247,1.023000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x)","\frac{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{5}}{2 f \,a^{2}}-\frac{d^{5}}{3 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}+\frac{5 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{5}}{f \,a^{2}}-\frac{5 d^{5}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{3 d^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{5}}{3 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{5 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{5}}{f \,a^{2}}-\frac{5 d^{5}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{3 d^{5}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{5}}{2 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{5}}{6 f \,a^{2}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{5}}{6 f \,a^{2}}+\frac{25 d^{4} c}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{5 d^{4} c}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{20 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d^{3}}{f \,a^{2}}-\frac{15 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3} d^{2}}{f \,a^{2}}+\frac{25 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{3}}{f \,a^{2}}-\frac{35 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{4}}{2 f \,a^{2}}-\frac{10 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3} d^{2}}{f \,a^{2}}+\frac{20 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d^{3}}{f \,a^{2}}-\frac{35 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{4}}{2 f \,a^{2}}-\frac{10 d^{3} c^{2}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{4} d}{2 f \,a^{2}}+\frac{35 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{4}}{2 f \,a^{2}}-\frac{10 d^{3} c^{2}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4} d}{6 f \,a^{2}}-\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d^{2}}{3 f \,a^{2}}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{3}}{3 f \,a^{2}}-\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{4}}{6 f \,a^{2}}+\frac{25 d^{4} c}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 d^{4} c}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{10 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3} d^{2}}{f \,a^{2}}"," ",0,"9/2/f/a^2*tan(1/2*e+1/2*f*x)*d^5-1/3/f/a^2*d^5/(tan(1/2*e+1/2*f*x)-1)^3+5/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*d^5-5/f/a^2*d^5/(tan(1/2*e+1/2*f*x)-1)-1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*c^5-3/2/f/a^2*d^5/(tan(1/2*e+1/2*f*x)-1)^2-1/3/f/a^2*d^5/(tan(1/2*e+1/2*f*x)+1)^3-5/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*d^5-5/f/a^2*d^5/(tan(1/2*e+1/2*f*x)+1)+3/2/f/a^2*d^5/(tan(1/2*e+1/2*f*x)+1)^2+1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*d^5+1/2/f/a^2*tan(1/2*e+1/2*f*x)*c^5+25/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)-1)*c+5/6/f/a^2*tan(1/2*e+1/2*f*x)^3*c^4*d-5/3/f/a^2*tan(1/2*e+1/2*f*x)^3*c^3*d^2-5/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)+1)^2*c-20/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d^3-15/f/a^2*tan(1/2*e+1/2*f*x)*c^3*d^2+25/f/a^2*tan(1/2*e+1/2*f*x)*c^2*d^3-35/2/f/a^2*tan(1/2*e+1/2*f*x)*c*d^4-10/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*c^3*d^2+20/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d^3-35/2/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*c*d^4-10/f/a^2*d^3/(tan(1/2*e+1/2*f*x)-1)*c^2+5/3/f/a^2*tan(1/2*e+1/2*f*x)^3*c^2*d^3-5/6/f/a^2*tan(1/2*e+1/2*f*x)^3*c*d^4+5/2/f/a^2*tan(1/2*e+1/2*f*x)*c^4*d+35/2/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*c*d^4-10/f/a^2*d^3/(tan(1/2*e+1/2*f*x)+1)*c^2+25/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)+1)*c+5/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)-1)^2*c+10/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*c^3*d^2","B"
218,1,514,184,0.840000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x)","-\frac{c^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 f \,a^{2}}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d}{3 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{2}}{f \,a^{2}}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{3}}{3 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{4}}{6 f \,a^{2}}+\frac{c^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 f \,a^{2}}+\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3} d}{f \,a^{2}}-\frac{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{2}}{f \,a^{2}}+\frac{10 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{3}}{f \,a^{2}}-\frac{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{4}}{2 f \,a^{2}}-\frac{4 d^{3} c}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{5 d^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d^{2}}{f \,a^{2}}+\frac{8 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{3}}{f \,a^{2}}-\frac{7 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{4}}{2 f \,a^{2}}+\frac{6 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d^{2}}{f \,a^{2}}-\frac{8 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{3}}{f \,a^{2}}+\frac{7 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{4}}{2 f \,a^{2}}-\frac{4 d^{3} c}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 d^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{4}}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}"," ",0,"-1/6/f*c^4/a^2*tan(1/2*e+1/2*f*x)^3+2/3/f/a^2*tan(1/2*e+1/2*f*x)^3*c^3*d-1/f/a^2*tan(1/2*e+1/2*f*x)^3*c^2*d^2+2/3/f/a^2*tan(1/2*e+1/2*f*x)^3*c*d^3-1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*d^4+1/2/f*c^4/a^2*tan(1/2*e+1/2*f*x)+2/f/a^2*tan(1/2*e+1/2*f*x)*c^3*d-9/f/a^2*tan(1/2*e+1/2*f*x)*c^2*d^2+10/f/a^2*tan(1/2*e+1/2*f*x)*c*d^3-7/2/f/a^2*tan(1/2*e+1/2*f*x)*d^4-4/f/a^2*d^3/(tan(1/2*e+1/2*f*x)-1)*c+5/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)-1)+1/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)-1)^2-6/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d^2+8/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*c*d^3-7/2/f/a^2*ln(tan(1/2*e+1/2*f*x)-1)*d^4+6/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d^2-8/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*c*d^3+7/2/f/a^2*ln(tan(1/2*e+1/2*f*x)+1)*d^4-4/f/a^2*d^3/(tan(1/2*e+1/2*f*x)+1)*c+5/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)+1)-1/2/f/a^2*d^4/(tan(1/2*e+1/2*f*x)+1)^2","B"
219,1,316,129,0.679000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x)","-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3}}{6 f \,a^{2}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d}{2 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{2}}{2 f \,a^{2}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{3}}{6 f \,a^{2}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3}}{2 f \,a^{2}}+\frac{3 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{2 f \,a^{2}}-\frac{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{2}}{2 f \,a^{2}}+\frac{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{3}}{2 f \,a^{2}}-\frac{d^{3}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,a^{2}}+\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}-\frac{d^{3}}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,a^{2}}-\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{2}}"," ",0,"-1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*c^3+1/2/f/a^2*tan(1/2*e+1/2*f*x)^3*c^2*d-1/2/f/a^2*tan(1/2*e+1/2*f*x)^3*c*d^2+1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*d^3+1/2/f/a^2*tan(1/2*e+1/2*f*x)*c^3+3/2/f/a^2*c^2*tan(1/2*e+1/2*f*x)*d-9/2/f/a^2*tan(1/2*e+1/2*f*x)*c*d^2+5/2/f/a^2*tan(1/2*e+1/2*f*x)*d^3-1/f/a^2*d^3/(tan(1/2*e+1/2*f*x)-1)-3/f/a^2*d^2*ln(tan(1/2*e+1/2*f*x)-1)*c+2/f/a^2*d^3*ln(tan(1/2*e+1/2*f*x)-1)-1/f/a^2*d^3/(tan(1/2*e+1/2*f*x)+1)+3/f/a^2*d^2*ln(tan(1/2*e+1/2*f*x)+1)*c-2/f/a^2*d^3*ln(tan(1/2*e+1/2*f*x)+1)","B"
220,1,170,85,0.767000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x)","\frac{c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{2}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{3 f \,a^{2}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}}{2 f \,a^{2}}-\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{2 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{6 f \,a^{2}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{6 f \,a^{2}}-\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{2}}+\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{2}}"," ",0,"1/f/a^2*c*d*tan(1/2*e+1/2*f*x)+1/3/f/a^2*tan(1/2*e+1/2*f*x)^3*c*d+1/2/f/a^2*tan(1/2*e+1/2*f*x)*c^2-3/2/f/a^2*tan(1/2*e+1/2*f*x)*d^2-1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*c^2-1/6/f/a^2*tan(1/2*e+1/2*f*x)^3*d^2-1/f/a^2*d^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f/a^2*d^2*ln(tan(1/2*e+1/2*f*x)+1)","A"
221,1,60,61,0.724000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^2,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c}{3}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d}{3}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c +\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{2 f \,a^{2}}"," ",0,"1/2/f/a^2*(-1/3*tan(1/2*e+1/2*f*x)^3*c+1/3*tan(1/2*e+1/2*f*x)^3*d+tan(1/2*e+1/2*f*x)*c+tan(1/2*e+1/2*f*x)*d)","A"
222,1,122,116,0.742000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e)),x)","\frac{-\frac{\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c}{3}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d}{3}-\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c +3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{\left(c -d \right)^{2}}+\frac{4 d^{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)}{\left(c -d \right)^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}}{2 f \,a^{2}}"," ",0,"1/2/f/a^2*(-1/(c-d)^2*(1/3*tan(1/2*e+1/2*f*x)^3*c-1/3*tan(1/2*e+1/2*f*x)^3*d-tan(1/2*e+1/2*f*x)*c+3*tan(1/2*e+1/2*f*x)*d)+4*d^2/(c-d)^2/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2)))","A"
223,1,203,196,0.796000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x)","\frac{-\frac{\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c}{3}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d}{3}-\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c +5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{\left(c^{2}-2 c d +d^{2}\right) \left(c -d \right)}-\frac{4 d^{2} \left(-\frac{d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\left(c +d \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{\left(3 c +2 d \right) \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)}{\left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{3}}}{2 f \,a^{2}}"," ",0,"1/2/f/a^2*(-1/(c^2-2*c*d+d^2)/(c-d)*(1/3*tan(1/2*e+1/2*f*x)^3*c-1/3*tan(1/2*e+1/2*f*x)^3*d-tan(1/2*e+1/2*f*x)*c+5*tan(1/2*e+1/2*f*x)*d)-4*d^2/(c-d)^3*(-d/(c+d)*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)-(3*c+2*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"
224,1,280,267,0.954000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x)","\frac{-\frac{\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c}{3}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d}{3}-\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c +7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{\left(c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}\right) \left(c -d \right)}-\frac{8 d^{2} \left(\frac{-\frac{d \left(8 c^{2}-3 c d -5 d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{4 \left(c^{2}+2 c d +d^{2}\right)}+\frac{d \left(8 c +3 d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 c +4 d}}{\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}}-\frac{\left(12 c^{2}+16 c d +7 d^{2}\right) \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)}{4 \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{4}}}{2 f \,a^{2}}"," ",0,"1/2/f/a^2*(-1/(c^3-3*c^2*d+3*c*d^2-d^3)/(c-d)*(1/3*tan(1/2*e+1/2*f*x)^3*c-1/3*tan(1/2*e+1/2*f*x)^3*d-tan(1/2*e+1/2*f*x)*c+7*tan(1/2*e+1/2*f*x)*d)-8*d^2/(c-d)^4*((-1/4*d*(8*c^2-3*c*d-5*d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/4*d*(8*c+3*d)/(c+d)*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)^2-1/4*(12*c^2+16*c*d+7*d^2)/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))))","A"
225,1,956,349,0.835000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^6/(a+a*sec(f*x+e))^3,x)","\frac{49 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{6}}{4 f \,a^{3}}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4} d^{2}}{2 f \,a^{3}}+\frac{15 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{4}}{2 f \,a^{3}}-\frac{4 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{5}}{f \,a^{3}}-\frac{20 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3} d^{3}}{f \,a^{3}}+\frac{45 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d^{4}}{f \,a^{3}}-\frac{39 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{5}}{f \,a^{3}}-\frac{15 d^{4} c^{2}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{6}}{6 f \,a^{3}}+\frac{c^{6} \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{20 f \,a^{3}}-\frac{c^{6} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{6}}{20 f \,a^{3}}+\frac{c^{6} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 f \,a^{3}}+\frac{23 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{6}}{2 f \,a^{3}}-\frac{17 d^{6}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{2 d^{6}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{17 d^{6}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d^{6}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{23 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{6}}{2 f \,a^{3}}-\frac{d^{6}}{3 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{d^{6}}{3 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{35 c^{3} d^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{f \,a^{3}}+\frac{21 d^{5} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{3 d^{5} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{20 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3} d^{3}}{f \,a^{3}}-\frac{45 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d^{4}}{f \,a^{3}}+\frac{39 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{5}}{f \,a^{3}}+\frac{255 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{4}}{4 f \,a^{3}}+\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{5} d}{2 f \,a^{3}}+\frac{15 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{4} d^{2}}{4 f \,a^{3}}-\frac{93 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{5}}{2 f \,a^{3}}-\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{5} d}{10 f \,a^{3}}+\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4} d^{2}}{4 f \,a^{3}}+\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{4}}{4 f \,a^{3}}-\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{5}}{10 f \,a^{3}}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d^{3}}{f \,a^{3}}-\frac{20 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d^{3}}{3 f \,a^{3}}+\frac{21 d^{5} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{3 d^{5} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{15 d^{4} c^{2}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}"," ",0,"5/6/f/a^3*tan(1/2*e+1/2*f*x)^3*d^6+49/4/f/a^3*tan(1/2*e+1/2*f*x)*d^6+5/2/f/a^3*tan(1/2*e+1/2*f*x)^3*c^4*d^2+15/2/f/a^3*tan(1/2*e+1/2*f*x)^3*c^2*d^4-20/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*c^3*d^3+45/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d^4-39/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*c*d^5-15/f/a^3*d^4/(tan(1/2*e+1/2*f*x)-1)*c^2-4/f/a^3*tan(1/2*e+1/2*f*x)^3*c*d^5+1/20/f*c^6/a^3*tan(1/2*e+1/2*f*x)^5-1/6/f*c^6/a^3*tan(1/2*e+1/2*f*x)^3+1/4/f*c^6/a^3*tan(1/2*e+1/2*f*x)+23/2/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*d^6-17/2/f/a^3*d^6/(tan(1/2*e+1/2*f*x)-1)-2/f/a^3*d^6/(tan(1/2*e+1/2*f*x)-1)^2-17/2/f/a^3*d^6/(tan(1/2*e+1/2*f*x)+1)+2/f/a^3*d^6/(tan(1/2*e+1/2*f*x)+1)^2-23/2/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*d^6-1/3/f/a^3*d^6/(tan(1/2*e+1/2*f*x)-1)^3-1/3/f/a^3*d^6/(tan(1/2*e+1/2*f*x)+1)^3+1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*d^6-35/f/a^3*c^3*d^3*tan(1/2*e+1/2*f*x)+21/f/a^3*d^5/(tan(1/2*e+1/2*f*x)+1)*c-3/f/a^3*d^5/(tan(1/2*e+1/2*f*x)+1)^2*c+20/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*c^3*d^3-45/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d^4+39/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*c*d^5+255/4/f/a^3*tan(1/2*e+1/2*f*x)*c^2*d^4+3/2/f/a^3*tan(1/2*e+1/2*f*x)*c^5*d+15/4/f/a^3*tan(1/2*e+1/2*f*x)*c^4*d^2-93/2/f/a^3*tan(1/2*e+1/2*f*x)*c*d^5-3/10/f/a^3*tan(1/2*e+1/2*f*x)^5*c^5*d+3/4/f/a^3*tan(1/2*e+1/2*f*x)^5*c^4*d^2+3/4/f/a^3*tan(1/2*e+1/2*f*x)^5*c^2*d^4-3/10/f/a^3*tan(1/2*e+1/2*f*x)^5*c*d^5+21/f/a^3*d^5/(tan(1/2*e+1/2*f*x)-1)*c+3/f/a^3*d^5/(tan(1/2*e+1/2*f*x)-1)^2*c-15/f/a^3*d^4/(tan(1/2*e+1/2*f*x)+1)*c^2-1/f/a^3*tan(1/2*e+1/2*f*x)^5*c^3*d^3-20/3/f/a^3*tan(1/2*e+1/2*f*x)^3*c^3*d^3","B"
226,1,679,275,0.792000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x)","-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4} d}{4 f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d^{2}}{2 f \,a^{3}}-\frac{c^{5} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 f \,a^{3}}+\frac{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{4} d}{4 f \,a^{3}}-\frac{10 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2} d^{3}}{f \,a^{3}}+\frac{15 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c \,d^{4}}{f \,a^{3}}-\frac{5 d^{4} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{3}}{2 f \,a^{3}}+\frac{7 d^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{5}}{4 f \,a^{3}}-\frac{31 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{5}}{4 f \,a^{3}}-\frac{35 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{3}}{2 f \,a^{3}}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{4}}{2 f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{4}}{4 f \,a^{3}}+\frac{10 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2} d^{3}}{f \,a^{3}}-\frac{15 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c \,d^{4}}{f \,a^{3}}-\frac{d^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{d^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{13 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) d^{5}}{2 f \,a^{3}}+\frac{13 \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) d^{5}}{2 f \,a^{3}}+\frac{7 d^{5}}{2 f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{5}}{20 f \,a^{3}}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{5}}{3 f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{5}}{20 f \,a^{3}}+\frac{85 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{4}}{4 f \,a^{3}}-\frac{5 d^{4} c}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d^{2}}{3 f \,a^{3}}-\frac{10 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{3}}{3 f \,a^{3}}+\frac{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3} d^{2}}{2 f \,a^{3}}"," ",0,"-1/4/f/a^3*tan(1/2*e+1/2*f*x)^5*c^4*d+1/2/f/a^3*tan(1/2*e+1/2*f*x)^5*c^3*d^2-1/2/f/a^3*tan(1/2*e+1/2*f*x)^5*c^2*d^3+5/4/f/a^3*tan(1/2*e+1/2*f*x)*c^4*d+5/2/f/a^3*tan(1/2*e+1/2*f*x)^3*c*d^4-10/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*c^2*d^3+15/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*c*d^4-5/f/a^3*d^4/(tan(1/2*e+1/2*f*x)-1)*c+7/2/f/a^3*d^5/(tan(1/2*e+1/2*f*x)-1)-1/6/f/a^3*tan(1/2*e+1/2*f*x)^3*c^5-1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*d^5-2/3/f/a^3*tan(1/2*e+1/2*f*x)^3*d^5+1/4/f/a^3*tan(1/2*e+1/2*f*x)*c^5-31/4/f/a^3*tan(1/2*e+1/2*f*x)*d^5-35/2/f/a^3*tan(1/2*e+1/2*f*x)*c^2*d^3+10/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*c^2*d^3-15/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*c*d^4-1/2/f/a^3*d^5/(tan(1/2*e+1/2*f*x)+1)^2+1/2/f/a^3*d^5/(tan(1/2*e+1/2*f*x)-1)^2-13/2/f/a^3*ln(tan(1/2*e+1/2*f*x)-1)*d^5+13/2/f/a^3*ln(tan(1/2*e+1/2*f*x)+1)*d^5+7/2/f/a^3*d^5/(tan(1/2*e+1/2*f*x)+1)+1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*c^5+85/4/f/a^3*tan(1/2*e+1/2*f*x)*c*d^4+1/4/f/a^3*tan(1/2*e+1/2*f*x)^5*c*d^4-5/f/a^3*d^4/(tan(1/2*e+1/2*f*x)+1)*c+5/3/f/a^3*tan(1/2*e+1/2*f*x)^3*c^3*d^2-10/3/f/a^3*tan(1/2*e+1/2*f*x)^3*c^2*d^3+5/2/f/a^3*tan(1/2*e+1/2*f*x)*c^3*d^2","B"
227,1,454,199,0.707000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x)","\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4}}{20 f \,a^{3}}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3} d}{5 f \,a^{3}}+\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{2}}{10 f \,a^{3}}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{3}}{5 f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{4}}{20 f \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{4}}{6 f \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d^{2}}{f \,a^{3}}-\frac{4 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{3}}{3 f \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{4}}{2 f \,a^{3}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{4}}{4 f \,a^{3}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3} d}{f \,a^{3}}+\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2} d^{2}}{2 f \,a^{3}}-\frac{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{3}}{f \,a^{3}}+\frac{17 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{4}}{4 f \,a^{3}}-\frac{d^{4}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,a^{3}}+\frac{3 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}-\frac{d^{4}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,a^{3}}-\frac{3 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{3}}"," ",0,"1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*c^4-1/5/f/a^3*tan(1/2*e+1/2*f*x)^5*c^3*d+3/10/f/a^3*tan(1/2*e+1/2*f*x)^5*c^2*d^2-1/5/f/a^3*tan(1/2*e+1/2*f*x)^5*c*d^3+1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*d^4-1/6/f/a^3*tan(1/2*e+1/2*f*x)^3*c^4+1/f/a^3*tan(1/2*e+1/2*f*x)^3*c^2*d^2-4/3/f/a^3*tan(1/2*e+1/2*f*x)^3*c*d^3+1/2/f/a^3*tan(1/2*e+1/2*f*x)^3*d^4+1/4/f/a^3*tan(1/2*e+1/2*f*x)*c^4+1/f/a^3*tan(1/2*e+1/2*f*x)*c^3*d+3/2/f/a^3*tan(1/2*e+1/2*f*x)*c^2*d^2-7/f/a^3*tan(1/2*e+1/2*f*x)*c*d^3+17/4/f/a^3*tan(1/2*e+1/2*f*x)*d^4-1/f/a^3*d^4/(tan(1/2*e+1/2*f*x)-1)-4/f/a^3*d^3*ln(tan(1/2*e+1/2*f*x)-1)*c+3/f/a^3*d^4*ln(tan(1/2*e+1/2*f*x)-1)-1/f/a^3*d^4/(tan(1/2*e+1/2*f*x)+1)+4/f/a^3*d^3*ln(tan(1/2*e+1/2*f*x)+1)*c-3/f/a^3*d^4*ln(tan(1/2*e+1/2*f*x)+1)","B"
228,1,286,126,0.835000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x)","\frac{3 c^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{4 f \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{2}}{2 f \,a^{3}}+\frac{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c \,d^{2}}{4 f \,a^{3}}-\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2} d}{20 f \,a^{3}}+\frac{3 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c \,d^{2}}{20 f \,a^{3}}-\frac{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{3}}{4 f \,a^{3}}-\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3}}{6 f \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{3}}{3 f \,a^{3}}+\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3}}{4 f \,a^{3}}+\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,a^{3}}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{3}}{20 f \,a^{3}}-\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{3}}{20 f \,a^{3}}"," ",0,"3/4/f/a^3*c^2*tan(1/2*e+1/2*f*x)*d+1/2/f/a^3*tan(1/2*e+1/2*f*x)^3*c*d^2+3/4/f/a^3*tan(1/2*e+1/2*f*x)*c*d^2-3/20/f/a^3*tan(1/2*e+1/2*f*x)^5*c^2*d+3/20/f/a^3*tan(1/2*e+1/2*f*x)^5*c*d^2-7/4/f/a^3*tan(1/2*e+1/2*f*x)*d^3-1/f/a^3*d^3*ln(tan(1/2*e+1/2*f*x)-1)-1/6/f/a^3*tan(1/2*e+1/2*f*x)^3*c^3-1/3/f/a^3*tan(1/2*e+1/2*f*x)^3*d^3+1/4/f/a^3*tan(1/2*e+1/2*f*x)*c^3+1/f/a^3*d^3*ln(tan(1/2*e+1/2*f*x)+1)+1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*c^3-1/20/f/a^3*tan(1/2*e+1/2*f*x)^5*d^3","B"
229,1,128,109,0.834000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x)","\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{5}-\frac{2 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{5}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{5}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{3}+\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{3}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}+2 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{4 f \,a^{3}}"," ",0,"1/4/f/a^3*(1/5*tan(1/2*e+1/2*f*x)^5*c^2-2/5*tan(1/2*e+1/2*f*x)^5*c*d+1/5*tan(1/2*e+1/2*f*x)^5*d^2-2/3*tan(1/2*e+1/2*f*x)^3*c^2+2/3*tan(1/2*e+1/2*f*x)^3*d^2+tan(1/2*e+1/2*f*x)*c^2+2*c*d*tan(1/2*e+1/2*f*x)+tan(1/2*e+1/2*f*x)*d^2)","A"
230,1,64,96,0.731000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^3,x)","\frac{\frac{\left(c -d \right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{5}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c}{3}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c +\tan \left(\frac{e}{2}+\frac{f x}{2}\right) d}{4 f \,a^{3}}"," ",0,"1/4/f/a^3*(1/5*(c-d)*tan(1/2*e+1/2*f*x)^5-2/3*tan(1/2*e+1/2*f*x)^3*c+tan(1/2*e+1/2*f*x)*c+tan(1/2*e+1/2*f*x)*d)","A"
231,1,203,166,0.873000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e)),x)","\frac{\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{5}-\frac{2 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{5}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{5}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{3}+2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d -\frac{4 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{3}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}-4 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{\left(c -d \right)^{3}}-\frac{8 d^{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)}{\left(c -d \right)^{3} \sqrt{\left(c +d \right) \left(c -d \right)}}}{4 f \,a^{3}}"," ",0,"1/4/f/a^3*(1/(c-d)^3*(1/5*tan(1/2*e+1/2*f*x)^5*c^2-2/5*tan(1/2*e+1/2*f*x)^5*c*d+1/5*tan(1/2*e+1/2*f*x)^5*d^2-2/3*tan(1/2*e+1/2*f*x)^3*c^2+2*tan(1/2*e+1/2*f*x)^3*c*d-4/3*tan(1/2*e+1/2*f*x)^3*d^2+tan(1/2*e+1/2*f*x)*c^2-4*c*d*tan(1/2*e+1/2*f*x)+7*tan(1/2*e+1/2*f*x)*d^2)-8*d^3/(c-d)^3/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2)))","A"
232,1,284,271,0.936000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^2,x)","\frac{\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{5}-\frac{2 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{5}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{5}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{3}+\frac{8 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{3}-2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}-6 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+17 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{\left(c^{2}-2 c d +d^{2}\right) \left(c -d \right)^{2}}+\frac{16 d^{3} \left(-\frac{d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \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{\left(4 c +3 d \right) \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)}{2 \left(c +d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{4}}}{4 f \,a^{3}}"," ",0,"1/4/f/a^3*(1/(c^2-2*c*d+d^2)/(c-d)^2*(1/5*tan(1/2*e+1/2*f*x)^5*c^2-2/5*tan(1/2*e+1/2*f*x)^5*c*d+1/5*tan(1/2*e+1/2*f*x)^5*d^2-2/3*tan(1/2*e+1/2*f*x)^3*c^2+8/3*tan(1/2*e+1/2*f*x)^3*c*d-2*tan(1/2*e+1/2*f*x)^3*d^2+tan(1/2*e+1/2*f*x)*c^2-6*c*d*tan(1/2*e+1/2*f*x)+17*tan(1/2*e+1/2*f*x)*d^2)+16*d^3/(c-d)^4*(-1/2*d/(c+d)*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)-1/2*(4*c+3*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"
233,1,365,349,0.970000," ","int(sec(f*x+e)/(a+a*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x)","\frac{\frac{\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{5}-\frac{2 \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{5}+\frac{\left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{5}-\frac{2 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c^{2}}{3}+\frac{10 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c d}{3}-\frac{8 \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d^{2}}{3}+\tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}-8 c d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)+31 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) d^{2}}{\left(c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}\right) \left(c^{2}-2 c d +d^{2}\right)}+\frac{16 d^{3} \left(\frac{-\frac{d \left(10 c^{2}-3 c d -7 d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{4 \left(c^{2}+2 c d +d^{2}\right)}+\frac{5 d \left(2 c +d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{4 \left(c +d \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)^{2}}-\frac{\left(20 c^{2}+30 c d +13 d^{2}\right) \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)}{4 \left(c^{2}+2 c d +d^{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(c -d \right)^{5}}}{4 f \,a^{3}}"," ",0,"1/4/f/a^3*(1/(c^3-3*c^2*d+3*c*d^2-d^3)/(c^2-2*c*d+d^2)*(1/5*tan(1/2*e+1/2*f*x)^5*c^2-2/5*tan(1/2*e+1/2*f*x)^5*c*d+1/5*tan(1/2*e+1/2*f*x)^5*d^2-2/3*tan(1/2*e+1/2*f*x)^3*c^2+10/3*tan(1/2*e+1/2*f*x)^3*c*d-8/3*tan(1/2*e+1/2*f*x)^3*d^2+tan(1/2*e+1/2*f*x)*c^2-8*c*d*tan(1/2*e+1/2*f*x)+31*tan(1/2*e+1/2*f*x)*d^2)+16*d^3/(c-d)^5*((-1/4*d*(10*c^2-3*c*d-7*d^2)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+5/4*d*(2*c+d)/(c+d)*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)^2-1/4*(20*c^2+30*c*d+13*d^2)/(c^2+2*c*d+d^2)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))))","A"
234,1,301,49,2.194000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*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{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(\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 \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right)-\ln \left(\frac{2 \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)-2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right)\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{-d}}"," ",0,"1/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))*(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*sin(f*x+e)-d*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(f*x+e)))-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*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e))))/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)*2^(1/2)/(-d)^(1/2)","B"
235,1,503,113,1.993000," ","int(sec(f*x+e)*(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(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 \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{c -d}-d \ln \left(\frac{2 \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)-2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{c -d}+\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 -\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 \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)}}\, a \sqrt{c -d}\, \sqrt{-d}}"," ",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))*(d*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*sin(f*x+e)-d*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(f*x+e)))*(c-d)^(1/2)-d*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*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*(c-d)^(1/2)+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)*c-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)/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)/a/(c-d)^(1/2)*2^(1/2)/(-d)^(1/2)","B"
236,1,170,63,1.952000," ","int(sec(f*x+e)/(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)}}\, \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)}{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}}"," ",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)*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))/sin(f*x+e)^2/(-2*(d+c*cos(f*x+e))/(1+cos(f*x+e)))^(1/2)/a/(c-d)^(1/2)","B"
237,1,403,114,2.033000," ","int(sec(f*x+e)^2/(a+a*sec(f*x+e))^(1/2)/(c+d*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{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(-\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}+\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 \sin \left(f x +e \right)-d \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \cos \left(f x +e \right)+c -d \right)}{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{c -d}-\ln \left(\frac{2 \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)-2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{c -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)}}\, a \sqrt{c -d}\, \sqrt{-d}}"," ",0,"1/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))*(-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)+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*sin(f*x+e)-d*sin(f*x+e)-c*cos(f*x+e)+d*cos(f*x+e)+c-d)/(-1+cos(f*x+e)+sin(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*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*(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)*2^(1/2)/(-d)^(1/2)","B"
238,1,433,47,1.498000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x)","-\frac{\left(\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)+\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \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)}\right)}{c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c +d}\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)\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)}}"," ",0,"-1/2/f*(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*cos(f*x+e)-d*cos(f*x+e)-((c+d)*(c-d))^(1/2)*sin(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+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)","B"
239,1,566,117,2.168000," ","int((g*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x)","\frac{2 \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \left(-1+\cos \left(f x +e \right)\right)^{2} \sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \left(\sqrt{\frac{c}{c -d}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}+\sqrt{\frac{c}{c -d}}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right) \sqrt{\left(c +d \right) \left(c -d \right)}+c \ln \left(\frac{4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, d \sin \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)}\, \cos \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 \ln \left(-\frac{2 \left(2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{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)\right) \left(c -d \right)}{f \sin \left(f x +e \right)^{4} \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{\left(c +d \right) \left(c -d \right)}\, \left(c -d +\sqrt{\left(c +d \right) \left(c -d \right)}\right) \left(-c +d +\sqrt{\left(c +d \right) \left(c -d \right)}\right) \sqrt{\frac{c}{c -d}}}"," ",0,"2/f*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2*(-1+cos(f*x+e))^2*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*((c/(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))*((c+d)*(c-d))^(1/2)+(c/(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e)))*((c+d)*(c-d))^(1/2)+c*ln(2*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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)^4/(1/(1+cos(f*x+e)))^(3/2)*(c-d)/((c+d)*(c-d))^(1/2)/(c-d+((c+d)*(c-d))^(1/2))/(-c+d+((c+d)*(c-d))^(1/2))/(c/(c-d))^(1/2)","B"
240,1,520,99,1.477000," ","int(sec(f*x+e)/(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)}\, \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}}+d \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)+\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \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)}\right)}{c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c +d}\right)-d \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)\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) \sqrt{\left(c +d \right) \left(c -d \right)}\, a}"," ",0,"1/2/f*(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)+d*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*cos(f*x+e)-d*cos(f*x+e)-((c+d)*(c-d))^(1/2)*sin(f*x+e)-c+d))-d*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)))*(-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+d)*(c-d))^(1/2)/a","B"
241,1,520,101,1.426000," ","int(sec(f*x+e)^2/(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(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 \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)+\sqrt{\left(c +d \right) \left(c -d \right)}\, \cos \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)}\right)}{c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-\sqrt{\left(c +d \right) \left(c -d \right)}\, \sin \left(f x +e \right)-c +d}\right)-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)\right)}{2 f a \sqrt{\left(c +d \right) \left(c -d \right)}\, \left(c -d \right) \sqrt{\frac{d}{c -d}}}"," ",0,"-1/2/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*((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*cos(f*x+e)-d*cos(f*x+e)-((c+d)*(c-d))^(1/2)*sin(f*x+e)-c+d))-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)))/a/((c+d)*(c-d))^(1/2)/(c-d)/(d/(c-d))^(1/2)","B"
242,1,472,132,2.219000," ","int((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","\frac{\left(\frac{g}{\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)}}\, \left(\cos^{2}\left(f x +e \right)\right) \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}-c \ln \left(\frac{4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, d \sin \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)}\, \cos \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 \ln \left(-\frac{2 \left(2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{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)\right)}{f \sin \left(f x +e \right)^{4} \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} a \sqrt{\frac{c}{c -d}}\, \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}"," ",0,"1/f*(g/cos(f*x+e))^(3/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^2*(-1+cos(f*x+e))^2*(arcsinh((-1+cos(f*x+e))/sin(f*x+e))*2^(1/2)*(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)-c*ln(2*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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)^4/(1/(1+cos(f*x+e)))^(3/2)/a/(c/(c-d))^(1/2)/(c-d)/((c+d)*(c-d))^(1/2)","B"
243,1,725,184,2.198000," ","int((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x)","\frac{2 \left(\frac{g}{\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^{3}\left(f x +e \right)\right) \left(-1+\cos \left(f x +e \right)\right)^{3} \left(\sqrt{2}\, \sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right) d -\sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right) c +\sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1+\sin \left(f x +e \right)\right)}{2}\right) d -\sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right) c +\sqrt{\frac{c}{c -d}}\, \sqrt{\left(c +d \right) \left(c -d \right)}\, \arctanh \left(\frac{\sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(-\cos \left(f x +e \right)-1+\sin \left(f x +e \right)\right)}{2}\right) d -c^{2} \ln \left(\frac{4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-4 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, d \sin \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)}\, \cos \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^{2} \ln \left(-\frac{2 \left(2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, c \sin \left(f x +e \right)-2 \sqrt{\frac{c}{c -d}}\, \sqrt{\frac{1}{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)\right)}{f \sin \left(f x +e \right)^{6} \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{5}{2}} a \sqrt{\frac{c}{c -d}}\, \left(-c +d +\sqrt{\left(c +d \right) \left(c -d \right)}\right) \left(c -d +\sqrt{\left(c +d \right) \left(c -d \right)}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}"," ",0,"2/f*(g/cos(f*x+e))^(5/2)*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*cos(f*x+e)^3*(-1+cos(f*x+e))^3*(2^(1/2)*(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*arcsinh((-1+cos(f*x+e))/sin(f*x+e))*d-(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))*c+(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e)))*d-(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e)))*c+(c/(c-d))^(1/2)*((c+d)*(c-d))^(1/2)*arctanh(1/2*(1/(1+cos(f*x+e)))^(1/2)*(-cos(f*x+e)-1+sin(f*x+e)))*d-c^2*ln(2*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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^2*ln(-2*(2*(c/(c-d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*c*sin(f*x+e)-2*(c/(c-d))^(1/2)*(1/(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)^6/(1/(1+cos(f*x+e)))^(5/2)/a/(c/(c-d))^(1/2)/(-c+d+((c+d)*(c-d))^(1/2))/(c-d+((c+d)*(c-d))^(1/2))/((c+d)*(c-d))^(1/2)","B"
244,1,431,238,1.688000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^4,x)","\frac{a \,c^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 a \,c^{3} d \tan \left(f x +e \right)}{f}+\frac{3 a \,c^{2} d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{3 a \,c^{2} d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{8 a c \,d^{3} \tan \left(f x +e \right)}{3 f}+\frac{4 a c \,d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{a \,d^{4} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 a \,d^{4} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 a \,d^{4} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}+\frac{b \,c^{4} \tan \left(f x +e \right)}{f}+\frac{2 b \,c^{3} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{2 b \,c^{3} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{4 b \,c^{2} d^{2} \tan \left(f x +e \right)}{f}+\frac{2 b \,c^{2} d^{2} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{b c \,d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{f}+\frac{3 b c \,d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 b c \,d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{8 b \,d^{4} \tan \left(f x +e \right)}{15 f}+\frac{b \,d^{4} \tan \left(f x +e \right) \left(\sec^{4}\left(f x +e \right)\right)}{5 f}+\frac{4 b \,d^{4} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{15 f}"," ",0,"1/f*a*c^4*ln(sec(f*x+e)+tan(f*x+e))+4/f*a*c^3*d*tan(f*x+e)+3/f*a*c^2*d^2*sec(f*x+e)*tan(f*x+e)+3/f*a*c^2*d^2*ln(sec(f*x+e)+tan(f*x+e))+8/3/f*a*c*d^3*tan(f*x+e)+4/3/f*a*c*d^3*tan(f*x+e)*sec(f*x+e)^2+1/4/f*a*d^4*tan(f*x+e)*sec(f*x+e)^3+3/8/f*a*d^4*sec(f*x+e)*tan(f*x+e)+3/8/f*a*d^4*ln(sec(f*x+e)+tan(f*x+e))+1/f*b*c^4*tan(f*x+e)+2/f*b*c^3*d*sec(f*x+e)*tan(f*x+e)+2/f*b*c^3*d*ln(sec(f*x+e)+tan(f*x+e))+4/f*b*c^2*d^2*tan(f*x+e)+2/f*b*c^2*d^2*tan(f*x+e)*sec(f*x+e)^2+1/f*b*c*d^3*tan(f*x+e)*sec(f*x+e)^3+3/2/f*b*c*d^3*sec(f*x+e)*tan(f*x+e)+3/2/f*b*c*d^3*ln(sec(f*x+e)+tan(f*x+e))+8/15/f*b*d^4*tan(f*x+e)+1/5/f*b*d^4*tan(f*x+e)*sec(f*x+e)^4+4/15/f*b*d^4*tan(f*x+e)*sec(f*x+e)^2","A"
245,1,290,170,1.372000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^3,x)","\frac{a \,c^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{3 a \,c^{2} d \tan \left(f x +e \right)}{f}+\frac{3 a c \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 a c \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{2 a \,d^{3} \tan \left(f x +e \right)}{3 f}+\frac{a \,d^{3} \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}+\frac{c^{3} b \tan \left(f x +e \right)}{f}+\frac{3 b \,c^{2} d \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{3 b \,c^{2} d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{2 c \,d^{2} b \tan \left(f x +e \right)}{f}+\frac{c \,d^{2} b \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{f}+\frac{b \,d^{3} \tan \left(f x +e \right) \left(\sec^{3}\left(f x +e \right)\right)}{4 f}+\frac{3 b \,d^{3} \sec \left(f x +e \right) \tan \left(f x +e \right)}{8 f}+\frac{3 b \,d^{3} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{8 f}"," ",0,"1/f*a*c^3*ln(sec(f*x+e)+tan(f*x+e))+3/f*a*c^2*d*tan(f*x+e)+3/2/f*a*c*d^2*sec(f*x+e)*tan(f*x+e)+3/2/f*a*c*d^2*ln(sec(f*x+e)+tan(f*x+e))+2/3/f*a*d^3*tan(f*x+e)+1/3/f*a*d^3*tan(f*x+e)*sec(f*x+e)^2+1/f*c^3*b*tan(f*x+e)+3/2/f*b*c^2*d*sec(f*x+e)*tan(f*x+e)+3/2/f*b*c^2*d*ln(sec(f*x+e)+tan(f*x+e))+2/f*c*d^2*b*tan(f*x+e)+1/f*c*d^2*b*tan(f*x+e)*sec(f*x+e)^2+1/4/f*b*d^3*tan(f*x+e)*sec(f*x+e)^3+3/8/f*b*d^3*sec(f*x+e)*tan(f*x+e)+3/8/f*b*d^3*ln(sec(f*x+e)+tan(f*x+e))","A"
246,1,174,107,1.120000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e))^2,x)","\frac{a \,c^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{2 a c d \tan \left(f x +e \right)}{f}+\frac{a \,d^{2} \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{a \,d^{2} \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}+\frac{c^{2} b \tan \left(f x +e \right)}{f}+\frac{b c d \sec \left(f x +e \right) \tan \left(f x +e \right)}{f}+\frac{b c d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{2 d^{2} b \tan \left(f x +e \right)}{3 f}+\frac{d^{2} b \tan \left(f x +e \right) \left(\sec^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"1/f*a*c^2*ln(sec(f*x+e)+tan(f*x+e))+2/f*a*c*d*tan(f*x+e)+1/2/f*a*d^2*sec(f*x+e)*tan(f*x+e)+1/2/f*a*d^2*ln(sec(f*x+e)+tan(f*x+e))+1/f*c^2*b*tan(f*x+e)+1/f*b*c*d*sec(f*x+e)*tan(f*x+e)+1/f*b*c*d*ln(sec(f*x+e)+tan(f*x+e))+2/3/f*d^2*b*tan(f*x+e)+1/3/f*d^2*b*tan(f*x+e)*sec(f*x+e)^2","A"
247,1,86,57,0.917000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))*(c+d*sec(f*x+e)),x)","\frac{c a \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{f}+\frac{d a \tan \left(f x +e \right)}{f}+\frac{c b \tan \left(f x +e \right)}{f}+\frac{b d \sec \left(f x +e \right) \tan \left(f x +e \right)}{2 f}+\frac{b d \ln \left(\sec \left(f x +e \right)+\tan \left(f x +e \right)\right)}{2 f}"," ",0,"1/f*c*a*ln(sec(f*x+e)+tan(f*x+e))+1/f*d*a*tan(f*x+e)+1/f*c*b*tan(f*x+e)+1/2*b*d*sec(f*x+e)*tan(f*x+e)/f+1/2/f*b*d*ln(sec(f*x+e)+tan(f*x+e))","A"
248,1,135,67,0.591000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x)","\frac{2 a \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)}{f \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) c b}{f d \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{b \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f d}+\frac{b \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f d}"," ",0,"2/f*a/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))-2/f/d/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))*c*b-1/f/d*b*ln(tan(1/2*e+1/2*f*x)-1)+1/f/d*b*ln(tan(1/2*e+1/2*f*x)+1)","A"
249,1,132,90,0.657000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x)","\frac{\frac{2 \left(d a -c b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\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 \left(c a -b d \right) \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)}{\left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}}{f}"," ",0,"1/f*(2*(a*d-b*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)+2*(a*c-b*d)/(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"
250,1,236,153,0.594000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^3,x)","\frac{-\frac{2 \left(-\frac{\left(4 a c d +a \,d^{2}-2 c^{2} b -b c d -2 d^{2} b \right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{2 \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{\left(4 a c d -a \,d^{2}-2 c^{2} b +b c d -2 d^{2} b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \right) \left(c^{2}-2 c d +d^{2}\right)}\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)^{2}}+\frac{\left(2 a \,c^{2}+a \,d^{2}-3 b c d \right) \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)}{\left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}}{f}"," ",0,"1/f*(-2*(-1/2*(4*a*c*d+a*d^2-2*b*c^2-b*c*d-2*b*d^2)/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3+1/2*(4*a*c*d-a*d^2-2*b*c^2+b*c*d-2*b*d^2)/(c+d)/(c^2-2*c*d+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)^2+(2*a*c^2+a*d^2-3*b*c*d)/(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"
251,1,376,222,0.760000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^4,x)","\frac{-\frac{2 \left(-\frac{\left(6 a \,c^{2} d +3 a c \,d^{2}+2 a \,d^{3}-2 c^{3} b -2 b \,c^{2} d -6 b c \,d^{2}-b \,d^{3}\right) \left(\tan^{5}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{2 \left(c -d \right) \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{2 \left(9 a \,c^{2} d +a \,d^{3}-3 c^{3} b -7 b c \,d^{2}\right) \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 \left(c^{2}+2 c d +d^{2}\right) \left(c^{2}-2 c d +d^{2}\right)}-\frac{\left(6 a \,c^{2} d -3 a c \,d^{2}+2 a \,d^{3}-2 c^{3} b +2 b \,c^{2} d -6 b c \,d^{2}+b \,d^{3}\right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 \left(c +d \right) \left(c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}\right)}\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)^{3}}+\frac{\left(2 a \,c^{3}+3 a c \,d^{2}-4 b \,c^{2} d -b \,d^{3}\right) \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)}{\left(c^{6}-3 c^{4} d^{2}+3 c^{2} d^{4}-d^{6}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}}{f}"," ",0,"1/f*(-2*(-1/2*(6*a*c^2*d+3*a*c*d^2+2*a*d^3-2*b*c^3-2*b*c^2*d-6*b*c*d^2-b*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+2/3*(9*a*c^2*d+a*d^3-3*b*c^3-7*b*c*d^2)/(c^2+2*c*d+d^2)/(c^2-2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3-1/2*(6*a*c^2*d-3*a*c*d^2+2*a*d^3-2*b*c^3+2*b*c^2*d-6*b*c*d^2+b*d^3)/(c+d)/(c^3-3*c^2*d+3*c*d^2-d^3)*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)^3+(2*a*c^3+3*a*c*d^2-4*b*c^2*d-b*d^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"
252,1,1066,232,0.898000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e)),x)","\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{4}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{4}}{3 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{d^{4}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{4}}{3 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{d^{4}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{4}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{8 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a \,c^{3} d}{f b \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} c \,d^{3}}{f \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} c^{2} d^{2}}{f \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 d^{3} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{d^{4} a}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a}{2 f \,b^{2}}+\frac{4 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3}}{f b}+\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f b}-\frac{d^{4} a^{2}}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{4} a}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{6 d^{2} c^{2}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d^{3} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{3}}{f \,b^{4}}-\frac{6 d^{2} c^{2}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{4 d^{3} a c}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{4} d^{4}}{f \,b^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{2} c}{f \,b^{3}}+\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a \,c^{2}}{f \,b^{2}}+\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{2} c}{f \,b^{3}}-\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a \,c^{2}}{f \,b^{2}}+\frac{4 d^{3} a c}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d^{3} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4} a}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{2 d^{3} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{3}}{f \,b^{4}}+\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a}{2 f \,b^{2}}-\frac{4 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3}}{f b}-\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f b}-\frac{d^{4} a^{2}}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4} a}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}"," ",0,"2/f/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^4-1/3/f*d^4/b/(tan(1/2*e+1/2*f*x)-1)^3-1/f*d^4/b/(tan(1/2*e+1/2*f*x)-1)-1/2/f*d^4/b/(tan(1/2*e+1/2*f*x)-1)^2-1/3/f*d^4/b/(tan(1/2*e+1/2*f*x)+1)^3-1/f*d^4/b/(tan(1/2*e+1/2*f*x)+1)+1/2/f*d^4/b/(tan(1/2*e+1/2*f*x)+1)^2-8/f/b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c^3*d-8/f/b^3/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*c*d^3+12/f/b^2/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*c^2*d^2-2/f*d^3/b/(tan(1/2*e+1/2*f*x)+1)^2*c+1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)^2*a-1/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)+1)*a+4/f*d/b*ln(tan(1/2*e+1/2*f*x)+1)*c^3+2/f*d^3/b*ln(tan(1/2*e+1/2*f*x)+1)*c-1/f*d^4/b^3/(tan(1/2*e+1/2*f*x)+1)*a^2-1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)*a-6/f*d^2/b/(tan(1/2*e+1/2*f*x)+1)*c^2+2/f*d^3/b/(tan(1/2*e+1/2*f*x)+1)*c-1/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)+1)*a^3-6/f*d^2/b/(tan(1/2*e+1/2*f*x)-1)*c^2+4/f*d^3/b^2/(tan(1/2*e+1/2*f*x)-1)*a*c-4/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a^2*c+6/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*a*c^2+4/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a^2*c-6/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*a*c^2+4/f*d^3/b^2/(tan(1/2*e+1/2*f*x)+1)*a*c+2/f/b^4/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^4*d^4+2/f*d^3/b/(tan(1/2*e+1/2*f*x)-1)*c-1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)^2*a+2/f*d^3/b/(tan(1/2*e+1/2*f*x)-1)^2*c+1/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)-1)*a^3+1/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)-1)*a-4/f*d/b*ln(tan(1/2*e+1/2*f*x)-1)*c^3-2/f*d^3/b*ln(tan(1/2*e+1/2*f*x)-1)*c-1/f*d^4/b^3/(tan(1/2*e+1/2*f*x)-1)*a^2-1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)*a","B"
253,1,593,157,0.671000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e)),x)","-\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} d^{3}}{f \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} c \,d^{2}}{f \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a \,c^{2} d}{f b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{3}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{d^{3}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{2}}{f \,b^{3}}+\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a c}{f \,b^{2}}-\frac{3 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2}}{f b}-\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f b}+\frac{d^{3} a}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{3 d^{2} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{3}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{3}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{2}}{f \,b^{3}}-\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a c}{f \,b^{2}}+\frac{3 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2}}{f b}+\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f b}+\frac{d^{3} a}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{3 d^{2} c}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{3}}{2 f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}"," ",0,"-2/f/b^3/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*d^3+6/f/b^2/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*c*d^2-6/f/b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c^2*d+2/f/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^3+1/2/f*d^3/b/(tan(1/2*e+1/2*f*x)-1)^2-1/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a^2+3/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*a*c-3/f*d/b*ln(tan(1/2*e+1/2*f*x)-1)*c^2-1/2/f*d^3/b*ln(tan(1/2*e+1/2*f*x)-1)+1/f*d^3/b^2/(tan(1/2*e+1/2*f*x)-1)*a-3/f*d^2/b/(tan(1/2*e+1/2*f*x)-1)*c+1/2/f*d^3/b/(tan(1/2*e+1/2*f*x)-1)-1/2/f*d^3/b/(tan(1/2*e+1/2*f*x)+1)^2+1/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a^2-3/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*a*c+3/f*d/b*ln(tan(1/2*e+1/2*f*x)+1)*c^2+1/2/f*d^3/b*ln(tan(1/2*e+1/2*f*x)+1)+1/f*d^3/b^2/(tan(1/2*e+1/2*f*x)+1)*a-3/f*d^2/b/(tan(1/2*e+1/2*f*x)+1)*c+1/2/f*d^3/b/(tan(1/2*e+1/2*f*x)+1)","B"
254,1,288,94,0.643000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e)),x)","\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} d^{2}}{f \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a c d}{f b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{2}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{2}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a}{f \,b^{2}}-\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f b}-\frac{d^{2}}{f b \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a}{f \,b^{2}}+\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f b}"," ",0,"2/f/b^2/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*d^2-4/f/b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c*d+2/f/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^2-1/f*d^2/b/(tan(1/2*e+1/2*f*x)-1)+1/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*a-2/f*d/b*ln(tan(1/2*e+1/2*f*x)-1)*c-1/f*d^2/b/(tan(1/2*e+1/2*f*x)+1)-1/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*a+2/f*d/b*ln(tan(1/2*e+1/2*f*x)+1)*c","B"
255,1,135,67,0.660000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e)),x)","-\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) d a}{f b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f b}+\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f b}"," ",0,"-2/f/b/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*d*a+2/f/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c-1/f*d/b*ln(tan(1/2*e+1/2*f*x)-1)+1/f*d/b*ln(tan(1/2*e+1/2*f*x)+1)","A"
256,1,108,103,0.632000," ","int(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x)","\frac{\frac{2 d \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)}{\left(d a -c b \right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(d a -c b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{f}"," ",0,"1/f*(2*d/(a*d-b*c)/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))-2*b/(a*d-b*c)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2)))","A"
257,1,208,169,0.713000," ","int(sec(f*x+e)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x)","\frac{-\frac{2 d \left(-\frac{d \left(d a -c b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\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{\left(a c d -2 c^{2} b +d^{2} b \right) \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)}{\left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{\left(d a -c b \right)^{2}}+\frac{2 b^{2} \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(d a -c b \right)^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}}{f}"," ",0,"1/f*(-2*d/(a*d-b*c)^2*(-d*(a*d-b*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*c*d-2*b*c^2+b*d^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)))+2*b^2/(a*d-b*c)^2/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2)))","A"
258,1,1870,355,0.765000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^5/(a+b*sec(f*x+e))^2,x)","\frac{10 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{4} c \,d^{4}}{f \,b^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{d^{5}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{5}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{5}}{3 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{d^{5}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{5}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{d^{5}}{3 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}-\frac{10 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{4} d^{5}}{f \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{40 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a \,c^{3} d^{2}}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{6} d^{5}}{f \,b^{5} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{10 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{4} d}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{20 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} c^{2} d^{3}}{f \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{20 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c^{3} d^{2}}{f b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{40 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{4} c^{2} d^{3}}{f \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{40 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} c \,d^{4}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{30 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{5} c \,d^{4}}{f \,b^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{20 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} c^{3} d^{2}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{60 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} c^{2} d^{3}}{f b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{5} a}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{10 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,c^{4} d}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{5} d^{5}}{f \,b^{4} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{15 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{2} c}{f \,b^{4}}+\frac{20 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a \,c^{2}}{f \,b^{3}}+\frac{10 d^{4} a c}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{15 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{2} c}{f \,b^{4}}-\frac{20 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a \,c^{2}}{f \,b^{3}}+\frac{10 d^{4} a c}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 b \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{5}}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{d^{5} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{5 d^{4} c}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}+\frac{d^{5} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{5 d^{4} c}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{3 d^{5} a^{2}}{f \,b^{4} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{5} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{10 d^{3} c^{2}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{5 d^{4} c}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a}{f \,b^{3}}+\frac{4 d^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{3}}{f \,b^{5}}+\frac{d^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a}{f \,b^{3}}-\frac{10 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3}}{f \,b^{2}}-\frac{5 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{2 f \,b^{2}}-\frac{3 d^{5} a^{2}}{f \,b^{4} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{5} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{10 d^{3} c^{2}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{5 d^{4} c}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{10 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3}}{f \,b^{2}}+\frac{5 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{2 f \,b^{2}}-\frac{4 d^{5} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{3}}{f \,b^{5}}"," ",0,"-1/f*d^5/b^2/(tan(1/2*e+1/2*f*x)-1)-1/2/f*d^5/b^2/(tan(1/2*e+1/2*f*x)-1)^2-1/3/f*d^5/b^2/(tan(1/2*e+1/2*f*x)+1)^3-1/f*d^5/b^2/(tan(1/2*e+1/2*f*x)+1)+1/2/f*d^5/b^2/(tan(1/2*e+1/2*f*x)+1)^2-1/3/f*d^5/b^2/(tan(1/2*e+1/2*f*x)-1)^3-20/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*c^3*d^2-10/f/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^4*d^5+40/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c^3*d^2+8/f/b^5/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^6*d^5-10/f*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^4*d-20/f/b^2/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^3*c^2*d^3+20/f/b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^2*c^3*d^2+10/f/b^3/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^4*c*d^4-60/f/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*c^2*d^3-30/f/b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^5*c*d^4+40/f/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^4*c^2*d^3+40/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*c*d^4-10/f/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a*c^4*d+2/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^5*a-2/f/b^4/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^5*d^5-15/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)-1)*a^2*c+20/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a*c^2+10/f*d^4/b^3/(tan(1/2*e+1/2*f*x)-1)*a*c+15/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)+1)*a^2*c-20/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a*c^2+10/f*d^4/b^3/(tan(1/2*e+1/2*f*x)+1)*a*c+2/f*b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*c^5-1/f*d^5/b^3/(tan(1/2*e+1/2*f*x)-1)^2*a+5/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)^2*c+1/f*d^5/b^3/(tan(1/2*e+1/2*f*x)+1)^2*a-5/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)^2*c-3/f*d^5/b^4/(tan(1/2*e+1/2*f*x)+1)*a^2-1/f*d^5/b^3/(tan(1/2*e+1/2*f*x)+1)*a-10/f*d^3/b^2/(tan(1/2*e+1/2*f*x)+1)*c^2+5/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)*c-1/f*d^5/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a+4/f*d^5/b^5*ln(tan(1/2*e+1/2*f*x)-1)*a^3+1/f*d^5/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a-10/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*c^3-5/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)-1)*c-3/f*d^5/b^4/(tan(1/2*e+1/2*f*x)-1)*a^2-1/f*d^5/b^3/(tan(1/2*e+1/2*f*x)-1)*a-10/f*d^3/b^2/(tan(1/2*e+1/2*f*x)-1)*c^2+5/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)*c+10/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*c^3+5/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)+1)*c-4/f*d^5/b^5*ln(tan(1/2*e+1/2*f*x)+1)*a^3","B"
259,1,1249,275,0.677000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^4/(a+b*sec(f*x+e))^2,x)","-\frac{8 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} c \,d^{3}}{f \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{12 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c^{2} d^{2}}{f b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{24 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a \,c^{2} d^{2}}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{5} d^{4}}{f \,b^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} d^{4}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{3} d}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f \,b^{2}}+\frac{d^{4}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{4}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f \,b^{2}}+\frac{d^{4}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4}}{2 f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{4} a}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,c^{3} d}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{4} d^{4}}{f \,b^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{24 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} c \,d^{3}}{f b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{16 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{4} c \,d^{3}}{f \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{12 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} c^{2} d^{2}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 d^{4} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{4 d^{3} c}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{8 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a c}{f \,b^{3}}+\frac{8 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a c}{f \,b^{3}}+\frac{2 b \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{4}}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{3 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a^{2}}{f \,b^{4}}-\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2}}{f \,b^{2}}+\frac{2 d^{4} a}{f \,b^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{4 d^{3} c}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{3 d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a^{2}}{f \,b^{4}}+\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2}}{f \,b^{2}}"," ",0,"-8/f/b^2/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^3*c*d^3+1/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)+1)+1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)+1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)^2-1/2/f*d^4/b^2*ln(tan(1/2*e+1/2*f*x)-1)+1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)-1)-1/2/f*d^4/b^2/(tan(1/2*e+1/2*f*x)+1)^2+24/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c^2*d^2+12/f/b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^2*c^2*d^2-6/f/b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^5*d^4+8/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*d^4-8/f*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^3*d-8/f/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a*c^3*d+2/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^4*a+2/f/b^3/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^4*d^4+2/f*d^4/b^3/(tan(1/2*e+1/2*f*x)+1)*a-4/f*d^3/b^2/(tan(1/2*e+1/2*f*x)+1)*c-8/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a*c+2/f*b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*c^4+8/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a*c-3/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)-1)*a^2-6/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*c^2+2/f*d^4/b^3/(tan(1/2*e+1/2*f*x)-1)*a-4/f*d^3/b^2/(tan(1/2*e+1/2*f*x)-1)*c+3/f*d^4/b^4*ln(tan(1/2*e+1/2*f*x)+1)*a^2+6/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*c^2-24/f/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*c*d^3+16/f/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^4*c*d^3-12/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*c^2*d^2","B"
260,1,790,210,0.601000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^3/(a+b*sec(f*x+e))^2,x)","-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{3} d^{3}}{f \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c \,d^{2}}{f b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{6 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a \,c^{2} d}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{2 b \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{3}}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{4 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{4} d^{3}}{f \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} c \,d^{2}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} d^{3}}{f b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{3} a}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a c \,d^{2}}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{2} d}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{3}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) a}{f \,b^{3}}-\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f \,b^{2}}-\frac{d^{3}}{f \,b^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) a}{f \,b^{3}}+\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f \,b^{2}}"," ",0,"-2/f/b^2/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^3*d^3+6/f/b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^2*c*d^2-6/f/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a*c^2*d+2/f*b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*c^3+4/f/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^4*d^3-6/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*c*d^2-6/f/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^2*d^3+2/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^3*a+12/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*c*d^2-6/f*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^2*d-1/f*d^3/b^2/(tan(1/2*e+1/2*f*x)-1)+2/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)-1)*a-3/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)*c-1/f*d^3/b^2/(tan(1/2*e+1/2*f*x)+1)-2/f*d^3/b^3*ln(tan(1/2*e+1/2*f*x)+1)*a+3/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)*c","B"
261,1,486,180,0.844000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))^2/(a+b*sec(f*x+e))^2,x)","\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} d^{2}}{f b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{4 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a c d}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{2 b \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c^{2}}{f \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} d^{2}}{f \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{2} a}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a \,d^{2}}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 b \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c d}{f \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f \,b^{2}}+\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f \,b^{2}}"," ",0,"2/f/b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a^2*d^2-4/f/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*a*c*d+2/f*b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)*c^2-2/f/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a^3*d^2+2/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c^2*a+4/f/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*a*d^2-4/f*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))*c*d-1/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)-1)+1/f*d^2/b^2*ln(tan(1/2*e+1/2*f*x)+1)","B"
262,1,132,91,0.628000," ","int(sec(f*x+e)*(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^2,x)","\frac{-\frac{2 \left(d a -c b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}+\frac{2 \left(c a -b d \right) \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{f}"," ",0,"1/f*(-2*(a*d-b*c)/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)+2*(a*c-b*d)/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2)))","A"
263,1,210,168,0.719000," ","int(sec(f*x+e)/(a+b*sec(f*x+e))^2/(c+d*sec(f*x+e)),x)","\frac{\frac{2 d^{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)}{\left(d a -c b \right)^{2} \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 b \left(-\frac{\left(d a -c b \right) b \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)-\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b -a -b \right)}-\frac{\left(2 a^{2} d -a b c -b^{2} d \right) \arctanh \left(\frac{\left(a -b \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(d a -c b \right)^{2}}}{f}"," ",0,"1/f*(2*d^2/(a*d-b*c)^2/((c+d)*(c-d))^(1/2)*arctanh(tan(1/2*e+1/2*f*x)*(c-d)/((c+d)*(c-d))^(1/2))+2*b/(a*d-b*c)^2*(-(a*d-b*c)*b/(a^2-b^2)*tan(1/2*e+1/2*f*x)/(a*tan(1/2*e+1/2*f*x)^2-tan(1/2*e+1/2*f*x)^2*b-a-b)-(2*a^2*d-a*b*c-b^2*d)/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh((a-b)*tan(1/2*e+1/2*f*x)/((a-b)*(a+b))^(1/2))))","A"
264,1,355,199,1.671000," ","int(sec(f*x+e)*(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 +\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 -\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 -\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 -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 \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 \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} \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+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*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*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*b*c)*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(c-d)/(c+d)","A"
265,1,351,185,2.396000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+d*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) 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 +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 \right) \cos \left(f x +e \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)}}\, \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*(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+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)*cos(f*x+e)*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)*((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"
266,1,219,177,2.087000," ","int(sec(f*x+e)/(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x)","\frac{2 \left(\sin^{2}\left(f x +e \right)\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)}}\, \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) \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*sin(f*x+e)^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)*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+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"
267,1,177,104,2.251000," ","int(sec(f*x+e)/(2+3*sec(f*x+e))^(1/2)/(-4+5*sec(f*x+e))^(1/2),x)","\frac{i \left(\sin^{2}\left(f x +e \right)\right) \sqrt{\frac{2 \cos \left(f x +e \right)+3}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{4 \cos \left(f x +e \right)-5}{\cos \left(f x +e \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right) \sqrt{5}}{5 \sin \left(f x +e \right)}, 3 \sqrt{5}\right) \cos \left(f x +e \right) \sqrt{10}\, \sqrt{\frac{2 \cos \left(f x +e \right)+3}{1+\cos \left(f x +e \right)}}\, \sqrt{-\frac{2 \left(4 \cos \left(f x +e \right)-5\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{5}}{5 f \left(8 \left(\cos^{3}\left(f x +e \right)\right)-6 \left(\cos^{2}\left(f x +e \right)\right)-17 \cos \left(f x +e \right)+15\right)}"," ",0,"1/5*I/f*sin(f*x+e)^2*((2*cos(f*x+e)+3)/cos(f*x+e))^(1/2)*(-(4*cos(f*x+e)-5)/cos(f*x+e))^(1/2)*EllipticF(1/5*I*(-1+cos(f*x+e))*5^(1/2)/sin(f*x+e),3*5^(1/2))*cos(f*x+e)*10^(1/2)*((2*cos(f*x+e)+3)/(1+cos(f*x+e)))^(1/2)*(-2*(4*cos(f*x+e)-5)/(1+cos(f*x+e)))^(1/2)/(8*cos(f*x+e)^3-6*cos(f*x+e)^2-17*cos(f*x+e)+15)*5^(1/2)","C"
268,1,170,109,2.066000," ","int(sec(f*x+e)/(4-5*sec(f*x+e))^(1/2)/(2+3*sec(f*x+e))^(1/2),x)","-\frac{i \sqrt{-\frac{2 \left(4 \cos \left(f x +e \right)-5\right)}{1+\cos \left(f x +e \right)}}\, \sqrt{10}\, \sqrt{\frac{2 \cos \left(f x +e \right)+3}{1+\cos \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{3 i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \frac{\sqrt{5}}{15}\right) \cos \left(f x +e \right) \sqrt{\frac{4 \cos \left(f x +e \right)-5}{\cos \left(f x +e \right)}}\, \sqrt{\frac{2 \cos \left(f x +e \right)+3}{\cos \left(f x +e \right)}}}{15 f \left(8 \left(\cos^{3}\left(f x +e \right)\right)-6 \left(\cos^{2}\left(f x +e \right)\right)-17 \cos \left(f x +e \right)+15\right)}"," ",0,"-1/15*I/f*(-2*(4*cos(f*x+e)-5)/(1+cos(f*x+e)))^(1/2)*10^(1/2)*((2*cos(f*x+e)+3)/(1+cos(f*x+e)))^(1/2)*sin(f*x+e)^2*EllipticF(3*I*(-1+cos(f*x+e))/sin(f*x+e),1/15*5^(1/2))*cos(f*x+e)*((4*cos(f*x+e)-5)/cos(f*x+e))^(1/2)*((2*cos(f*x+e)+3)/cos(f*x+e))^(1/2)/(8*cos(f*x+e)^3-6*cos(f*x+e)^2-17*cos(f*x+e)+15)","A"
269,1,291,370,2.166000," ","int(sec(f*x+e)^2/(a+b*sec(f*x+e))^(1/2)/(c+d*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) \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{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)*((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*((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"
270,1,465,216,2.235000," ","int((g*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e)),x)","-\frac{2 i \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, i \sqrt{\frac{c -d}{c +d}}\right) a^{2} d -2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, i \sqrt{\frac{c -d}{c +d}}\right) a b c +\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a b c -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a b d +\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) b^{2} c -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) b^{2} d -2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{c -d}{c +d}}\right) a^{2} d +2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{c -d}{c +d}}\right) b^{2} d \right) \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{f \left(d +c \cos \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, b \left(a -b \right) \left(a +b \right)}"," ",0,"-2*I/f*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),I*((c-d)/(c+d))^(1/2))*a^2*d-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),I*((c-d)/(c+d))^(1/2))*a*b*c+EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a*b*c-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a*b*d+EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*b^2*c-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*b^2*d-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((c-d)/(c+d))^(1/2))*a^2*d+2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((c-d)/(c+d))^(1/2))*b^2*d)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2/(d+c*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)/b/(a-b)/(a+b)","C"
271,1,236,106,2.154000," ","int((g*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x)","-\frac{2 i \left(a \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right)+b \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right)-2 a \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, i \sqrt{\frac{c -d}{c +d}}\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)}}\, \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\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) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(a -b \right) \left(a +b \right)}"," ",0,"-2*I/f*(a*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))+b*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))-2*a*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),I*((c-d)/(c+d))^(1/2)))*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)/(d+c*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)/(a-b)/(a+b)","C"
272,1,479,214,2.233000," ","int((g*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x)","-\frac{2 i \left(2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{c -d}{c +d}}\right) a^{2} d -2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{c -d}{c +d}}\right) b^{2} d +\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a^{2} c -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a^{2} d +\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a b c -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{c -d}{c +d}}\right) a b d -2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \frac{a -b}{a +b}, i \sqrt{\frac{c -d}{c +d}}\right) a b c +2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \frac{a -b}{a +b}, i \sqrt{\frac{c -d}{c +d}}\right) b^{2} 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{1}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{g}{\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)}{f \left(-1+\cos \left(f x +e \right)\right) \left(d +c \cos \left(f x +e \right)\right) a \left(a -b \right) \left(a +b \right)}"," ",0,"-2*I/f*(2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((c-d)/(c+d))^(1/2))*a^2*d-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((c-d)/(c+d))^(1/2))*b^2*d+EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a^2*c-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a^2*d+EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a*b*c-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(c-d)/(c+d))^(1/2))*a*b*d-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),(a-b)/(a+b),I*((c-d)/(c+d))^(1/2))*a*b*c+2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),(a-b)/(a+b),I*((c-d)/(c+d))^(1/2))*b^2*d)*cos(f*x+e)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(1/(1+cos(f*x+e)))^(1/2)*(g/cos(f*x+e))^(1/2)*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*sin(f*x+e)^2/(-1+cos(f*x+e))/(d+c*cos(f*x+e))/a/(a-b)/(a+b)","C"
273,1,153,90,1.967000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x)","-\frac{\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{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \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) \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(-a -b \right)}{c f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2}}"," ",0,"-1/c/f*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-1+cos(f*x+e))*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2/(b+a*cos(f*x+e))/sin(f*x+e)^2*(-a-b)","A"
274,1,292,360,2.220000," ","int((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x)","\frac{i \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(2 a \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-2 b \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-a \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-b \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)+4 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) b \right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{c f \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}}"," ",0,"I/c/f*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(2*a*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-2*b*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-a*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-b*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))+4*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*b)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)","C"
275,1,225,195,2.008000," ","int(sec(f*x+e)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","-\frac{\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(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 -a \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-b \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{c f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \left(a -b \right)}"," ",0,"-1/c/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))*(2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b-a*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-b*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2)))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(a-b)","A"
276,1,224,200,1.897000," ","int(sec(f*x+e)^2/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","\frac{\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(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 -a \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)-b \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{c f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \left(a -b \right)}"," ",0,"1/c/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*(2*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a-a*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))-b*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2)))*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(a-b)","A"
277,1,222,271,2.308000," ","int((g*sec(f*x+e))^(3/2)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","\frac{i \left(2 a \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-a \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-b \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)\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(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{c f \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(a -b \right)}"," ",0,"I/c/f*(2*a*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-a*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-b*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2)))*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)/(a-b)","C"
278,1,355,377,2.497000," ","int((g*sec(f*x+e))^(5/2)/(c+c*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","\frac{i \left(4 a \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-2 b \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-a \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-b \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-4 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) a +4 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) b \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{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{c f \left(b +a \cos \left(f x +e \right)\right) \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{2} \left(a -b \right)}"," ",0,"I/c/f*(4*a*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-2*b*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-a*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-b*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-4*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*a+4*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*b)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(g/cos(f*x+e))^(5/2)*cos(f*x+e)^3/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(3/2)/sin(f*x+e)^2/(a-b)","C"
279,1,355,199,1.621000," ","int(sec(f*x+e)*(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 +\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 -\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 -\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 -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 \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 \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} \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+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*a*d-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*c-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*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*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*b*c)*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(c-d)/(c+d)","A"
280,1,465,216,2.031000," ","int((g*sec(f*x+e))^(3/2)*(a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x)","-\frac{2 i \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a c d +\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a \,d^{2}-\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b c d -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b \,d^{2}-2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{c -d}{c +d}, i \sqrt{\frac{a -b}{a +b}}\right) a c d +2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{c -d}{c +d}, i \sqrt{\frac{a -b}{a +b}}\right) b \,c^{2}-2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) b \,c^{2}+2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) b \,d^{2}\right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, d \left(c +d \right) \left(c -d \right)}"," ",0,"-2*I/f*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*a*c*d+EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*a*d^2-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*b*c*d-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*b*d^2-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(c-d)/(c+d),I*((a-b)/(a+b))^(1/2))*a*c*d+2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(c-d)/(c+d),I*((a-b)/(a+b))^(1/2))*b*c^2-2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*b*c^2+2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*b*d^2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)/d/(c+d)/(c-d)","C"
281,1,238,97,1.806000," ","int(sec(f*x+e)/(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(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 -\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 \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} \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*(2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2))*d-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)*(-1+cos(f*x+e))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(c-d)/(c+d)","B"
282,1,236,195,1.786000," ","int(sec(f*x+e)^2/(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 c \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)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \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))*(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*c*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),(c-d)/(c+d),((a-b)/(a+b))^(1/2)))/(b+a*cos(f*x+e))/sin(f*x+e)^2/(c-d)/(c+d)","A"
283,1,238,106,2.082000," ","int((g*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","\frac{2 i \left(2 c \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{c -d}{c +d}, i \sqrt{\frac{a -b}{a +b}}\right)-c \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)-d \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right)\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(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}}{f \left(b +a \cos \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}\, \left(c +d \right) \left(c -d \right)}"," ",0,"2*I/f*(2*c*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(c-d)/(c+d),I*((a-b)/(a+b))^(1/2))-c*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))-d*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2)))*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*(g/cos(f*x+e))^(3/2)*cos(f*x+e)^2*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)/(c+d)/(c-d)","C"
284,1,346,212,2.135000," ","int((g*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","\frac{2 i \left(2 c^{2} \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -\frac{c -d}{c +d}, i \sqrt{\frac{a -b}{a +b}}\right)-\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) d c -\EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, \sqrt{-\frac{a -b}{a +b}}\right) d^{2}-2 c^{2} \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right)+2 \EllipticPi \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, -1, i \sqrt{\frac{a -b}{a +b}}\right) d^{2}\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{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(\frac{g}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(f x +e \right)\right)}{f \left(b +a \cos \left(f x +e \right)\right) \left(\frac{1}{1+\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{2} d \left(c +d \right) \left(c -d \right)}"," ",0,"2*I/f*(2*c^2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-(c-d)/(c+d),I*((a-b)/(a+b))^(1/2))-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*d*c-EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),(-(a-b)/(a+b))^(1/2))*d^2-2*c^2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))+2*EllipticPi(I*(-1+cos(f*x+e))/sin(f*x+e),-1,I*((a-b)/(a+b))^(1/2))*d^2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(g/cos(f*x+e))^(5/2)*cos(f*x+e)^3/(b+a*cos(f*x+e))/(1/(1+cos(f*x+e)))^(3/2)/sin(f*x+e)^2/d/(c+d)/(c-d)","C"
285,1,49,58,1.037000," ","int(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^7,x)","\frac{-\frac{2}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{9 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}}{4 f \,c^{7}}"," ",0,"1/4/f/c^7*(-2/7/tan(1/2*e+1/2*f*x)^7+1/9/tan(1/2*e+1/2*f*x)^9+1/5/tan(1/2*e+1/2*f*x)^5)","A"
286,1,62,77,1.197000," ","int(sec(f*x+e)*tan(f*x+e)^4/(c-c*sec(f*x+e))^8,x)","\frac{-\frac{1}{11 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{11}}-\frac{3}{7 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{7}}+\frac{1}{3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{9}}+\frac{1}{5 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)^{5}}}{8 f \,c^{8}}"," ",0,"1/8/f/c^8*(-1/11/tan(1/2*e+1/2*f*x)^11-3/7/tan(1/2*e+1/2*f*x)^7+1/3/tan(1/2*e+1/2*f*x)^9+1/5/tan(1/2*e+1/2*f*x)^5)","A"