1,1,92,77,0.698000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c)),x)","\frac{2 a \tan \left(d x +c \right)}{3 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"2/3*a*tan(d*x+c)/d+1/3/d*a*tan(d*x+c)*sec(d*x+c)^2+1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
2,1,72,57,0.702000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c)),x)","\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a \tan \left(d x +c \right)}{3 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+2/3*a*tan(d*x+c)/d+1/3/d*a*tan(d*x+c)*sec(d*x+c)^2","A"
3,1,51,43,0.720000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c)),x)","\frac{a \tan \left(d x +c \right)}{d}+\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a*tan(d*x+c)/d+1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
4,1,32,24,0.520000," ","int(sec(d*x+c)*(a+a*sec(d*x+c)),x)","\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a \tan \left(d x +c \right)}{d}"," ",0,"1/d*a*ln(sec(d*x+c)+tan(d*x+c))+a*tan(d*x+c)/d","A"
5,1,24,16,0.028000," ","int(a+a*sec(d*x+c),x)","a x +\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"a*x+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
6,1,21,15,0.478000," ","int(cos(d*x+c)*(a+a*sec(d*x+c)),x)","\frac{a \left(d x +c \right)+a \sin \left(d x +c \right)}{d}"," ",0,"1/d*(a*(d*x+c)+a*sin(d*x+c))","A"
7,1,38,34,0.579000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c)),x)","\frac{a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a \sin \left(d x +c \right)}{d}"," ",0,"1/d*(a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*sin(d*x+c))","A"
8,1,49,48,0.820000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c)),x)","\frac{\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c)+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
9,1,60,68,0.957000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c)),x)","\frac{a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
10,1,124,110,0.907000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))^2,x)","\frac{6 a^{2} \tan \left(d x +c \right)}{5 d}+\frac{3 a^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}"," ",0,"6/5*a^2*tan(d*x+c)/d+3/5*a^2*sec(d*x+c)^2*tan(d*x+c)/d+1/2*a^2*sec(d*x+c)^3*tan(d*x+c)/d+3/4*a^2*sec(d*x+c)*tan(d*x+c)/d+3/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/5*a^2*sec(d*x+c)^4*tan(d*x+c)/d","A"
11,1,102,88,0.870000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^2,x)","\frac{7 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{7 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{4 a^{2} \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}"," ",0,"7/8*a^2*sec(d*x+c)*tan(d*x+c)/d+7/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+4/3*a^2*tan(d*x+c)/d+2/3*a^2*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a^2*sec(d*x+c)^3*tan(d*x+c)/d","A"
12,1,78,70,0.852000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^2,x)","\frac{5 a^{2} \tan \left(d x +c \right)}{3 d}+\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}"," ",0,"5/3*a^2*tan(d*x+c)/d+a^2*sec(d*x+c)*tan(d*x+c)/d+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/3*a^2*sec(d*x+c)^2*tan(d*x+c)/d","A"
13,1,58,50,0.711000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^2,x)","\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} \tan \left(d x +c \right)}{d}+\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"3/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2*a^2*tan(d*x+c)/d+1/2*a^2*sec(d*x+c)*tan(d*x+c)/d","A"
14,1,50,34,0.523000," ","int((a+a*sec(d*x+c))^2,x)","a^{2} x +\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} c}{d}"," ",0,"a^2*x+a^2*tan(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*c","A"
15,1,51,34,0.536000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^2,x)","2 a^{2} x +\frac{a^{2} \sin \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a^{2} c}{d}"," ",0,"2*a^2*x+a^2*sin(d*x+c)/d+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a^2*c","A"
16,1,52,41,0.518000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+2 a^{2} \sin \left(d x +c \right)+a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*a^2*sin(d*x+c)+a^2*(d*x+c))","A"
17,1,64,55,0.902000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^2,x)","\frac{\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a^{2} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+2*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^2*sin(d*x+c))","A"
18,1,90,79,0.982000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{2 a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
19,1,96,95,1.254000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^2,x)","\frac{\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+2 a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+2*a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
20,1,124,104,1.056000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^3,x)","\frac{13 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{13 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{38 a^{3} \tan \left(d x +c \right)}{15 d}+\frac{19 a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{3 a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"13/8*a^3*sec(d*x+c)*tan(d*x+c)/d+13/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+38/15*a^3*tan(d*x+c)/d+19/15/d*a^3*tan(d*x+c)*sec(d*x+c)^2+3/4*a^3*sec(d*x+c)^3*tan(d*x+c)/d+1/5/d*a^3*tan(d*x+c)*sec(d*x+c)^4","A"
21,1,101,87,1.016000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^3,x)","\frac{3 a^{3} \tan \left(d x +c \right)}{d}+\frac{15 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{15 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}"," ",0,"3*a^3*tan(d*x+c)/d+15/8*a^3*sec(d*x+c)*tan(d*x+c)/d+15/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3*tan(d*x+c)*sec(d*x+c)^2+1/4*a^3*sec(d*x+c)^3*tan(d*x+c)/d","A"
22,1,80,66,0.854000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^3,x)","\frac{5 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{11 a^{3} \tan \left(d x +c \right)}{3 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"5/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+11/3*a^3*tan(d*x+c)/d+3/2*a^3*sec(d*x+c)*tan(d*x+c)/d+1/3/d*a^3*tan(d*x+c)*sec(d*x+c)^2","A"
23,1,71,60,0.692000," ","int((a+a*sec(d*x+c))^3,x)","a^{3} x +\frac{a^{3} c}{d}+\frac{7 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"a^3*x+1/d*a^3*c+7/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3*a^3*tan(d*x+c)/d+1/2*a^3*sec(d*x+c)*tan(d*x+c)/d","A"
24,1,65,48,0.649000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^3,x)","3 a^{3} x +\frac{a^{3} \sin \left(d x +c \right)}{d}+\frac{a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} c}{d}"," ",0,"3*a^3*x+a^3*sin(d*x+c)/d+a^3*tan(d*x+c)/d+3/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*c","A"
25,1,72,55,0.486000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{7 a^{3} x}{2}+\frac{7 a^{3} c}{2 d}+\frac{3 a^{3} \sin \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+7/2*a^3*x+7/2/d*a^3*c+3*a^3*sin(d*x+c)/d+1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))","A"
26,1,74,57,0.730000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^3,x)","\frac{\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+3 a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 \sin \left(d x +c \right) a^{3}+a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*sin(d*x+c)*a^3+a^3*(d*x+c))","A"
27,1,100,79,0.791000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+\sin \left(d x +c \right) a^{3}}{d}"," ",0,"1/d*(a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+sin(d*x+c)*a^3)","A"
28,1,121,95,1.272000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^3,x)","\frac{\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+3 a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3*a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
29,1,143,117,1.432000," ","int(cos(d*x+c)^6*(a+a*sec(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{3 a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+3 a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^3*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+3/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3*a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
30,1,146,126,1.186000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^4,x)","\frac{49 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{49 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{24 a^{4} \tan \left(d x +c \right)}{5 d}+\frac{12 a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{5 d}+\frac{41 a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{4 a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}"," ",0,"49/16*a^4*sec(d*x+c)*tan(d*x+c)/d+49/16/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+24/5*a^4*tan(d*x+c)/d+12/5/d*a^4*tan(d*x+c)*sec(d*x+c)^2+41/24*a^4*sec(d*x+c)^3*tan(d*x+c)/d+4/5/d*a^4*tan(d*x+c)*sec(d*x+c)^4+1/6*a^4*sec(d*x+c)^5*tan(d*x+c)/d","A"
31,1,123,103,1.392000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^4,x)","\frac{83 a^{4} \tan \left(d x +c \right)}{15 d}+\frac{7 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{7 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{34 a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{d}+\frac{a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"83/15*a^4*tan(d*x+c)/d+7/2*a^4*sec(d*x+c)*tan(d*x+c)/d+7/2/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+34/15/d*a^4*tan(d*x+c)*sec(d*x+c)^2+a^4*sec(d*x+c)^3*tan(d*x+c)/d+1/5/d*a^4*tan(d*x+c)*sec(d*x+c)^4","A"
32,1,102,88,1.162000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^4,x)","\frac{35 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{20 a^{4} \tan \left(d x +c \right)}{3 d}+\frac{27 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{4 a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}"," ",0,"35/8/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+20/3*a^4*tan(d*x+c)/d+27/8*a^4*sec(d*x+c)*tan(d*x+c)/d+4/3/d*a^4*tan(d*x+c)*sec(d*x+c)^2+1/4*a^4*sec(d*x+c)^3*tan(d*x+c)/d","A"
33,1,93,87,0.849000," ","int((a+a*sec(d*x+c))^4,x)","a^{4} x +\frac{a^{4} c}{d}+\frac{6 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{20 a^{4} \tan \left(d x +c \right)}{3 d}+\frac{2 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a^4*x+1/d*a^4*c+6/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+20/3*a^4*tan(d*x+c)/d+2*a^4*sec(d*x+c)*tan(d*x+c)/d+1/3/d*a^4*tan(d*x+c)*sec(d*x+c)^2","A"
34,1,86,69,0.827000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^4,x)","\frac{a^{4} \sin \left(d x +c \right)}{d}+4 a^{4} x +\frac{4 a^{4} c}{d}+\frac{13 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"a^4*sin(d*x+c)/d+4*a^4*x+4/d*a^4*c+13/2/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4*a^4*tan(d*x+c)/d+1/2*a^4*sec(d*x+c)*tan(d*x+c)/d","A"
35,1,86,69,0.663000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^4,x)","\frac{a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 a^{4} x}{2}+\frac{13 a^{4} c}{2 d}+\frac{4 a^{4} \sin \left(d x +c \right)}{d}+\frac{4 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{4} \tan \left(d x +c \right)}{d}"," ",0,"1/2*a^4*cos(d*x+c)*sin(d*x+c)/d+13/2*a^4*x+13/2/d*a^4*c+4*a^4*sin(d*x+c)/d+4/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+a^4*tan(d*x+c)/d","A"
36,1,94,71,0.734000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^4,x)","\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}}{3 d}+\frac{20 a^{4} \sin \left(d x +c \right)}{3 d}+\frac{2 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+6 a^{4} x +\frac{6 a^{4} c}{d}+\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*cos(d*x+c)^2*sin(d*x+c)*a^4+20/3*a^4*sin(d*x+c)/d+2*a^4*cos(d*x+c)*sin(d*x+c)/d+6*a^4*x+6/d*a^4*c+1/d*a^4*ln(sec(d*x+c)+tan(d*x+c))","A"
37,1,111,79,0.896000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{4 a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+6 a^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+4 a^{4} \sin \left(d x +c \right)+a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4/3*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+6*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*a^4*sin(d*x+c)+a^4*(d*x+c))","A"
38,1,133,94,1.217000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+4 a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 a^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a^{4} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+4*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^4*sin(d*x+c))","A"
39,1,169,117,1.357000," ","int(cos(d*x+c)^6*(a+a*sec(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{4 a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+6 a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{4 a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^4*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+4/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+6*a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4/3*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
40,1,185,133,1.583000," ","int(cos(d*x+c)^7*(a+a*sec(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}+4 a^{4} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{6 a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+4 a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/7*a^4*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)+4*a^4*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+6/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*a^4*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
41,1,168,142,1.338000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^5,x)","\frac{93 a^{5} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{93 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{958 a^{5} \tan \left(d x +c \right)}{105 d}+\frac{479 a^{5} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{105 d}+\frac{85 a^{5} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{76 a^{5} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{35 d}+\frac{5 a^{5} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{a^{5} \tan \left(d x +c \right) \left(\sec^{6}\left(d x +c \right)\right)}{7 d}"," ",0,"93/16*a^5*sec(d*x+c)*tan(d*x+c)/d+93/16/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+958/105*a^5*tan(d*x+c)/d+479/105/d*a^5*tan(d*x+c)*sec(d*x+c)^2+85/24*a^5*sec(d*x+c)^3*tan(d*x+c)/d+76/35/d*a^5*tan(d*x+c)*sec(d*x+c)^4+5/6*a^5*sec(d*x+c)^5*tan(d*x+c)/d+1/7/d*a^5*tan(d*x+c)*sec(d*x+c)^6","A"
42,1,183,97,0.358000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{3 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d a}-\frac{1}{3 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d a}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)-1/3/d/a/(tan(1/2*d*x+1/2*c)-1)^3-1/d/a/(tan(1/2*d*x+1/2*c)-1)^2-5/2/d/a/(tan(1/2*d*x+1/2*c)-1)+3/2/d/a*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/a/(tan(1/2*d*x+1/2*c)+1)^3+1/d/a/(tan(1/2*d*x+1/2*c)+1)^2-5/2/d/a/(tan(1/2*d*x+1/2*c)+1)-3/2/d/a*ln(tan(1/2*d*x+1/2*c)+1)","A"
43,1,143,81,0.412000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{1}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d a}-\frac{1}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3}{2 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d a}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)+1/2/d/a/(tan(1/2*d*x+1/2*c)-1)^2+3/2/d/a/(tan(1/2*d*x+1/2*c)-1)-3/2/d/a*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/a/(tan(1/2*d*x+1/2*c)+1)^2+3/2/d/a/(tan(1/2*d*x+1/2*c)+1)+3/2/d/a*ln(tan(1/2*d*x+1/2*c)+1)","A"
44,1,99,51,0.354000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d a}-\frac{1}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d a}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)-1/d/a/(tan(1/2*d*x+1/2*c)-1)+1/d/a*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a/(tan(1/2*d*x+1/2*c)+1)-1/d/a*ln(tan(1/2*d*x+1/2*c)+1)","A"
45,1,58,38,0.332000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d a}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d a}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-1/d/a*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a*ln(tan(1/2*d*x+1/2*c)+1)","A"
46,1,17,22,0.362000," ","int(sec(d*x+c)/(a+a*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)","A"
47,1,37,29,0.405000," ","int(1/(a+a*sec(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)+2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
48,1,68,44,0.548000," ","int(cos(d*x+c)/(a+a*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)+2/d/a*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
49,1,103,70,0.511000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+3/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
50,1,136,88,0.585000," ","int(cos(d*x+c)^3/(a+a*sec(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{16 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)+5/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+16/3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-3/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
51,1,171,110,0.556000," ","int(cos(d*x+c)^4/(a+a*sec(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{25 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{115 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{109 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-25/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-115/12/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-109/12/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-7/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+15/4/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
52,1,162,113,0.359000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}+\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{2} d}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{2} d}"," ",0,"-1/6/a^2/d*tan(1/2*d*x+1/2*c)^3-7/2/a^2/d*tan(1/2*d*x+1/2*c)+1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2+5/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)-7/2/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+5/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)+7/2/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
53,1,120,85,0.396000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{2} d}-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{2} d}"," ",0,"1/6/a^2/d*tan(1/2*d*x+1/2*c)^3+5/2/a^2/d*tan(1/2*d*x+1/2*c)-1/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/a^2/d/(tan(1/2*d*x+1/2*c)+1)-2/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
54,1,77,62,0.350000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{2} d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{2} d}"," ",0,"-1/6/a^2/d*tan(1/2*d*x+1/2*c)^3-3/2/a^2/d*tan(1/2*d*x+1/2*c)-1/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
55,1,32,51,0.409000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}"," ",0,"1/2/d/a^2*(1/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
56,1,32,51,0.334000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^2,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}"," ",0,"1/2/d/a^2*(-1/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
57,1,56,53,0.458000," ","int(1/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/6/a^2/d*tan(1/2*d*x+1/2*c)^3-3/2/a^2/d*tan(1/2*d*x+1/2*c)+2/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
58,1,88,68,0.502000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"-1/6/a^2/d*tan(1/2*d*x+1/2*c)^3+5/2/a^2/d*tan(1/2*d*x+1/2*c)+2/a^2/d*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-4/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
59,1,122,100,0.598000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/6/a^2/d*tan(1/2*d*x+1/2*c)^3-7/2/a^2/d*tan(1/2*d*x+1/2*c)-5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+7/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
60,1,156,120,0.599000," ","int(cos(d*x+c)^3/(a+a*sec(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 a^{2} d}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d}+\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{40 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"-1/6/a^2/d*tan(1/2*d*x+1/2*c)^3+9/2/a^2/d*tan(1/2*d*x+1/2*c)+10/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+40/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+6/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-10/a^2/d*arctan(tan(1/2*d*x+1/2*c))","A"
61,1,181,150,0.424000," ","int(sec(d*x+c)^6/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}-\frac{31 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{7}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{3}}"," ",0,"-1/20/d/a^3*tan(1/2*d*x+1/2*c)^5-2/3/d/a^3*tan(1/2*d*x+1/2*c)^3-31/4/d/a^3*tan(1/2*d*x+1/2*c)+1/2/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2+7/2/d/a^3/(tan(1/2*d*x+1/2*c)-1)-13/2/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+7/2/d/a^3/(tan(1/2*d*x+1/2*c)+1)+13/2/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)","A"
62,1,139,122,0.357000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^3,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{17 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{1}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}-\frac{1}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{3}}"," ",0,"1/20/d/a^3*tan(1/2*d*x+1/2*c)^5+1/2/d/a^3*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*tan(1/2*d*x+1/2*c)-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)+3/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)-3/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)","A"
63,1,96,99,0.410000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{3}}"," ",0,"-1/20/d/a^3*tan(1/2*d*x+1/2*c)^5-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3-7/4/d/a^3*tan(1/2*d*x+1/2*c)-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)","A"
64,1,45,77,0.409000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^3,x)","\frac{\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*tan(1/2*d*x+1/2*c)^5+2/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
65,1,32,77,0.357000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^3,x)","\frac{-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(-1/5*tan(1/2*d*x+1/2*c)^5+tan(1/2*d*x+1/2*c))","A"
66,1,45,77,0.386000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^3,x)","\frac{\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*tan(1/2*d*x+1/2*c)^5-2/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
67,1,75,82,0.420000," ","int(1/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \,a^{3}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/20/d/a^3*tan(1/2*d*x+1/2*c)^5+1/3/d/a^3*tan(1/2*d*x+1/2*c)^3-7/4/d/a^3*tan(1/2*d*x+1/2*c)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
68,1,107,97,0.614000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^3,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{17 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/20/d/a^3*tan(1/2*d*x+1/2*c)^5-1/2/d/a^3*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*tan(1/2*d*x+1/2*c)+2/d/a^3*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-6/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
69,1,141,135,0.557000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^3,x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{20 d \,a^{3}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}-\frac{31 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/20/d/a^3*tan(1/2*d*x+1/2*c)^5+2/3/d/a^3*tan(1/2*d*x+1/2*c)^3-31/4/d/a^3*tan(1/2*d*x+1/2*c)-7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+13/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
70,1,200,179,0.441000," ","int(sec(d*x+c)^7/(a+a*sec(d*x+c))^4,x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}-\frac{9 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{111 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{1}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{9}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{21 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{4}}-\frac{1}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{9}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{21 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7-9/40/d/a^4*tan(1/2*d*x+1/2*c)^5-13/8/d/a^4*tan(1/2*d*x+1/2*c)^3-111/8/d/a^4*tan(1/2*d*x+1/2*c)+1/2/d/a^4/(tan(1/2*d*x+1/2*c)-1)^2+9/2/d/a^4/(tan(1/2*d*x+1/2*c)-1)-21/2/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^4/(tan(1/2*d*x+1/2*c)+1)^2+9/2/d/a^4/(tan(1/2*d*x+1/2*c)+1)+21/2/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)","A"
71,1,158,151,0.507000," ","int(sec(d*x+c)^6/(a+a*sec(d*x+c))^4,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}+\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}+\frac{49 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{1}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}-\frac{1}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*tan(1/2*d*x+1/2*c)^5+23/24/d/a^4*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*tan(1/2*d*x+1/2*c)-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)+4/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^4/(tan(1/2*d*x+1/2*c)+1)-4/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)","A"
72,1,115,128,0.402000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^4,x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{15 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7-1/8/d/a^4*tan(1/2*d*x+1/2*c)^5-11/24/d/a^4*tan(1/2*d*x+1/2*c)^3-15/8/d/a^4*tan(1/2*d*x+1/2*c)-1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)","A"
73,1,56,112,0.414000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^4,x)","\frac{\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*tan(1/2*d*x+1/2*c)^7+3/5*tan(1/2*d*x+1/2*c)^5+tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
74,1,58,104,0.362000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^4,x)","\frac{-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(-1/7*tan(1/2*d*x+1/2*c)^7-1/5*tan(1/2*d*x+1/2*c)^5+1/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
75,1,58,104,0.411000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^4,x)","\frac{\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*tan(1/2*d*x+1/2*c)^7-1/5*tan(1/2*d*x+1/2*c)^5-1/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
76,1,58,104,0.341000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^4,x)","\frac{-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(-1/7*tan(1/2*d*x+1/2*c)^7+3/5*tan(1/2*d*x+1/2*c)^5-tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
77,1,94,103,0.472000," ","int(1/(a+a*sec(d*x+c))^4,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{15 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7-1/8/d/a^4*tan(1/2*d*x+1/2*c)^5+11/24/d/a^4*tan(1/2*d*x+1/2*c)^3-15/8/d/a^4*tan(1/2*d*x+1/2*c)+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))","A"
78,1,126,118,0.605000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^4,x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}+\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}+\frac{49 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*tan(1/2*d*x+1/2*c)^5-23/24/d/a^4*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*tan(1/2*d*x+1/2*c)+2/d/a^4*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-8/d/a^4*arctan(tan(1/2*d*x+1/2*c))","A"
79,1,160,162,0.644000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^4,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{56 d \,a^{4}}-\frac{9 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{111 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{9 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{21 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7-9/40/d/a^4*tan(1/2*d*x+1/2*c)^5+13/8/d/a^4*tan(1/2*d*x+1/2*c)^3-111/8/d/a^4*tan(1/2*d*x+1/2*c)-9/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-7/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+21/d/a^4*arctan(tan(1/2*d*x+1/2*c))","A"
80,1,177,190,0.363000," ","int(sec(d*x+c)^7/(a+a*sec(d*x+c))^5,x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{144 d \,a^{5}}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{14 d \,a^{5}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{5}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{5}}+\frac{129 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}-\frac{1}{d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{5}}-\frac{1}{d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{5}}"," ",0,"1/144/d/a^5*tan(1/2*d*x+1/2*c)^9+1/14/d/a^5*tan(1/2*d*x+1/2*c)^7+3/8/d/a^5*tan(1/2*d*x+1/2*c)^5+3/2/d/a^5*tan(1/2*d*x+1/2*c)^3+129/16/d/a^5*tan(1/2*d*x+1/2*c)-1/d/a^5/(tan(1/2*d*x+1/2*c)-1)+5/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^5/(tan(1/2*d*x+1/2*c)+1)-5/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)","A"
81,1,134,167,0.416000," ","int(sec(d*x+c)^6/(a+a*sec(d*x+c))^5,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{144 d \,a^{5}}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{5}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{5 d \,a^{5}}-\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{5}}-\frac{31 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{5}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{5}}"," ",0,"-1/144/d/a^5*tan(1/2*d*x+1/2*c)^9-3/56/d/a^5*tan(1/2*d*x+1/2*c)^7-1/5/d/a^5*tan(1/2*d*x+1/2*c)^5-13/24/d/a^5*tan(1/2*d*x+1/2*c)^3-31/16/d/a^5*tan(1/2*d*x+1/2*c)-1/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)","A"
82,1,71,149,0.409000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^5,x)","\frac{\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{4 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}"," ",0,"1/16/d/a^5*(1/9*tan(1/2*d*x+1/2*c)^9+4/7*tan(1/2*d*x+1/2*c)^7+6/5*tan(1/2*d*x+1/2*c)^5+4/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
83,1,58,149,0.407000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^5,x)","\frac{-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}"," ",0,"1/16/d/a^5*(-1/9*tan(1/2*d*x+1/2*c)^9-2/7*tan(1/2*d*x+1/2*c)^7+2/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
84,1,45,129,0.403000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^5,x)","\frac{\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}"," ",0,"1/16/d/a^5*(1/9*tan(1/2*d*x+1/2*c)^9-2/5*tan(1/2*d*x+1/2*c)^5+tan(1/2*d*x+1/2*c))","A"
85,1,58,133,0.357000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^5,x)","\frac{-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}"," ",0,"1/16/d/a^5*(-1/9*tan(1/2*d*x+1/2*c)^9+2/7*tan(1/2*d*x+1/2*c)^7-2/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
86,1,71,133,0.389000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^5,x)","\frac{\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{4 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}"," ",0,"1/16/d/a^5*(1/9*tan(1/2*d*x+1/2*c)^9-4/7*tan(1/2*d*x+1/2*c)^7+6/5*tan(1/2*d*x+1/2*c)^5-4/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
87,1,113,134,0.474000," ","int(1/(a+a*sec(d*x+c))^5,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{144 d \,a^{5}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{5}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{5 d \,a^{5}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{5}}-\frac{31 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}"," ",0,"-1/144/d/a^5*tan(1/2*d*x+1/2*c)^9+3/56/d/a^5*tan(1/2*d*x+1/2*c)^7-1/5/d/a^5*tan(1/2*d*x+1/2*c)^5+13/24/d/a^5*tan(1/2*d*x+1/2*c)^3-31/16/d/a^5*tan(1/2*d*x+1/2*c)+2/d/a^5*arctan(tan(1/2*d*x+1/2*c))","A"
88,1,145,149,0.646000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^5,x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{144 d \,a^{5}}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{14 d \,a^{5}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{5}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{5}}+\frac{129 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}"," ",0,"1/144/d/a^5*tan(1/2*d*x+1/2*c)^9-1/14/d/a^5*tan(1/2*d*x+1/2*c)^7+3/8/d/a^5*tan(1/2*d*x+1/2*c)^5-3/2/d/a^5*tan(1/2*d*x+1/2*c)^3+129/16/d/a^5*tan(1/2*d*x+1/2*c)+2/d/a^5*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-10/d/a^5*arctan(tan(1/2*d*x+1/2*c))","A"
89,1,179,199,0.665000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^5,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{144 d \,a^{5}}+\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{5}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{5}}+\frac{25 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{5}}-\frac{351 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{5}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{31 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}"," ",0,"-1/144/d/a^5*tan(1/2*d*x+1/2*c)^9+5/56/d/a^5*tan(1/2*d*x+1/2*c)^7-3/5/d/a^5*tan(1/2*d*x+1/2*c)^5+25/8/d/a^5*tan(1/2*d*x+1/2*c)^3-351/16/d/a^5*tan(1/2*d*x+1/2*c)-11/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-9/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+31/d/a^5*arctan(tan(1/2*d*x+1/2*c))","A"
90,1,82,106,1.104000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(16 \left(\cos^{4}\left(d x +c \right)\right)-8 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-5\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{35 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-2/35/d*(16*cos(d*x+c)^4-8*cos(d*x+c)^3-2*cos(d*x+c)^2-cos(d*x+c)-5)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)","A"
91,1,72,74,1.011000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(8 \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-3\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-2/15/d*(8*cos(d*x+c)^3-4*cos(d*x+c)^2-cos(d*x+c)-3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)","A"
92,1,62,48,0.927000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-1\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-2/3/d*(2*cos(d*x+c)^2-cos(d*x+c)-1)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)","A"
93,1,42,24,0.902000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))/sin(d*x+c)","A"
94,1,89,31,1.014000," ","int((a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}}{d}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)","B"
95,1,123,54,1.096000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","B"
96,1,221,86,1.132000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(3 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 \left(\cos^{4}\left(d x +c \right)\right)-4 \left(\cos^{3}\left(d x +c \right)\right)+12 \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"1/16/d*(3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*2^(1/2)*sin(d*x+c)+3*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*cos(d*x+c)^4-4*cos(d*x+c)^3+12*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)","B"
97,1,310,118,1.228000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(15 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+30 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+15 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+64 \left(\cos^{6}\left(d x +c \right)\right)+16 \left(\cos^{5}\left(d x +c \right)\right)+40 \left(\cos^{4}\left(d x +c \right)\right)-120 \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/192/d*(15*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)+30*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)*2^(1/2)+15*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+64*cos(d*x+c)^6+16*cos(d*x+c)^5+40*cos(d*x+c)^4-120*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^2","B"
98,1,399,150,1.260000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-105 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-315 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-315 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-105 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+768 \left(\cos^{8}\left(d x +c \right)\right)+128 \left(\cos^{7}\left(d x +c \right)\right)+224 \left(\cos^{6}\left(d x +c \right)\right)+560 \left(\cos^{5}\left(d x +c \right)\right)-1680 \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3072 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-1/3072/d*(-105*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-315*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-315*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-105*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+768*cos(d*x+c)^8+128*cos(d*x+c)^7+224*cos(d*x+c)^6+560*cos(d*x+c)^5-1680*cos(d*x+c)^4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)","B"
99,1,93,142,0.986000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(272 \left(\cos^{5}\left(d x +c \right)\right)-136 \left(\cos^{4}\left(d x +c \right)\right)-34 \left(\cos^{3}\left(d x +c \right)\right)-17 \left(\cos^{2}\left(d x +c \right)\right)-50 \cos \left(d x +c \right)-35\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{315 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"-2/315/d*(272*cos(d*x+c)^5-136*cos(d*x+c)^4-34*cos(d*x+c)^3-17*cos(d*x+c)^2-50*cos(d*x+c)-35)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/sin(d*x+c)*a","A"
100,1,83,100,0.844000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(104 \left(\cos^{4}\left(d x +c \right)\right)-52 \left(\cos^{3}\left(d x +c \right)\right)-13 \left(\cos^{2}\left(d x +c \right)\right)-24 \cos \left(d x +c \right)-15\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{105 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-2/105/d*(104*cos(d*x+c)^4-52*cos(d*x+c)^3-13*cos(d*x+c)^2-24*cos(d*x+c)-15)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)*a","A"
101,1,73,74,0.841000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(6 \left(\cos^{3}\left(d x +c \right)\right)-3 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)-1\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{5 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-2/5/d*(6*cos(d*x+c)^3-3*cos(d*x+c)^2-2*cos(d*x+c)-1)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)*a","A"
102,1,63,51,0.862000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(5 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-1\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-2/3/d*(5*cos(d*x+c)^2-4*cos(d*x+c)-1)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)*a","A"
103,1,180,58,0.925000," ","int((a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right)+\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-2 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"-1/d*(2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)+2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-2*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(1+cos(d*x+c))*a","B"
104,1,125,57,0.991000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*(3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a","B"
105,1,222,90,1.037000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-7 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)-7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 \left(\cos^{4}\left(d x +c \right)\right)+20 \left(\cos^{3}\left(d x +c \right)\right)-28 \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"-1/16/d*(-7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*2^(1/2)*sin(d*x+c)-7*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*cos(d*x+c)^4+20*cos(d*x+c)^3-28*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)*a","B"
106,1,311,124,1.084000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(33 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+66 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+33 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+64 \left(\cos^{6}\left(d x +c \right)\right)+112 \left(\cos^{5}\left(d x +c \right)\right)+88 \left(\cos^{4}\left(d x +c \right)\right)-264 \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{192 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-1/192/d*(33*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)+66*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)*2^(1/2)+33*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+64*cos(d*x+c)^6+112*cos(d*x+c)^5+88*cos(d*x+c)^4-264*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)*a","B"
107,1,105,179,0.964000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(1136 \left(\cos^{6}\left(d x +c \right)\right)-568 \left(\cos^{5}\left(d x +c \right)\right)-142 \left(\cos^{4}\left(d x +c \right)\right)-71 \left(\cos^{3}\left(d x +c \right)\right)-131 \left(\cos^{2}\left(d x +c \right)\right)-161 \cos \left(d x +c \right)-63\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{693 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right)}"," ",0,"-2/693/d*(1136*cos(d*x+c)^6-568*cos(d*x+c)^5-142*cos(d*x+c)^4-71*cos(d*x+c)^3-131*cos(d*x+c)^2-161*cos(d*x+c)-63)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/sin(d*x+c)*a^2","A"
108,1,95,126,0.872000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(584 \left(\cos^{5}\left(d x +c \right)\right)-292 \left(\cos^{4}\left(d x +c \right)\right)-73 \left(\cos^{3}\left(d x +c \right)\right)-89 \left(\cos^{2}\left(d x +c \right)\right)-95 \cos \left(d x +c \right)-35\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{315 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"-2/315/d*(584*cos(d*x+c)^5-292*cos(d*x+c)^4-73*cos(d*x+c)^3-89*cos(d*x+c)^2-95*cos(d*x+c)-35)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/sin(d*x+c)*a^2","A"
109,1,85,100,0.819000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(46 \left(\cos^{4}\left(d x +c \right)\right)-23 \left(\cos^{3}\left(d x +c \right)\right)-11 \left(\cos^{2}\left(d x +c \right)\right)-9 \cos \left(d x +c \right)-3\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{21 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(46*cos(d*x+c)^4-23*cos(d*x+c)^3-11*cos(d*x+c)^2-9*cos(d*x+c)-3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^3*a^2","A"
110,1,75,77,0.951000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(43 \left(\cos^{3}\left(d x +c \right)\right)-29 \left(\cos^{2}\left(d x +c \right)\right)-11 \cos \left(d x +c \right)-3\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{15 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-2/15/d*(43*cos(d*x+c)^3-29*cos(d*x+c)^2-11*cos(d*x+c)-3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^2*a^2","A"
111,1,214,84,1.135000," ","int((a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right)+3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right)-16 \cos \left(d x +c \right) \sin \left(d x +c \right)-2 \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{3 d \left(1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"-1/3/d*(3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2+3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)-16*cos(d*x+c)*sin(d*x+c)-2*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(1+cos(d*x+c))/cos(d*x+c)*a^2","B"
112,1,128,84,1.015000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)-4\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*(5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2+2*cos(d*x+c)-4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a^2","A"
113,1,224,90,1.031000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(19 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+19 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 \left(\cos^{4}\left(d x +c \right)\right)-36 \left(\cos^{3}\left(d x +c \right)\right)+44 \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{16 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"1/16/d*(19*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*2^(1/2)*sin(d*x+c)+19*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*cos(d*x+c)^4-36*cos(d*x+c)^3+44*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)*a^2","B"
114,1,313,124,1.071000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(75 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+150 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}+75 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+64 \left(\cos^{6}\left(d x +c \right)\right)+208 \left(\cos^{5}\left(d x +c \right)\right)+328 \left(\cos^{4}\left(d x +c \right)\right)-600 \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{192 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/192/d*(75*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)^2*2^(1/2)+150*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)*cos(d*x+c)*2^(1/2)+75*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+64*cos(d*x+c)^6+208*cos(d*x+c)^5+328*cos(d*x+c)^4-600*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^2*a^2","B"
115,1,402,158,1.142000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(489 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+1467 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+1467 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+489 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-768 \left(\cos^{8}\left(d x +c \right)\right)-2176 \left(\cos^{7}\left(d x +c \right)\right)-2272 \left(\cos^{6}\left(d x +c \right)\right)-2608 \left(\cos^{5}\left(d x +c \right)\right)+7824 \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{3072 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"1/3072/d*(489*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)+1467*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+1467*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+489*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-768*cos(d*x+c)^8-2176*cos(d*x+c)^7-2272*cos(d*x+c)^6-2608*cos(d*x+c)^5+7824*cos(d*x+c)^4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^3*a^2","B"
116,1,42,25,1.120000," ","int(sec(d*x+c)*(a-a*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)}{d \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"-2/d*(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)/(-1+cos(d*x+c))","A"
117,1,91,32,1.051000," ","int((a-a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)}{d \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"-1/d*2^(1/2)*(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))/(-1+cos(d*x+c))","B"
118,1,103,57,1.277000," ","int(cos(d*x+c)*(a-a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{2 d \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"1/2/d*(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)*sin(d*x+c)*(arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)*2^(1/2))/(-1+cos(d*x+c))*2^(1/2)","A"
119,1,314,119,1.145000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(15 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right)+30 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right)+15 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+104 \left(\cos^{3}\left(d x +c \right)\right)-112 \left(\cos^{2}\left(d x +c \right)\right)+32 \cos \left(d x +c \right)-24\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{60 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right) a}"," ",0,"-1/60/d*(15*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2+30*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)+15*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+104*cos(d*x+c)^3-112*cos(d*x+c)^2+32*cos(d*x+c)-24)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)/a","B"
120,1,221,87,1.108000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(3 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right)-4\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right) a}"," ",0,"-1/6/d*(3*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*sin(d*x+c)+3*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-4*cos(d*x+c)^2+8*cos(d*x+c)-4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)/a","B"
121,1,121,62,0.867000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-2\right)}{d \sin \left(d x +c \right) a}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)-2)/sin(d*x+c)/a","A"
122,1,95,37,0.813000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right)}{d a}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))/a","B"
123,1,141,70,0.905000," ","int(1/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+\ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right)\right)}{d a}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c)))/a","A"
124,1,201,91,1.099000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right) a}"," ",0,"1/2/d*((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)^2+2*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/a","B"
125,1,380,122,1.156000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(7 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)+8 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 \left(\cos^{4}\left(d x +c \right)\right)+12 \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right) a}"," ",0,"1/16/d*(7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*2^(1/2)*sin(d*x+c)+7*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*sin(d*x+c)+8*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*cos(d*x+c)^4+12*cos(d*x+c)^3-4*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)/a","B"
126,1,417,156,1.031000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(75 \sin \left(d x +c \right) \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{4}\left(d x +c \right)\right)+150 \sin \left(d x +c \right) \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)-150 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right)-75 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)+392 \left(\cos^{5}\left(d x +c \right)\right)-496 \left(\cos^{4}\left(d x +c \right)\right)-216 \left(\cos^{3}\left(d x +c \right)\right)+384 \left(\cos^{2}\left(d x +c \right)\right)-96 \cos \left(d x +c \right)+32\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{80 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2} a^{2}}"," ",0,"1/80/d*(75*sin(d*x+c)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^4+150*sin(d*x+c)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3-150*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)-75*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*sin(d*x+c)+392*cos(d*x+c)^5-496*cos(d*x+c)^4-216*cos(d*x+c)^3+384*cos(d*x+c)^2-96*cos(d*x+c)+32)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^2/a^2","B"
127,1,322,122,1.029000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(33 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+66 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)+33 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-76 \left(\cos^{3}\left(d x +c \right)\right)+28 \left(\cos^{2}\left(d x +c \right)\right)+64 \cos \left(d x +c \right)-16\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{24 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) a^{2}}"," ",0,"1/24/d*(-1+cos(d*x+c))*(33*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)+66*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*sin(d*x+c)+33*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-76*cos(d*x+c)^3+28*cos(d*x+c)^2+64*cos(d*x+c)-16)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)/a^2","B"
128,1,225,88,0.993000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(7 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-7 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+10 \left(\cos^{3}\left(d x +c \right)\right)-12 \left(\cos^{2}\left(d x +c \right)\right)-6 \cos \left(d x +c \right)+8\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(7*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-7*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*cos(d*x+c)^3-12*cos(d*x+c)^2-6*cos(d*x+c)+8)/sin(d*x+c)^3/a^2","B"
129,1,222,62,0.822000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+3 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right)}{4 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}}"," ",0,"1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+3*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^2","B"
130,1,222,62,0.789000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-\sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)-\ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right)}{4 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)-ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^2","B"
131,1,370,93,0.900000," ","int(1/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(4 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right)+4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+5 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+5 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right)}{4 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)+4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+5*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+5*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)^2+2*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^2","B"
132,1,384,119,1.067000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(6 \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+9 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-6 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)-4 \left(\cos^{4}\left(d x +c \right)\right)-9 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right)-6 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/4/d*(6*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+9*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-6*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)-4*cos(d*x+c)^4-9*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^3+8*cos(d*x+c)^2-6*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/a^2","B"
133,1,560,156,1.134000," ","int(cos(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(19 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+26 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+38 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+52 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)+19 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+26 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 \left(\cos^{5}\left(d x +c \right)\right)+20 \left(\cos^{4}\left(d x +c \right)\right)+16 \left(\cos^{3}\left(d x +c \right)\right)-28 \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) a^{2}}"," ",0,"-1/16/d*(-1+cos(d*x+c))*(19*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+26*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)+38*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)*2^(1/2)*sin(d*x+c)+52*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*sin(d*x+c)+19*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+26*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*cos(d*x+c)^5+20*cos(d*x+c)^4+16*cos(d*x+c)^3-28*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)/a^2","B"
134,1,417,156,1.031000," ","int(sec(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-489 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-1467 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1467 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)-489 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+1196 \left(\cos^{4}\left(d x +c \right)\right)+816 \left(\cos^{3}\left(d x +c \right)\right)-1372 \left(\cos^{2}\left(d x +c \right)\right)-768 \cos \left(d x +c \right)+128\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) a^{3}}"," ",0,"1/192/d*(-1+cos(d*x+c))^2*(-489*cos(d*x+c)^3*sin(d*x+c)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-1467*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)-1467*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*sin(d*x+c)-489*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+1196*cos(d*x+c)^4+816*cos(d*x+c)^3-1372*cos(d*x+c)^2-768*cos(d*x+c)+128)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/cos(d*x+c)/a^3","B"
135,1,316,122,0.980000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(75 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+150 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+75 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+98 \left(\cos^{3}\left(d x +c \right)\right)+72 \left(\cos^{2}\left(d x +c \right)\right)-106 \cos \left(d x +c \right)-64\right)}{32 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(75*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+150*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+75*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+98*cos(d*x+c)^3+72*cos(d*x+c)^2-106*cos(d*x+c)-64)/sin(d*x+c)^5/a^3","B"
136,1,323,88,1.020000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(19 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+38 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+18 \left(\cos^{3}\left(d x +c \right)\right)+19 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \left(\cos^{2}\left(d x +c \right)\right)-26 \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(19*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+38*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+18*cos(d*x+c)^3+19*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*cos(d*x+c)^2-26*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)^3/a^3","B"
137,1,315,88,0.852000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(5 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+10 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+5 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \left(\cos^{3}\left(d x +c \right)\right)-8 \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(5*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+10*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+5*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)^3-8*cos(d*x+c)^2+10*cos(d*x+c))/(1+cos(d*x+c))^2/sin(d*x+c)/a^3","B"
138,1,315,88,0.777000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+3 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-14 \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right)+6 \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+6*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+3*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-14*cos(d*x+c)^3+8*cos(d*x+c)^2+6*cos(d*x+c))/(1+cos(d*x+c))^2/sin(d*x+c)/a^3","B"
139,1,550,119,1.019000," ","int(1/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(32 \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+64 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right)+43 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+32 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+86 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)+43 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-30 \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right)+22 \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(32*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+64*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)+43*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+32*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+86*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)+43*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-30*cos(d*x+c)^3+8*cos(d*x+c)^2+22*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)^3/a^3","B"
140,1,552,145,1.095000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-80 \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-115 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-160 \sqrt{2}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \cos \left(d x +c \right)+32 \left(\cos^{4}\left(d x +c \right)\right)-230 \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right)-80 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+78 \left(\cos^{3}\left(d x +c \right)\right)-115 \ln \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\cos \left(d x +c \right)+1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-40 \left(\cos^{2}\left(d x +c \right)\right)-70 \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{32 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/32/d*(-1+cos(d*x+c))^2*(-80*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-115*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-160*2^(1/2)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*cos(d*x+c)+32*cos(d*x+c)^4-230*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*cos(d*x+c)-80*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+78*cos(d*x+c)^3-115*ln(((-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)+1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-40*cos(d*x+c)^2-70*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/a^3","B"
141,1,83,39,1.017000," ","int(sec(d*x+c)/(a-a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)}{d \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-2/d*(-1+cos(d*x+c))*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","B"
142,1,119,72,1.069000," ","int(1/(a-a*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{d \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*(-1+cos(d*x+c))*(2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)","A"
143,0,0,420,0.720000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(2/3),x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(2/3),x)","F"
144,0,0,394,0.639000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(2/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(2/3),x)","F"
145,0,0,371,0.619000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(2/3),x)","\int \sec \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+a*sec(d*x+c))^(2/3),x)","F"
146,0,0,61,0.794000," ","int((a+a*sec(d*x+c))^(2/3),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(2/3),x)","F"
147,0,0,61,0.827000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(2/3),x)","\int \cos \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)*(a+a*sec(d*x+c))^(2/3),x)","F"
148,0,0,446,0.717000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/3),x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/3),x)","F"
149,0,0,420,0.727000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/3),x)","F"
150,0,0,397,0.697000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(5/3),x)","\int \sec \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+a*sec(d*x+c))^(5/3),x)","F"
151,0,0,70,0.707000," ","int((a+a*sec(d*x+c))^(5/3),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(5/3),x)","F"
152,0,0,70,0.882000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(5/3),x)","\int \cos \left(d x +c \right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(cos(d*x+c)*(a+a*sec(d*x+c))^(5/3),x)","F"
153,0,0,408,0.783000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{4}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/3),x)","F"
154,0,0,377,0.817000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/3),x)","F"
155,0,0,351,0.694000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/3),x)","F"
156,0,0,327,0.710000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+a*sec(d*x+c))^(1/3),x)","F"
157,0,0,61,0.776000," ","int(1/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{1}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+a*sec(d*x+c))^(1/3),x)","F"
158,0,0,61,0.853000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(a+a*sec(d*x+c))^(1/3),x)","F"
159,0,0,832,0.789000," ","int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{4}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/3),x)","F"
160,0,0,801,0.767000," ","int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/3),x)","F"
161,0,0,801,0.708000," ","int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/3),x)","F"
162,0,0,814,0.663000," ","int(sec(d*x+c)/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+a*sec(d*x+c))^(5/3),x)","F"
163,0,0,74,0.699000," ","int(1/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{1}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(1/(a+a*sec(d*x+c))^(5/3),x)","F"
164,0,0,74,0.778000," ","int(cos(d*x+c)/(a+a*sec(d*x+c))^(5/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(a+a*sec(d*x+c))^(5/3),x)","F"
165,1,384,179,5.935000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x)","-\frac{a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{28 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/10*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-12/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+28/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
166,1,369,159,5.777000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x)","\frac{2 a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
167,1,146,139,3.893000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x)","-\frac{2 a \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*a*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
168,1,150,119,2.823000," ","int((a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
169,1,225,139,3.334000," ","int((a+a*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
170,1,219,159,3.078000," ","int((a+a*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(24*cos(1/2*d*x+1/2*c)^7-28*cos(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+4*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
171,1,270,179,3.514000," ","int((a+a*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(240 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-528 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+448 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-122 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(240*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-528*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+448*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+25*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-122*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
172,1,439,211,6.524000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{28 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{7 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{124 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{35 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{24 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/28*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-4/7*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+124/35*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/5*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-24/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-12/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
173,1,386,189,5.977000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x)","-\frac{a^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{32 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{68 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{16 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-32/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+68/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/10*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-2/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
174,1,371,167,5.522000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x)","\frac{4 a^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"4/3*a^2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(4*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+7*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
175,1,104,84,4.125000," ","int((a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x)","-\frac{4 a^{2} \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*a^2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
176,1,228,145,3.395000," ","int((a+a*sec(d*x+c))^2/sec(d*x+c)^(3/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
177,1,250,167,3.474000," ","int((a+a*sec(d*x+c))^2/sec(d*x+c)^(5/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-12 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+32 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-13 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-12*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+32*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-13*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
178,1,272,189,3.596000," ","int((a+a*sec(d*x+c))^2/sec(d*x+c)^(7/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-116 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+126 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-39 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/35*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-116*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+126*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-39*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
179,1,439,211,6.367000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x)","-\frac{a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{3 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{848 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{28 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{28 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{26 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{21 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-3/10*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-56/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+848/105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-28/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/28*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-26/21*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
180,1,386,189,6.512000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x)","-\frac{a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{56 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{72 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{36 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{\left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(56/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/10*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-72/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-36/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
181,1,371,167,5.599000," ","int((a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x)","\frac{4 a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"4/3*a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-18*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
182,1,172,167,3.683000," ","int((a+a*sec(d*x+c))^3/sec(d*x+c)^(3/2),x)","-\frac{4 a^{3} \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*a^3*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
183,1,250,167,3.755000," ","int((a+a*sec(d*x+c))^3/sec(d*x+c)^(5/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(-4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/5*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(-4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+14*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
184,1,272,189,3.565000," ","int((a+a*sec(d*x+c))^3/sec(d*x+c)^(7/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(120 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+602 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+65 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-208 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(120*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-432*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+602*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+65*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-208*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
185,1,260,211,4.049000," ","int((a+a*sec(d*x+c))^3/sec(d*x+c)^(9/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(560 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-600 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+212 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+66 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-430 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+165 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(560*cos(1/2*d*x+1/2*c)^11-600*cos(1/2*d*x+1/2*c)^9+212*cos(1/2*d*x+1/2*c)^7+66*cos(1/2*d*x+1/2*c)^5-430*cos(1/2*d*x+1/2*c)^3+165*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+192*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
186,1,492,233,7.016000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4,x)","-\frac{a^{4} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{72 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{61 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{90 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{304 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{1544 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{152 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{7 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{7 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/72*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-61/90*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-304/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1544/105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-152/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/7*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-16/7*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
187,1,439,211,6.307000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4,x)","-\frac{a^{4} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2024 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{128 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{64 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{28 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{47 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{21 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2024/105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2/5*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-128/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-64/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/28*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-47/21*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
188,1,386,189,6.321000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(1/2),x)","-\frac{a^{4} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{56 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{328 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{132 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-56/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+328/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-132/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-1/10*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-4/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
189,1,292,128,4.750000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(3/2),x)","\frac{8 a^{4} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-14 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"8/3*a^4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2-14*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+7*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
190,1,194,189,3.592000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(5/2),x)","-\frac{8 a^{4} \left(-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+26 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+20 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-19 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8/15*a^4*(-6*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+26*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-19*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
191,1,272,189,3.292000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(7/2),x)","-\frac{8 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{4} \left(60 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-258 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+448 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+85 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-168 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-167 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(60*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-258*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+448*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+85*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-168*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-167*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
192,1,260,211,3.214000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(9/2),x)","-\frac{8 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{4} \left(280 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+34 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-485 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+180 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-399 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+219 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(280*cos(1/2*d*x+1/2*c)^11-120*cos(1/2*d*x+1/2*c)^9+34*cos(1/2*d*x+1/2*c)^7+72*cos(1/2*d*x+1/2*c)^5-485*cos(1/2*d*x+1/2*c)^3+180*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-399*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+219*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
193,1,273,233,3.745000," ","int((a+a*sec(d*x+c))^4/sec(d*x+c)^(11/2),x)","-\frac{8 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{4} \left(5040 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5320 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1740 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+326 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+678 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4465 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1695 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3696 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2001 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(5040*cos(1/2*d*x+1/2*c)^13-5320*cos(1/2*d*x+1/2*c)^11+1740*cos(1/2*d*x+1/2*c)^9+326*cos(1/2*d*x+1/2*c)^7+678*cos(1/2*d*x+1/2*c)^5-4465*cos(1/2*d*x+1/2*c)^3+1695*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3696*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2001*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
194,1,413,198,6.279000," ","int(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+44 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a/sin(1/2*d*x+1/2*c)^3/cos(1/2*d*x+1/2*c)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-36*sin(1/2*d*x+1/2*c)^6-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)+44*sin(1/2*d*x+1/2*c)^4-11*sin(1/2*d*x+1/2*c)^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
195,1,253,176,4.247000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
196,1,200,152,3.465000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
197,1,198,152,3.295000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/a/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
198,1,199,154,3.720000," ","int(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/a*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
199,1,215,176,3.614000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/3/a*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-8*sin(1/2*d*x+1/2*c)^6+18*sin(1/2*d*x+1/2*c)^4-7*sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
200,1,229,198,3.776000," ","int(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(25 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+63 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+23 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{15 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/15/a*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(25*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+63*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*sin(1/2*d*x+1/2*c)^8-56*sin(1/2*d*x+1/2*c)^6-30*sin(1/2*d*x+1/2*c)^4+23*sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
201,1,413,230,6.520000," ","int(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{22 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{14 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{2 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^2*(1/3*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)-22/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+14*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-2/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
202,1,405,208,4.005000," ","int(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-48 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+86 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-48*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6+86*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-37*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
203,1,257,185,3.553000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^6-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-16*cos(1/2*d*x+1/2*c)^4+3*cos(1/2*d*x+1/2*c)^2+1)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
204,1,188,93,3.397000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+2*cos(1/2*d*x+1/2*c)^4-3*cos(1/2*d*x+1/2*c)^2+1)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
205,1,257,185,3.976000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-20 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^6+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-20*cos(1/2*d*x+1/2*c)^4+9*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
206,1,257,186,4.019000," ","int(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^6+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+24*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*cos(1/2*d*x+1/2*c)^4+15*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
207,1,270,208,3.993000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+42 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-48 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*cos(1/2*d*x+1/2*c)^8+12*cos(1/2*d*x+1/2*c)^6+20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+42*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-48*cos(1/2*d*x+1/2*c)^4+21*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
208,1,283,230,4.286000," ","int(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(96 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-352 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-150 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+266 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-135 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5\right)}{30 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/30/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(96*cos(1/2*d*x+1/2*c)^10-352*cos(1/2*d*x+1/2*c)^8+120*cos(1/2*d*x+1/2*c)^6-150*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-336*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+266*cos(1/2*d*x+1/2*c)^4-135*cos(1/2*d*x+1/2*c)^2+5)/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
209,1,453,267,6.158000," ","int(sec(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{32 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{15 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{118 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{128 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{238 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{4 a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^3*(32/15*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3+118/5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)-128/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+238/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1/5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5-4/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
210,1,555,245,4.245000," ","int(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x)","-\frac{-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+588 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1634 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1488 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-439 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+588*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^8-1634*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6+1488*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-439*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
211,1,268,223,3.893000," ","int(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(36 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-46 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{20 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/20*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(36*cos(1/2*d*x+1/2*c)^8-10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-46*cos(1/2*d*x+1/2*c)^6+8*cos(1/2*d*x+1/2*c)^4+cos(1/2*d*x+1/2*c)^2+1)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
212,1,270,223,4.120000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^8-10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*cos(1/2*d*x+1/2*c)^6+6*cos(1/2*d*x+1/2*c)^4+7*cos(1/2*d*x+1/2*c)^2-3)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
213,1,270,223,4.043000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^8+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*cos(1/2*d*x+1/2*c)^6-24*cos(1/2*d*x+1/2*c)^4+17*cos(1/2*d*x+1/2*c)^2-3)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
214,1,270,223,4.668000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(36 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-66 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{20 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(36*cos(1/2*d*x+1/2*c)^8+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-66*cos(1/2*d*x+1/2*c)^6+38*cos(1/2*d*x+1/2*c)^4-9*cos(1/2*d*x+1/2*c)^2+1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
215,1,270,223,4.275000," ","int(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(348 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+294 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3\right)}{60 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(348*cos(1/2*d*x+1/2*c)^8+130*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+294*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*cos(1/2*d*x+1/2*c)^6+264*cos(1/2*d*x+1/2*c)^4-37*cos(1/2*d*x+1/2*c)^2+3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
216,1,283,245,4.532000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+468 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+714 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1058 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3\right)}{60 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(160*cos(1/2*d*x+1/2*c)^10+468*cos(1/2*d*x+1/2*c)^8+330*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+714*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1058*cos(1/2*d*x+1/2*c)^6+474*cos(1/2*d*x+1/2*c)^4-47*cos(1/2*d*x+1/2*c)^2+3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
217,1,296,267,4.236000," ","int(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(64 \left(\cos^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-288 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-76 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-210 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-462 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+530 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-248 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+19 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{20 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(64*cos(1/2*d*x+1/2*c)^12-288*cos(1/2*d*x+1/2*c)^10-76*cos(1/2*d*x+1/2*c)^8-210*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-462*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+530*cos(1/2*d*x+1/2*c)^6-248*cos(1/2*d*x+1/2*c)^4+19*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
218,1,219,96,1.766000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-6 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-6*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)","B"
219,1,188,62,1.627000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
220,1,150,31,1.422000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)*cos(d*x+c)*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2)))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*2^(1/2)","B"
221,1,52,32,1.474000," ","int((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"-2/d*(-1+cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(1/cos(d*x+c))^(1/2)","A"
222,1,68,65,1.601000," ","int((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(\cos^{2}\left(d x +c \right)+\cos \left(d x +c \right)-2\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(cos(d*x+c)^2+cos(d*x+c)-2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)","A"
223,1,80,97,1.544000," ","int((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right)+\cos^{2}\left(d x +c \right)+4 \cos \left(d x +c \right)-8\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(3*cos(d*x+c)^3+cos(d*x+c)^2+4*cos(d*x+c)-8)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^3/sin(d*x+c)","A"
224,1,90,129,1.548000," ","int((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(5 \left(\cos^{4}\left(d x +c \right)\right)+\cos^{3}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right)-16\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{35 d \sin \left(d x +c \right)}"," ",0,"-2/35/d*(5*cos(d*x+c)^4+cos(d*x+c)^3+2*cos(d*x+c)^2+8*cos(d*x+c)-16)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)","A"
225,1,244,134,1.518000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-66 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-44 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-16 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}{48 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"1/48/d*(-1+cos(d*x+c))*(33*2^(1/2)*cos(d*x+c)^3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-33*2^(1/2)*cos(d*x+c)^3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-66*cos(d*x+c)^2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-44*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-16*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*a","A"
226,1,214,100,1.533000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+14 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(7*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-7*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+14*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*a","B"
227,1,182,65,1.492000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) a}{2 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/2/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)*a","B"
228,1,174,66,1.511000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \cos \left(d x +c \right)-4\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{2 d \sin \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*cos(d*x+c)-4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(1/cos(d*x+c))^(1/2)*a","B"
229,1,71,67,1.559000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(\cos^{2}\left(d x +c \right)+4 \cos \left(d x +c \right)-5\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(cos(d*x+c)^2+4*cos(d*x+c)-5)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)*a","A"
230,1,81,98,1.671000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(\cos^{3}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)-6\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right) a}{5 d \sin \left(d x +c \right)}"," ",0,"-2/5/d*(cos(d*x+c)^3+2*cos(d*x+c)^2+3*cos(d*x+c)-6)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^3/sin(d*x+c)*a","A"
231,1,93,137,1.704000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(15 \left(\cos^{4}\left(d x +c \right)\right)+24 \left(\cos^{3}\left(d x +c \right)\right)+13 \left(\cos^{2}\left(d x +c \right)\right)+52 \cos \left(d x +c \right)-104\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(15*cos(d*x+c)^4+24*cos(d*x+c)^3+13*cos(d*x+c)^2+52*cos(d*x+c)-104)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)*a","A"
232,1,103,171,1.692000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),x)","-\frac{2 \left(35 \left(\cos^{5}\left(d x +c \right)\right)+50 \left(\cos^{4}\left(d x +c \right)\right)+17 \left(\cos^{3}\left(d x +c \right)\right)+34 \left(\cos^{2}\left(d x +c \right)\right)+136 \cos \left(d x +c \right)-272\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(35*cos(d*x+c)^5+50*cos(d*x+c)^4+17*cos(d*x+c)^3+34*cos(d*x+c)^2+136*cos(d*x+c)-272)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)*a","A"
233,1,286,168,1.755000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(489 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{4}\left(d x +c \right)\right)-489 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{4}\left(d x +c \right)\right)+978 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+652 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+368 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+96 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}{768 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"1/768/d*(489*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^4-489*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^4+978*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*sin(d*x+c)+652*cos(d*x+c)^2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+368*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+96*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)*(cos(d*x+c)^2-1)*a^2","A"
234,1,254,134,1.651000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(75 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-75 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+150 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+68 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+16 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a^{2}}{48 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)^{2}}"," ",0,"-1/48/d*(-1+cos(d*x+c))*(75*2^(1/2)*cos(d*x+c)^3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-75*2^(1/2)*cos(d*x+c)^3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+150*cos(d*x+c)^2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+68*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+16*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)/sin(d*x+c)^2*a^2","A"
235,1,224,100,1.443000," ","int(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(19 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-19 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-22 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{2}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)^{2}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(19*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-19*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-22*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)/sin(d*x+c)^2*a^2","B"
236,1,199,98,1.589000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(5 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-5 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+8 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-4\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{2}}{4 d \sin \left(d x +c \right)}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(5*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*2^(1/2)-5*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+8*cos(d*x+c)^2-4*cos(d*x+c)-4)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)*a^2","B"
237,1,195,100,1.655000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right)+28 \cos \left(d x +c \right)-32\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a^{2}}{6 d \sin \left(d x +c \right)}"," ",0,"-1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*cos(d*x+c)^2+28*cos(d*x+c)-32)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)*a^2","A"
238,1,85,101,1.681000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right)+11 \left(\cos^{2}\left(d x +c \right)\right)+29 \cos \left(d x +c \right)-43\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a^{2}}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(3*cos(d*x+c)^3+11*cos(d*x+c)^2+29*cos(d*x+c)-43)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)*a^2","A"
239,1,95,132,1.735000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(3 \left(\cos^{4}\left(d x +c \right)\right)+9 \left(\cos^{3}\left(d x +c \right)\right)+11 \left(\cos^{2}\left(d x +c \right)\right)+23 \cos \left(d x +c \right)-46\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{2}}{21 d \sin \left(d x +c \right)}"," ",0,"-2/21/d*(3*cos(d*x+c)^4+9*cos(d*x+c)^3+11*cos(d*x+c)^2+23*cos(d*x+c)-46)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)*a^2","A"
240,1,105,171,1.749000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x)","-\frac{2 \left(35 \left(\cos^{5}\left(d x +c \right)\right)+95 \left(\cos^{4}\left(d x +c \right)\right)+89 \left(\cos^{3}\left(d x +c \right)\right)+73 \left(\cos^{2}\left(d x +c \right)\right)+292 \cos \left(d x +c \right)-584\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{5}\left(d x +c \right)\right) a^{2}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(35*cos(d*x+c)^5+95*cos(d*x+c)^4+89*cos(d*x+c)^3+73*cos(d*x+c)^2+292*cos(d*x+c)-584)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(9/2)*cos(d*x+c)^5/sin(d*x+c)*a^2","A"
241,1,115,205,1.742000," ","int((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),x)","-\frac{2 \left(63 \left(\cos^{6}\left(d x +c \right)\right)+161 \left(\cos^{5}\left(d x +c \right)\right)+131 \left(\cos^{4}\left(d x +c \right)\right)+71 \left(\cos^{3}\left(d x +c \right)\right)+142 \left(\cos^{2}\left(d x +c \right)\right)+568 \cos \left(d x +c \right)-1136\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \left(\cos^{6}\left(d x +c \right)\right) a^{2}}{693 d \sin \left(d x +c \right)}"," ",0,"-2/693/d*(63*cos(d*x+c)^6+161*cos(d*x+c)^5+131*cos(d*x+c)^4+71*cos(d*x+c)^3+142*cos(d*x+c)^2+568*cos(d*x+c)-1136)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(11/2)*cos(d*x+c)^6/sin(d*x+c)*a^2","A"
242,0,0,34,1.336000," ","int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/4),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{1}{4}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/4),x)","F"
243,1,150,31,1.607000," ","int(sec(f*x+e)^(1/2)*(a+a*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(f x +e \right)\right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(\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{\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)\right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}\, \left(-1+\cos^{2}\left(f x +e \right)\right) \sqrt{2}}{2 f \sin \left(f x +e \right)^{2}}"," ",0,"1/2/f*(a*(1+cos(f*x+e))/cos(f*x+e))^(1/2)*(1/cos(f*x+e))^(1/2)*cos(f*x+e)*(arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1+sin(f*x+e))*2^(1/2))-arctan(1/4*(-2/(1+cos(f*x+e)))^(1/2)*(cos(f*x+e)+1-sin(f*x+e))*2^(1/2)))*(-2/(1+cos(f*x+e)))^(1/2)/sin(f*x+e)^2*(-1+cos(f*x+e)^2)*2^(1/2)","B"
244,1,126,32,1.704000," ","int((-sec(f*x+e))^(1/2)*(a-a*sec(f*x+e))^(1/2),x)","\frac{\left(\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) \cos \left(f x +e \right) \sqrt{-\frac{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 \sin \left(f x +e \right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}}"," ",0,"1/f*(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))))*cos(f*x+e)*(-1/cos(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/cos(f*x+e))^(1/2)/sin(f*x+e)/(1/(1+cos(f*x+e)))^(1/2)","B"
245,1,224,107,1.577000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+4 \cos \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/4/d*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^2*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+4*cos(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
246,1,184,78,1.546000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-2 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{2 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/2/d*(2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
247,1,99,45,1.381000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{d \sin \left(d x +c \right)^{2} a}"," ",0,"1/d*(1/cos(d*x+c))^(1/2)*cos(d*x+c)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
248,1,100,78,1.520000," ","int(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right)+2\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) a}"," ",0,"1/d*(arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)+2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/a","A"
249,1,120,108,1.627000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)+2\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right) a}"," ",0,"-1/3/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-4*cos(d*x+c)+2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)/a","A"
250,1,130,140,1.753000," ","int(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(6 \left(\cos^{3}\left(d x +c \right)\right)-15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \left(\cos^{2}\left(d x +c \right)\right)+28 \cos \left(d x +c \right)-26\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right) a}"," ",0,"-1/15/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(6*cos(d*x+c)^3-15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*cos(d*x+c)^2+28*cos(d*x+c)-26)*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^3/sin(d*x+c)/a","A"
251,1,282,143,1.530000," ","int(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-3 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+9 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+2 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^3*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-3*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+9*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+2*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","A"
252,1,240,109,1.486000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(2 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-2 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","B"
253,1,146,78,1.466000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{2 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/2/d*((-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/a^2","A"
254,1,146,78,1.383000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*((-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","A"
255,1,175,112,1.659000," ","int(1/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right)+12 \cos \left(d x +c \right)-10\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{4 d \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"-1/4/d*(7*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-7*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*cos(d*x+c)^3+6*cos(d*x+c)^2+12*cos(d*x+c)-10)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/(1/cos(d*x+c))^(1/2)/a^2","A"
256,1,193,146,1.756000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 \left(\cos^{4}\left(d x +c \right)\right)-33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-40 \left(\cos^{3}\left(d x +c \right)\right)+18 \left(\cos^{2}\left(d x +c \right)\right)+52 \cos \left(d x +c \right)-38\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/12/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+8*cos(d*x+c)^4-33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-40*cos(d*x+c)^3+18*cos(d*x+c)^2+52*cos(d*x+c)-38)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)^3/a^2","A"
257,1,203,180,1.817000," ","int(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(8 \left(\cos^{5}\left(d x +c \right)\right)-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-24 \left(\cos^{4}\left(d x +c \right)\right)+96 \left(\cos^{3}\left(d x +c \right)\right)+75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-54 \left(\cos^{2}\left(d x +c \right)\right)-124 \cos \left(d x +c \right)+98\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{20 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/20/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(8*cos(d*x+c)^5-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-24*cos(d*x+c)^4+96*cos(d*x+c)^3+75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-54*cos(d*x+c)^2-124*cos(d*x+c)+98)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)^3/a^2","A"
258,1,454,177,1.617000," ","int(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-40 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+40 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+35 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-115 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-40 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+40 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+20 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-115 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-39 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-16 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/16/d*(1/cos(d*x+c))^(9/2)*cos(d*x+c)^4*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-40*cos(d*x+c)^2*sin(d*x+c)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+40*cos(d*x+c)^2*sin(d*x+c)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)+35*cos(d*x+c)^3*(-2/(1+cos(d*x+c)))^(1/2)-115*cos(d*x+c)^2*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-40*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+40*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+20*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-115*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-39*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-16*(-2/(1+cos(d*x+c)))^(1/2))/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","B"
259,1,406,143,1.583000," ","int(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(16 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-16 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+16 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-16 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+11 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-43 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-43 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-15 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(16*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-16*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+16*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-16*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+11*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-43*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)+4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-43*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-15*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
260,1,210,112,1.507000," ","int(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-7 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/16/d*(-1+cos(d*x+c))^2*(3*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)+4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-7*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","A"
261,1,210,112,1.383000," ","int(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/16/d*(-1+cos(d*x+c))^2*(5*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","A"
262,1,208,112,1.343000," ","int(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(13 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-9 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(13*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+19*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+19*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-9*(-2/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","A"
263,1,236,146,1.657000," ","int(1/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-150 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+64 \left(\cos^{3}\left(d x +c \right)\right)-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+106 \left(\cos^{2}\left(d x +c \right)\right)-72 \cos \left(d x +c \right)-98\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{32 d \sin \left(d x +c \right)^{5} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/32/d*(-1+cos(d*x+c))^2*(-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-150*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)+64*cos(d*x+c)^3-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+106*cos(d*x+c)^2-72*cos(d*x+c)-98)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/(1/cos(d*x+c))^(1/2)/a^3","A"
264,1,254,180,1.704000," ","int(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+64 \left(\cos^{4}\left(d x +c \right)\right)+978 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-384 \left(\cos^{3}\left(d x +c \right)\right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-686 \left(\cos^{2}\left(d x +c \right)\right)+408 \cos \left(d x +c \right)+598\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{96 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/96/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+64*cos(d*x+c)^4+978*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)-384*cos(d*x+c)^3+489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-686*cos(d*x+c)^2+408*cos(d*x+c)+598)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^5/a^3","A"
265,1,253,108,1.457000," ","int(sec(d*x+c)^(7/2)/(1+sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-16 \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-2 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(7*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-7*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-16*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-2*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","B"
266,1,220,77,1.424000," ","int(sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+4 \cos \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{2}}"," ",0,"1/4/d*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^2*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+4*cos(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
267,1,180,50,1.544000," ","int(sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-2 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2/d*(2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
268,1,95,25,1.362000," ","int(sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{d \sin \left(d x +c \right)^{2}}"," ",0,"1/d*(1/cos(d*x+c))^(1/2)*cos(d*x+c)*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
269,1,98,56,1.497000," ","int(1/sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x)","-\frac{\left(-\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-2\right) \sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"-1/d*(-arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)-2)*((1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(1/cos(d*x+c))^(1/2)","A"
270,1,116,84,1.637000," ","int(1/sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)+2\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}"," ",0,"-1/3/d*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-4*cos(d*x+c)+2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)","A"
271,1,126,114,1.748000," ","int(1/sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{1+\cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(6 \left(\cos^{3}\left(d x +c \right)\right)-15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \left(\cos^{2}\left(d x +c \right)\right)+28 \cos \left(d x +c \right)-26\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right)}"," ",0,"-1/15/d*((1+cos(d*x+c))/cos(d*x+c))^(1/2)*(6*cos(d*x+c)^3-15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*cos(d*x+c)^2+28*cos(d*x+c)-26)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)","A"
272,0,0,266,1.240000," ","int((e*sec(d*x+c))^(4/3)*(a+a*sec(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{4}{3}} \sqrt{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^(4/3)*(a+a*sec(d*x+c))^(1/2),x)","F"
273,0,0,229,1.603000," ","int((e*sec(d*x+c))^(1/3)*(a+a*sec(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}} \sqrt{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^(1/3)*(a+a*sec(d*x+c))^(1/2),x)","F"
274,0,0,267,1.331000," ","int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(2/3),x)","\int \frac{\sqrt{a +a \sec \left(d x +c \right)}}{\left(e \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(2/3),x)","F"
275,0,0,580,1.255000," ","int((e*sec(d*x+c))^(8/3)*(a+a*sec(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{8}{3}} \sqrt{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^(8/3)*(a+a*sec(d*x+c))^(1/2),x)","F"
276,0,0,543,1.256000," ","int((e*sec(d*x+c))^(5/3)*(a+a*sec(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{5}{3}} \sqrt{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^(5/3)*(a+a*sec(d*x+c))^(1/2),x)","F"
277,0,0,506,1.248000," ","int((e*sec(d*x+c))^(2/3)*(a+a*sec(d*x+c))^(1/2),x)","\int \left(e \sec \left(d x +c \right)\right)^{\frac{2}{3}} \sqrt{a +a \sec \left(d x +c \right)}\, dx"," ",0,"int((e*sec(d*x+c))^(2/3)*(a+a*sec(d*x+c))^(1/2),x)","F"
278,0,0,538,1.306000," ","int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/3),x)","\int \frac{\sqrt{a +a \sec \left(d x +c \right)}}{\left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/3),x)","F"
279,0,0,579,1.213000," ","int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(4/3),x)","\int \frac{\sqrt{a +a \sec \left(d x +c \right)}}{\left(e \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(4/3),x)","F"
280,0,0,64,1.157000," ","int((e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{2}{3}}}{\sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x)","F"
281,0,0,64,1.122000," ","int((e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{\left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}}}{\sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int((e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x)","F"
282,0,0,64,1.184000," ","int(1/(e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \sec \left(d x +c \right)\right)^{\frac{1}{3}} \sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x)","F"
283,0,0,64,1.188000," ","int(1/(e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \sec \left(d x +c \right)\right)^{\frac{2}{3}} \sqrt{a +a \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x)","F"
284,0,0,60,1.411000," ","int(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(1/3),x)","\int \left(\sec^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(1/3),x)","F"
285,0,0,61,1.281000," ","int(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(2/3),x)","\int \left(\sec^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(2/3),x)","F"
286,0,0,275,1.298000," ","int(sec(d*x+c)^(5/3)*(a+a*sec(d*x+c))^(2/3),x)","\int \left(\sec^{\frac{5}{3}}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)*(a+a*sec(d*x+c))^(2/3),x)","F"
287,0,0,62,1.215000," ","int((a+a*sec(d*x+c))^(4/3)/sec(d*x+c)^(1/3),x)","\int \frac{\left(a +a \sec \left(d x +c \right)\right)^{\frac{4}{3}}}{\sec \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+a*sec(d*x+c))^(4/3)/sec(d*x+c)^(1/3),x)","F"
288,0,0,283,2.920000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^4,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{4}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^4,x)","F"
289,0,0,212,7.981000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^3,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^3,x)","F"
290,0,0,154,5.173000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^2,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^2,x)","F"
291,0,0,114,2.498000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e)),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e)),x)","F"
292,0,0,154,2.699000," ","int(sec(f*x+e)^n/(a+a*sec(f*x+e)),x)","\int \frac{\sec^{n}\left(f x +e \right)}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)^n/(a+a*sec(f*x+e)),x)","F"
293,0,0,191,0.938000," ","int(sec(f*x+e)^n/(a+a*sec(f*x+e))^2,x)","\int \frac{\sec^{n}\left(f x +e \right)}{\left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(sec(f*x+e)^n/(a+a*sec(f*x+e))^2,x)","F"
294,0,0,150,1.135000," ","int(sec(f*x+e)^n*(1+sec(f*x+e))^(5/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(1+\sec \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(f*x+e)^n*(1+sec(f*x+e))^(5/2),x)","F"
295,0,0,92,0.992000," ","int(sec(f*x+e)^n*(1+sec(f*x+e))^(3/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(f*x+e)^n*(1+sec(f*x+e))^(3/2),x)","F"
296,0,0,41,1.085000," ","int(sec(f*x+e)^n*(1+sec(f*x+e))^(1/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \sqrt{1+\sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)^n*(1+sec(f*x+e))^(1/2),x)","F"
297,0,0,49,0.957000," ","int(sec(f*x+e)^n/(1+sec(f*x+e))^(1/2),x)","\int \frac{\sec^{n}\left(f x +e \right)}{\sqrt{1+\sec \left(f x +e \right)}}\, dx"," ",0,"int(sec(f*x+e)^n/(1+sec(f*x+e))^(1/2),x)","F"
298,0,0,50,0.962000," ","int(sec(f*x+e)^n/(1+sec(f*x+e))^(3/2),x)","\int \frac{\sec^{n}\left(f x +e \right)}{\left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(f*x+e)^n/(1+sec(f*x+e))^(3/2),x)","F"
299,0,0,111,1.083000," ","int((-sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((-sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x)","F"
300,0,0,60,0.871000," ","int((-sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \sqrt{1+\sec \left(f x +e \right)}\, dx"," ",0,"int((-sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x)","F"
301,0,0,67,0.933000," ","int((-sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\sqrt{1+\sec \left(f x +e \right)}}\, dx"," ",0,"int((-sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x)","F"
302,0,0,67,0.976000," ","int((-sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x)","F"
303,0,0,111,1.068000," ","int((d*sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x)","F"
304,0,0,60,0.886000," ","int((d*sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \sqrt{1+\sec \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x)","F"
305,0,0,67,0.843000," ","int((d*sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\sqrt{1+\sec \left(f x +e \right)}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x)","F"
306,0,0,67,0.762000," ","int((d*sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\left(1+\sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x)","F"
307,0,0,165,1.192000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(5/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(5/2),x)","F"
308,0,0,102,1.089000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(3/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(3/2),x)","F"
309,0,0,44,1.231000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(1/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \sqrt{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^(1/2),x)","F"
310,0,0,51,1.141000," ","int(sec(f*x+e)^n/(a+a*sec(f*x+e))^(1/2),x)","\int \frac{\sec^{n}\left(f x +e \right)}{\sqrt{a +a \sec \left(f x +e \right)}}\, dx"," ",0,"int(sec(f*x+e)^n/(a+a*sec(f*x+e))^(1/2),x)","F"
311,0,0,55,1.070000," ","int(sec(f*x+e)^n/(a+a*sec(f*x+e))^(3/2),x)","\int \frac{\sec^{n}\left(f x +e \right)}{\left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(f*x+e)^n/(a+a*sec(f*x+e))^(3/2),x)","F"
312,0,0,124,0.948000," ","int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x)","F"
313,0,0,66,1.033000," ","int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \sqrt{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x)","F"
314,0,0,69,0.915000," ","int((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sec \left(f x +e \right)}}\, dx"," ",0,"int((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","F"
315,0,0,72,0.843000," ","int((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","F"
316,0,0,124,0.960000," ","int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x)","F"
317,0,0,66,1.071000," ","int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \sqrt{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x)","F"
318,0,0,69,0.917000," ","int((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sec \left(f x +e \right)}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x)","F"
319,0,0,72,0.870000," ","int((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x)","F"
320,0,0,166,1.277000," ","int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(5/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(a -a \sec \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(5/2),x)","F"
321,0,0,102,1.101000," ","int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(a -a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x)","F"
322,0,0,43,1.128000," ","int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \sqrt{a -a \sec \left(f x +e \right)}\, dx"," ",0,"int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x)","F"
323,0,0,50,1.023000," ","int((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(1/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\sqrt{a -a \sec \left(f x +e \right)}}\, dx"," ",0,"int((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(1/2),x)","F"
324,0,0,54,0.945000," ","int((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(3/2),x)","\int \frac{\left(-\sec \left(f x +e \right)\right)^{n}}{\left(a -a \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(3/2),x)","F"
325,0,0,124,1.286000," ","int(sec(f*x+e)^n*(a-a*sec(f*x+e))^(3/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a -a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(f*x+e)^n*(a-a*sec(f*x+e))^(3/2),x)","F"
326,0,0,65,1.258000," ","int(sec(f*x+e)^n*(a-a*sec(f*x+e))^(1/2),x)","\int \left(\sec^{n}\left(f x +e \right)\right) \sqrt{a -a \sec \left(f x +e \right)}\, dx"," ",0,"int(sec(f*x+e)^n*(a-a*sec(f*x+e))^(1/2),x)","F"
327,0,0,124,1.184000," ","int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a -a \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x)","F"
328,0,0,65,1.174000," ","int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \sqrt{a -a \sec \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x)","F"
329,0,0,58,2.438000," ","int(sec(f*x+e)^n*(1+sec(f*x+e))^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(1+\sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^n*(1+sec(f*x+e))^m,x)","F"
330,0,0,75,2.656000," ","int((1-sec(f*x+e))^m*sec(f*x+e)^n,x)","\int \left(1-\sec \left(f x +e \right)\right)^{m} \left(\sec^{n}\left(f x +e \right)\right)\, dx"," ",0,"int((1-sec(f*x+e))^m*sec(f*x+e)^n,x)","F"
331,0,0,74,2.674000," ","int(sec(f*x+e)^n*(a+a*sec(f*x+e))^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^n*(a+a*sec(f*x+e))^m,x)","F"
332,0,0,76,2.659000," ","int(sec(f*x+e)^n*(a-a*sec(f*x+e))^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a -a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^n*(a-a*sec(f*x+e))^m,x)","F"
333,0,0,73,2.358000," ","int((-sec(f*x+e))^n*(1+sec(f*x+e))^m,x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(1+\sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-sec(f*x+e))^n*(1+sec(f*x+e))^m,x)","F"
334,0,0,58,2.491000," ","int((1-sec(f*x+e))^m*(-sec(f*x+e))^n,x)","\int \left(1-\sec \left(f x +e \right)\right)^{m} \left(-\sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((1-sec(f*x+e))^m*(-sec(f*x+e))^n,x)","F"
335,0,0,75,2.885000," ","int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x)","F"
336,0,0,75,2.886000," ","int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x)","\int \left(-\sec \left(f x +e \right)\right)^{n} \left(a -a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x)","F"
337,0,0,71,2.414000," ","int((d*sec(f*x+e))^n*(1+sec(f*x+e))^m,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(1+\sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^n*(1+sec(f*x+e))^m,x)","F"
338,0,0,71,2.384000," ","int((1-sec(f*x+e))^m*(d*sec(f*x+e))^n,x)","\int \left(1-\sec \left(f x +e \right)\right)^{m} \left(d \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((1-sec(f*x+e))^m*(d*sec(f*x+e))^n,x)","F"
339,0,0,87,2.428000," ","int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x)","F"
340,0,0,88,2.500000," ","int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a -a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x)","F"
341,0,0,199,1.161000," ","int(sec(f*x+e)^4*(a+a*sec(f*x+e))^m,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^4*(a+a*sec(f*x+e))^m,x)","F"
342,0,0,143,1.064000," ","int(sec(f*x+e)^3*(a+a*sec(f*x+e))^m,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^3*(a+a*sec(f*x+e))^m,x)","F"
343,0,0,95,0.917000," ","int(sec(f*x+e)^2*(a+a*sec(f*x+e))^m,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^2*(a+a*sec(f*x+e))^m,x)","F"
344,0,0,61,0.989000," ","int(sec(f*x+e)*(a+a*sec(f*x+e))^m,x)","\int \sec \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)*(a+a*sec(f*x+e))^m,x)","F"
345,0,0,71,0.737000," ","int((a+a*sec(f*x+e))^m,x)","\int \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+a*sec(f*x+e))^m,x)","F"
346,0,0,72,1.410000," ","int(cos(f*x+e)*(a+a*sec(f*x+e))^m,x)","\int \cos \left(f x +e \right) \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sec(f*x+e))^m,x)","F"
347,0,0,82,1.100000," ","int((d*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^m,x)","\int \left(d \sec \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^m,x)","F"
348,0,0,82,1.177000," ","int((d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^m,x)","\int \sqrt{d \sec \left(f x +e \right)}\, \left(a +a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^m,x)","F"
349,0,0,82,1.155000," ","int((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sec \left(f x +e \right)\right)^{m}}{\sqrt{d \sec \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(1/2),x)","F"
350,0,0,82,1.107000," ","int((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sec \left(f x +e \right)\right)^{m}}{\left(d \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(3/2),x)","F"
351,1,270,147,3.646000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(240 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-528 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+448 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-122 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(240*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-528*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+448*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+25*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-122*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
352,1,219,127,3.599000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(24*cos(1/2*d*x+1/2*c)^7-28*cos(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+4*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
353,1,225,107,3.407000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
354,1,150,87,3.023000," ","int(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
355,1,146,107,3.630000," ","int((a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{2 a \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*a*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
356,1,369,127,5.690000," ","int((a+a*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{2 a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
357,1,384,147,5.626000," ","int((a+a*sec(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{40 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{12 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-1/40*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-3/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/12*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
358,1,437,167,6.009000," ","int((a+a*sec(d*x+c))/cos(d*x+c)^(7/2),x)","-\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{112 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{84 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{44 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{40 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-1/112*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/84*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+44/105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/40*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-3/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-3/10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
359,1,260,179,3.616000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(560 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-960 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+608 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-205 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+75 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-168 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+93 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(560*cos(1/2*d*x+1/2*c)^11-960*cos(1/2*d*x+1/2*c)^9+608*cos(1/2*d*x+1/2*c)^7-96*cos(1/2*d*x+1/2*c)^5-205*cos(1/2*d*x+1/2*c)^3+75*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-168*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+93*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
360,1,272,157,3.440000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-116 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+126 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-39 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/35*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-116*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+126*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-39*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
361,1,250,135,3.751000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-12 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+32 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-13 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-12*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+32*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-13*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
362,1,228,113,3.685000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
363,1,104,68,3.410000," ","int(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x)","-\frac{4 a^{2} \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*a^2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
364,1,371,135,5.791000," ","int((a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x)","\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"4/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(4*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+7*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
365,1,386,157,6.000000," ","int((a+a*sec(d*x+c))^2/cos(d*x+c)^(3/2),x)","-\frac{8 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-\frac{4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{17 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{30 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{80 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{12 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-4/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+17/30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/80*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-1/12*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
366,1,439,179,6.890000," ","int((a+a*sec(d*x+c))^2/cos(d*x+c)^(5/2),x)","-\frac{8 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{224 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{14 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{31 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{70 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{40 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{5 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-1/224*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-1/14*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+31/70*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/40*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-3/5*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-3/10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
367,1,260,179,3.886000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(560 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-600 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+212 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+66 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-430 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+165 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(560*cos(1/2*d*x+1/2*c)^11-600*cos(1/2*d*x+1/2*c)^9+212*cos(1/2*d*x+1/2*c)^7+66*cos(1/2*d*x+1/2*c)^5-430*cos(1/2*d*x+1/2*c)^3+165*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+192*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
368,1,272,157,3.998000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(120 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+602 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+65 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-208 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(120*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-432*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+602*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+65*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-208*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
369,1,250,135,3.300000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3,x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(-4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/5*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(-4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+14*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
370,1,172,135,4.089000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x)","-\frac{4 a^{3} \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*a^3*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
371,1,371,135,5.915000," ","int(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x)","\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"4/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-18*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
372,1,386,157,5.700000," ","int((a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x)","-\frac{16 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{160 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{9 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{10 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{20 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{16 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-16*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(7/10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/160*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-9/10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-9/20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/16*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
373,1,439,179,6.614000," ","int((a+a*sec(d*x+c))^3/cos(d*x+c)^(3/2),x)","-\frac{16 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(-\frac{3 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{160 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{10 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{53 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{20 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{448 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{13 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{168 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-16*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(-3/160*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-7/10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+53/105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-1/448*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-13/168*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
374,1,229,166,3.639000," ","int(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(25 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+63 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+23 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{15 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(25*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+63*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*sin(1/2*d*x+1/2*c)^8-56*sin(1/2*d*x+1/2*c)^6-30*sin(1/2*d*x+1/2*c)^4+23*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
375,1,215,144,3.931000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-8*sin(1/2*d*x+1/2*c)^6+18*sin(1/2*d*x+1/2*c)^4-7*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
376,1,199,122,3.316000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/a/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
377,1,198,120,3.347000," ","int(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/a/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
378,1,200,120,3.387000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
379,1,253,144,4.319000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
380,1,413,166,6.559000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+44 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a/sin(1/2*d*x+1/2*c)^3/cos(1/2*d*x+1/2*c)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-36*sin(1/2*d*x+1/2*c)^6-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*cos(1/2*d*x+1/2*c)+44*sin(1/2*d*x+1/2*c)^4-11*sin(1/2*d*x+1/2*c)^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
381,1,283,198,3.986000," ","int(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(96 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-352 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-150 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+266 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-135 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5\right)}{30 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/30*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(96*cos(1/2*d*x+1/2*c)^10-352*cos(1/2*d*x+1/2*c)^8+120*cos(1/2*d*x+1/2*c)^6-150*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-336*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+266*cos(1/2*d*x+1/2*c)^4-135*cos(1/2*d*x+1/2*c)^2+5)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
382,1,270,176,3.864000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+42 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-48 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*cos(1/2*d*x+1/2*c)^8+12*cos(1/2*d*x+1/2*c)^6+20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+42*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-48*cos(1/2*d*x+1/2*c)^4+21*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
383,1,257,154,3.765000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^6+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+24*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*cos(1/2*d*x+1/2*c)^4+15*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
384,1,257,153,3.967000," ","int(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-20 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^6+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-20*cos(1/2*d*x+1/2*c)^4+9*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
385,1,188,77,3.721000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+2*cos(1/2*d*x+1/2*c)^4-3*cos(1/2*d*x+1/2*c)^2+1)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
386,1,257,153,3.363000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^6-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-16*cos(1/2*d*x+1/2*c)^4+3*cos(1/2*d*x+1/2*c)^2+1)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
387,1,405,176,4.147000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-48 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+86 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*(2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-48*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6+86*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-37*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
388,1,413,198,6.661000," ","int(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{22 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{14 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{2 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^2*(1/3*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)-22/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+14*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)-2/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
389,1,296,235,3.724000," ","int(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(64 \left(\cos^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-288 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-76 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-210 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-462 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+530 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-248 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+19 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}{20 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(64*cos(1/2*d*x+1/2*c)^12-288*cos(1/2*d*x+1/2*c)^10-76*cos(1/2*d*x+1/2*c)^8-210*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-462*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+530*cos(1/2*d*x+1/2*c)^6-248*cos(1/2*d*x+1/2*c)^4+19*cos(1/2*d*x+1/2*c)^2-1)/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
390,1,283,213,3.641000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+468 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+714 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1058 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3\right)}{60 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(160*cos(1/2*d*x+1/2*c)^10+468*cos(1/2*d*x+1/2*c)^8+330*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+714*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1058*cos(1/2*d*x+1/2*c)^6+474*cos(1/2*d*x+1/2*c)^4-47*cos(1/2*d*x+1/2*c)^2+3)/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
391,1,270,191,3.760000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(348 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+294 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3\right)}{60 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(348*cos(1/2*d*x+1/2*c)^8+130*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+294*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*cos(1/2*d*x+1/2*c)^6+264*cos(1/2*d*x+1/2*c)^4-37*cos(1/2*d*x+1/2*c)^2+3)/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
392,1,270,191,3.608000," ","int(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(36 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-66 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)}{20 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(36*cos(1/2*d*x+1/2*c)^8+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-66*cos(1/2*d*x+1/2*c)^6+38*cos(1/2*d*x+1/2*c)^4-9*cos(1/2*d*x+1/2*c)^2+1)/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
393,1,270,191,4.184000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^8+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*cos(1/2*d*x+1/2*c)^6-24*cos(1/2*d*x+1/2*c)^4+17*cos(1/2*d*x+1/2*c)^2-3)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
394,1,270,191,3.556000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*cos(1/2*d*x+1/2*c)^8-10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*cos(1/2*d*x+1/2*c)^6+6*cos(1/2*d*x+1/2*c)^4+7*cos(1/2*d*x+1/2*c)^2-3)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
395,1,268,191,3.793000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(36 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-46 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{20 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/20*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(36*cos(1/2*d*x+1/2*c)^8-10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*cos(1/2*d*x+1/2*c)^5*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-46*cos(1/2*d*x+1/2*c)^6+8*cos(1/2*d*x+1/2*c)^4+cos(1/2*d*x+1/2*c)^2+1)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
396,1,555,213,4.089000," ","int(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x)","-\frac{-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(65 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+588 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1634 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1488 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-439 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*(-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+4*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(65*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+588*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^8-1634*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6+1488*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-439*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
397,1,453,235,6.666000," ","int(1/cos(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{32 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{15 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{118 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{128 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{238 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}\right)}{4 a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^3*(32/15*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^3+118/5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)-128/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+238/5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1/5*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)^5-4/3*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
398,1,80,129,1.150000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(5 \left(\cos^{4}\left(d x +c \right)\right)+\cos^{3}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+8 \cos \left(d x +c \right)-16\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)}"," ",0,"-2/35/d*(5*cos(d*x+c)^4+cos(d*x+c)^3+2*cos(d*x+c)^2+8*cos(d*x+c)-16)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
399,1,70,97,1.243000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right)+\cos^{2}\left(d x +c \right)+4 \cos \left(d x +c \right)-8\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(3*cos(d*x+c)^3+cos(d*x+c)^2+4*cos(d*x+c)-8)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
400,1,58,65,1.230000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(\cos^{2}\left(d x +c \right)+\cos \left(d x +c \right)-2\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(cos(d*x+c)^2+cos(d*x+c)-2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
401,1,50,32,0.965000," ","int(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-2/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))/sin(d*x+c)","A"
402,1,142,47,1.029000," ","int((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2)))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*2^(1/2)","B"
403,1,178,78,1.001000," ","int((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/2/d*(-1+cos(d*x+c))*(-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(1/2)","B"
404,1,213,112,1.012000," ","int((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","\frac{\left(3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+6 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{16 d \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"1/16/d*(3*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-3*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+6*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","A"
405,1,83,137,1.170000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(15 \left(\cos^{4}\left(d x +c \right)\right)+24 \left(\cos^{3}\left(d x +c \right)\right)+13 \left(\cos^{2}\left(d x +c \right)\right)+52 \cos \left(d x +c \right)-104\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(15*cos(d*x+c)^4+24*cos(d*x+c)^3+13*cos(d*x+c)^2+52*cos(d*x+c)-104)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a","A"
406,1,71,98,1.168000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\cos^{3}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)-6\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{5 d \sin \left(d x +c \right)}"," ",0,"-2/5/d*(cos(d*x+c)^3+2*cos(d*x+c)^2+3*cos(d*x+c)-6)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a","A"
407,1,61,67,1.024000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\cos^{2}\left(d x +c \right)+4 \cos \left(d x +c \right)-5\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(cos(d*x+c)^2+4*cos(d*x+c)-5)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a","A"
408,1,172,82,1.138000," ","int((a+a*sec(d*x+c))^(3/2)*cos(d*x+c)^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \cos \left(d x +c \right)-4\right) a}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*cos(d*x+c)-4)/sin(d*x+c)*a","B"
409,1,182,81,1.082000," ","int((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a}{4 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{2}}"," ",0,"1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a","B"
410,1,212,116,0.982000," ","int((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+14 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{8 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(7*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-7*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+14*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)*a","A"
411,1,242,150,1.014000," ","int((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-33 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-66 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-44 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-16 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{48 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/48/d*(-1+cos(d*x+c))*(33*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^3*2^(1/2)-33*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^3*2^(1/2)-66*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2-44*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-16*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(5/2)/(-2/(1+cos(d*x+c)))^(1/2)*a","A"
412,1,95,171,1.109000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(35 \left(\cos^{5}\left(d x +c \right)\right)+95 \left(\cos^{4}\left(d x +c \right)\right)+89 \left(\cos^{3}\left(d x +c \right)\right)+73 \left(\cos^{2}\left(d x +c \right)\right)+292 \cos \left(d x +c \right)-584\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(35*cos(d*x+c)^5+95*cos(d*x+c)^4+89*cos(d*x+c)^3+73*cos(d*x+c)^2+292*cos(d*x+c)-584)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a^2","A"
413,1,85,132,1.176000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(3 \left(\cos^{4}\left(d x +c \right)\right)+9 \left(\cos^{3}\left(d x +c \right)\right)+11 \left(\cos^{2}\left(d x +c \right)\right)+23 \cos \left(d x +c \right)-46\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{21 d \sin \left(d x +c \right)}"," ",0,"-2/21/d*(3*cos(d*x+c)^4+9*cos(d*x+c)^3+11*cos(d*x+c)^2+23*cos(d*x+c)-46)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a^2","A"
414,1,75,101,1.817000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right)+11 \left(\cos^{2}\left(d x +c \right)\right)+29 \cos \left(d x +c \right)-43\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(3*cos(d*x+c)^3+11*cos(d*x+c)^2+29*cos(d*x+c)-43)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a^2","A"
415,1,185,116,1.060000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right)+28 \cos \left(d x +c \right)-32\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) a^{2}}{6 d \sin \left(d x +c \right)}"," ",0,"-1/6/d*(3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*cos(d*x+c)^2+28*cos(d*x+c)-32)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)*a^2","A"
416,1,197,114,1.069000," ","int((a+a*sec(d*x+c))^(5/2)*cos(d*x+c)^(1/2),x)","-\frac{\left(5 \sin \left(d x +c \right) \cos \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-5 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+8 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-4\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{4 d \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/4/d*(5*sin(d*x+c)*cos(d*x+c)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*2^(1/2)-5*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+8*cos(d*x+c)^2-4*cos(d*x+c)-4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)*a^2","A"
417,1,214,116,1.043000," ","int((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(19 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-19 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-22 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(19*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-19*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-22*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)/sin(d*x+c)^2*a^2","A"
418,1,244,150,1.031000," ","int((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(75 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-75 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+150 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+68 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+16 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{48 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/48/d*(-1+cos(d*x+c))*(75*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^3*2^(1/2)-75*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^3*2^(1/2)+150*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2+68*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+16*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(5/2)/(-2/(1+cos(d*x+c)))^(1/2)*a^2","A"
419,1,276,184,1.074000," ","int((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x)","\frac{\left(489 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-489 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{4}\left(d x +c \right)\right)+978 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+652 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+368 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+96 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}{768 d \cos \left(d x +c \right)^{\frac{7}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"1/768/d*(489*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-489*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+978*sin(d*x+c)*cos(d*x+c)^3*(-2/(1+cos(d*x+c)))^(1/2)+652*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2+368*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+96*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(7/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a^2","A"
420,1,120,156,1.135000," ","int(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \left(\cos^{3}\left(d x +c \right)\right)+8 \left(\cos^{2}\left(d x +c \right)\right)-28 \cos \left(d x +c \right)+26\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right) a}"," ",0,"1/15/d*(15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*cos(d*x+c)^3+8*cos(d*x+c)^2-28*cos(d*x+c)+26)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)/a","A"
421,1,110,124,1.086000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)+2\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right) a}"," ",0,"-1/3/d*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2-4*cos(d*x+c)+2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)/a","A"
422,1,98,94,0.967000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right)+2\right)}{d \sin \left(d x +c \right) a}"," ",0,"1/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)+2)/sin(d*x+c)/a","A"
423,1,91,45,1.069000," ","int(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{d \sin \left(d x +c \right)^{2} a}"," ",0,"1/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","A"
424,1,174,110,0.982000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-2 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{2 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/2/d*(2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","A"
425,1,214,139,1.064000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-\arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+4 \cos \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+2 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{2} a}"," ",0,"1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+4*cos(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","A"
426,1,247,172,1.050000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+7 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+2 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+16 \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} a}"," ",0,"1/8/d*(-1+cos(d*x+c))*(-7*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+7*cos(d*x+c)^2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+2*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+16*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(3/2)/a","A"
427,1,193,196,1.145000," ","int(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 \left(\cos^{5}\left(d x +c \right)\right)+24 \left(\cos^{4}\left(d x +c \right)\right)-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-96 \left(\cos^{3}\left(d x +c \right)\right)+54 \left(\cos^{2}\left(d x +c \right)\right)+124 \cos \left(d x +c \right)-98\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{20 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/20/d*(75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-8*cos(d*x+c)^5+24*cos(d*x+c)^4-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-96*cos(d*x+c)^3+54*cos(d*x+c)^2+124*cos(d*x+c)-98)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)^3/a^2","A"
428,1,183,162,1.111000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 \left(\cos^{4}\left(d x +c \right)\right)-33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-40 \left(\cos^{3}\left(d x +c \right)\right)+18 \left(\cos^{2}\left(d x +c \right)\right)+52 \cos \left(d x +c \right)-38\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/12/d*(33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+8*cos(d*x+c)^4-33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-40*cos(d*x+c)^3+18*cos(d*x+c)^2+52*cos(d*x+c)-38)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)^3/a^2","A"
429,1,173,128,1.059000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \left(\cos^{3}\left(d x +c \right)\right)+6 \left(\cos^{2}\left(d x +c \right)\right)+12 \cos \left(d x +c \right)-10\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/4/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(7*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-7*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*cos(d*x+c)^3+6*cos(d*x+c)^2+12*cos(d*x+c)-10)/sin(d*x+c)^3/a^2","A"
430,1,138,94,1.125000," ","int(1/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","A"
431,1,136,94,0.993000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","A"
432,1,230,141,1.012000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(2 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-2 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-2*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","A"
433,1,270,175,1.011000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-3 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+9 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-3 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+2 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{2 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"-1/2/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-3*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+9*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-3*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+2*(-2/(1+cos(d*x+c)))^(1/2))/cos(d*x+c)^(1/2)/sin(d*x+c)^3/(-2/(1+cos(d*x+c)))^(1/2)/a^2","A"
434,1,244,196,1.176000," ","int(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+978 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+64 \left(\cos^{4}\left(d x +c \right)\right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-384 \left(\cos^{3}\left(d x +c \right)\right)-686 \left(\cos^{2}\left(d x +c \right)\right)+408 \cos \left(d x +c \right)+598\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{96 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/96/d*(-1+cos(d*x+c))^2*(489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+978*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)+64*cos(d*x+c)^4+489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-384*cos(d*x+c)^3-686*cos(d*x+c)^2+408*cos(d*x+c)+598)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)^5/a^3","A"
435,1,234,162,1.161000," ","int(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-150 \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+64 \left(\cos^{3}\left(d x +c \right)\right)-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+106 \left(\cos^{2}\left(d x +c \right)\right)-72 \cos \left(d x +c \right)-98\right)}{32 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/32/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)-150*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)+64*cos(d*x+c)^3-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+106*cos(d*x+c)^2-72*cos(d*x+c)-98)/sin(d*x+c)^5/a^3","A"
436,1,200,128,1.184000," ","int(1/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(13 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-9 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))^2*(13*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+19*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+19*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-9*(-2/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","A"
437,1,198,128,1.123000," ","int(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-5 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+5 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-5*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+5*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","A"
438,1,200,128,1.120000," ","int(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-7 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/16/d*(-1+cos(d*x+c))^2*(3*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)+4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-7*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","A"
439,1,396,175,1.105000," ","int(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(16 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-16 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+16 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-16 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+11 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-43 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-43 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-15 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(16*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-16*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+16*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-16*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)-43*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)+11*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-43*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-15*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
440,1,444,209,1.144000," ","int(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(40 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-40 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+40 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}-40 \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}+115 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-35 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+115 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)-20 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+39 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+16 \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sqrt{\cos \left(d x +c \right)}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/16/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(40*sin(d*x+c)*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)-40*sin(d*x+c)*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)+40*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)-40*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*sin(d*x+c)*2^(1/2)+115*sin(d*x+c)*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-35*cos(d*x+c)^3*(-2/(1+cos(d*x+c)))^(1/2)+115*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*sin(d*x+c)-20*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+39*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+16*(-2/(1+cos(d*x+c)))^(1/2))/cos(d*x+c)^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","B"
441,0,0,225,8.529000," ","int((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^3,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^3,x)","F"
442,0,0,164,5.463000," ","int((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^2,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^2,x)","F"
443,0,0,120,2.722000," ","int((d*cos(f*x+e))^n*(a+a*sec(f*x+e)),x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+a*sec(f*x+e)),x)","F"
444,0,0,166,2.769000," ","int((d*cos(f*x+e))^n/(a+a*sec(f*x+e)),x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{n}}{a +a \sec \left(f x +e \right)}\, dx"," ",0,"int((d*cos(f*x+e))^n/(a+a*sec(f*x+e)),x)","F"
445,0,0,195,1.189000," ","int((d*cos(f*x+e))^n/(a+a*sec(f*x+e))^2,x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{n}}{\left(a +a \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*cos(f*x+e))^n/(a+a*sec(f*x+e))^2,x)","F"
446,1,92,77,0.743000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c)),x)","\frac{2 a \tan \left(d x +c \right)}{3 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 b \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"2/3*a*tan(d*x+c)/d+1/3/d*a*tan(d*x+c)*sec(d*x+c)^2+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d+3/8*b*sec(d*x+c)*tan(d*x+c)/d+3/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
447,1,72,57,0.740000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c)),x)","\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 b \tan \left(d x +c \right)}{3 d}+\frac{b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+2/3*b*tan(d*x+c)/d+1/3/d*b*tan(d*x+c)*sec(d*x+c)^2","A"
448,1,51,43,0.735000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c)),x)","\frac{a \tan \left(d x +c \right)}{d}+\frac{b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a*tan(d*x+c)/d+1/2*b*sec(d*x+c)*tan(d*x+c)/d+1/2/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
449,1,32,24,0.557000," ","int(sec(d*x+c)*(a+b*sec(d*x+c)),x)","\frac{b \tan \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"b*tan(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
450,1,24,16,0.035000," ","int(a+b*sec(d*x+c),x)","a x +\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"a*x+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
451,1,21,15,0.501000," ","int(cos(d*x+c)*(a+b*sec(d*x+c)),x)","\frac{a \sin \left(d x +c \right)+\left(d x +c \right) b}{d}"," ",0,"1/d*(a*sin(d*x+c)+(d*x+c)*b)","A"
452,1,38,34,0.619000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c)),x)","\frac{a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b \sin \left(d x +c \right)}{d}"," ",0,"1/d*(a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b*sin(d*x+c))","A"
453,1,49,48,1.000000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c)),x)","\frac{\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c)+b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
454,1,60,68,1.021000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c)),x)","\frac{a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*b*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
455,1,70,82,1.032000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c)),x)","\frac{\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+b \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
456,1,157,123,0.911000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c))^2,x)","\frac{2 a^{2} \tan \left(d x +c \right)}{3 d}+\frac{a^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{a b \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{2 d}+\frac{3 a b \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{8 b^{2} \tan \left(d x +c \right)}{15 d}+\frac{b^{2} \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{4 b^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{15 d}"," ",0,"2/3*a^2*tan(d*x+c)/d+1/3*a^2*sec(d*x+c)^2*tan(d*x+c)/d+1/2*a*b*sec(d*x+c)^3*tan(d*x+c)/d+3/4*a*b*sec(d*x+c)*tan(d*x+c)/d+3/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+8/15*b^2*tan(d*x+c)/d+1/5*b^2*sec(d*x+c)^4*tan(d*x+c)/d+4/15*b^2*sec(d*x+c)^2*tan(d*x+c)/d","A"
457,1,142,102,0.924000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 a b \tan \left(d x +c \right)}{3 d}+\frac{2 a b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a^2*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+4/3*a*b*tan(d*x+c)/d+2/3/d*a*b*tan(d*x+c)*sec(d*x+c)^2+1/4*b^2*sec(d*x+c)^3*tan(d*x+c)/d+3/8*b^2*sec(d*x+c)*tan(d*x+c)/d+3/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
458,1,89,76,0.918000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{a b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 b^{2} \tan \left(d x +c \right)}{3 d}+\frac{b^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}"," ",0,"a^2*tan(d*x+c)/d+a*b*sec(d*x+c)*tan(d*x+c)/d+1/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+2/3*b^2*tan(d*x+c)/d+1/3*b^2*sec(d*x+c)^2*tan(d*x+c)/d","A"
459,1,78,55,0.736000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a b \tan \left(d x +c \right)}{d}+\frac{b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2*a*b*tan(d*x+c)/d+1/2*b^2*sec(d*x+c)*tan(d*x+c)/d+1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
460,1,49,33,0.559000," ","int((a+b*sec(d*x+c))^2,x)","a^{2} x +\frac{b^{2} \tan \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} c}{d}"," ",0,"a^2*x+b^2*tan(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*c","A"
461,1,49,33,0.568000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^2,x)","2 a b x +\frac{a^{2} \sin \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a b c}{d}"," ",0,"2*a*b*x+a^2*sin(d*x+c)/d+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a*b*c","A"
462,1,51,46,0.556000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(d x +c \right) a b +b^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*sin(d*x+c)*a*b+b^2*(d*x+c))","A"
463,1,63,56,0.908000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^2,x)","\frac{\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 a b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{2} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+2*a*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^2*sin(d*x+c))","A"
464,1,89,93,1.053000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{2 a b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+b^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2/3*a*b*(2+cos(d*x+c)^2)*sin(d*x+c)+b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
465,1,95,101,1.319000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^2,x)","\frac{\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+2 a b \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+2*a*b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*b^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
466,1,206,177,1.082000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} b \tan \left(d x +c \right)}{d}+\frac{a^{2} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{9 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 b^{3} \tan \left(d x +c \right)}{15 d}+\frac{b^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/2*a^3*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+2/d*a^2*b*tan(d*x+c)+1/d*a^2*b*tan(d*x+c)*sec(d*x+c)^2+3/4/d*b^2*a*tan(d*x+c)*sec(d*x+c)^3+9/8*a*b^2*sec(d*x+c)*tan(d*x+c)/d+9/8/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*b^3*tan(d*x+c)+1/5/d*b^3*tan(d*x+c)*sec(d*x+c)^4+4/15/d*b^3*tan(d*x+c)*sec(d*x+c)^2","A"
467,1,160,120,1.098000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{2} a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"a^3*tan(d*x+c)/d+3/2/d*a^2*b*sec(d*x+c)*tan(d*x+c)+3/2/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+2*a*b^2*tan(d*x+c)/d+1/d*b^2*a*tan(d*x+c)*sec(d*x+c)^2+1/4/d*b^3*tan(d*x+c)*sec(d*x+c)^3+3/8*b^3*sec(d*x+c)*tan(d*x+c)/d+3/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
468,1,118,91,0.908000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \tan \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 b^{3} \tan \left(d x +c \right)}{3 d}+\frac{b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^2*b*tan(d*x+c)+3/2*a*b^2*sec(d*x+c)*tan(d*x+c)/d+3/2/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*b^3*tan(d*x+c)+1/3/d*b^3*tan(d*x+c)*sec(d*x+c)^2","A"
469,1,95,67,0.731000," ","int((a+b*sec(d*x+c))^3,x)","a^{3} x +\frac{a^{3} c}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a^3*x+1/d*a^3*c+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3*a*b^2*tan(d*x+c)/d+1/2*b^3*sec(d*x+c)*tan(d*x+c)/d+1/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
470,1,68,67,0.641000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^3,x)","3 a^{2} b x +\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{3} \sin \left(d x +c \right)}{d}+\frac{b^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b c}{d}"," ",0,"3*a^2*b*x+3/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+a^3*sin(d*x+c)/d+1/d*b^3*tan(d*x+c)+3/d*a^2*b*c","A"
471,1,90,73,0.499000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}+\frac{3 a^{2} b \sin \left(d x +c \right)}{d}+3 b^{2} a x +\frac{3 a \,b^{2} c}{d}+\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c+3*a^2*b*sin(d*x+c)/d+3*b^2*a*x+3/d*a*b^2*c+1/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
472,1,76,92,0.763000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^3,x)","\frac{\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+3 a^{2} b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 b^{2} a \sin \left(d x +c \right)+b^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*a^2*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*b^2*a*sin(d*x+c)+b^3*(d*x+c))","A"
473,1,102,113,0.997000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a^{2} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 b^{2} a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{3} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+a^2*b*(2+cos(d*x+c)^2)*sin(d*x+c)+3*b^2*a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^3*sin(d*x+c))","A"
474,1,123,148,1.275000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^3,x)","\frac{\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+3 a^{2} b \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+b^{2} a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+b^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3*a^2*b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+b^2*a*(2+cos(d*x+c)^2)*sin(d*x+c)+b^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
475,1,145,171,1.489000," ","int(cos(d*x+c)^6*(a+b*sec(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{3 a^{2} b \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+3 b^{2} a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^3*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+3/5*a^2*b*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3*b^2*a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*b^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
476,1,302,230,1.239000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{8 a^{3} b \tan \left(d x +c \right)}{3 d}+\frac{4 a^{3} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{9 a^{2} b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{9 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{32 a \,b^{3} \tan \left(d x +c \right)}{15 d}+\frac{4 a \,b^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{16 a \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{b^{4} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 b^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/2*a^4*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+8/3/d*a^3*b*tan(d*x+c)+4/3/d*a^3*b*tan(d*x+c)*sec(d*x+c)^2+3/2/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)^3+9/4/d*a^2*b^2*sec(d*x+c)*tan(d*x+c)+9/4/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+32/15*a*b^3*tan(d*x+c)/d+4/5/d*a*b^3*tan(d*x+c)*sec(d*x+c)^4+16/15/d*a*b^3*tan(d*x+c)*sec(d*x+c)^2+1/6/d*b^4*tan(d*x+c)*sec(d*x+c)^5+5/24/d*b^4*tan(d*x+c)*sec(d*x+c)^3+5/16/d*b^4*sec(d*x+c)*tan(d*x+c)+5/16/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
477,1,225,167,1.336000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \tan \left(d x +c \right)}{d}+\frac{2 a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{2 a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{a \,b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{3 a \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{8 b^{4} \tan \left(d x +c \right)}{15 d}+\frac{b^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"a^4*tan(d*x+c)/d+2/d*a^3*b*sec(d*x+c)*tan(d*x+c)+2/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+4*a^2*b^2*tan(d*x+c)/d+2/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)^2+1/d*a*b^3*tan(d*x+c)*sec(d*x+c)^3+3/2*a*b^3*sec(d*x+c)*tan(d*x+c)/d+3/2/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*b^4*tan(d*x+c)+1/5/d*b^4*tan(d*x+c)*sec(d*x+c)^4+4/15/d*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
478,1,188,136,1.125000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{3} b \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{8 a \,b^{3} \tan \left(d x +c \right)}{3 d}+\frac{4 a \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/d*a^3*b*tan(d*x+c)+3/d*a^2*b^2*sec(d*x+c)*tan(d*x+c)+3/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+8/3*a*b^3*tan(d*x+c)/d+4/3/d*a*b^3*tan(d*x+c)*sec(d*x+c)^2+1/4/d*b^4*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^4*sec(d*x+c)*tan(d*x+c)+3/8/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
479,1,135,101,0.982000," ","int((a+b*sec(d*x+c))^4,x)","a^{4} x +\frac{a^{4} c}{d}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 b^{4} \tan \left(d x +c \right)}{3 d}+\frac{b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a^4*x+1/d*a^4*c+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6*a^2*b^2*tan(d*x+c)/d+2*a*b^3*sec(d*x+c)*tan(d*x+c)/d+2/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*b^4*tan(d*x+c)+1/3/d*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
480,1,114,98,0.954000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \sin \left(d x +c \right)}{d}+4 a^{3} b x +\frac{4 a^{3} b c}{d}+\frac{6 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a^4*sin(d*x+c)/d+4*a^3*b*x+4/d*a^3*b*c+6/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4*a*b^3*tan(d*x+c)/d+1/2/d*b^4*sec(d*x+c)*tan(d*x+c)+1/2/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
481,1,109,102,0.764000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{4} x}{2}+\frac{a^{4} c}{2 d}+\frac{4 a^{3} b \sin \left(d x +c \right)}{d}+6 a^{2} b^{2} x +\frac{6 a^{2} b^{2} c}{d}+\frac{4 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4} \tan \left(d x +c \right)}{d}"," ",0,"1/2*a^4*cos(d*x+c)*sin(d*x+c)/d+1/2*a^4*x+1/2/d*a^4*c+4*a^3*b*sin(d*x+c)/d+6*a^2*b^2*x+6/d*a^2*b^2*c+4/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^4*tan(d*x+c)","A"
482,1,131,109,0.839000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^4,x)","\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{2 a^{4} \sin \left(d x +c \right)}{3 d}+\frac{2 a^{3} b \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+2 a^{3} b x +\frac{2 a^{3} b c}{d}+\frac{6 a^{2} b^{2} \sin \left(d x +c \right)}{d}+4 a \,b^{3} x +\frac{4 a \,b^{3} c}{d}+\frac{b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*sin(d*x+c)*cos(d*x+c)^2*a^4+2/3*a^4*sin(d*x+c)/d+2*a^3*b*cos(d*x+c)*sin(d*x+c)/d+2*a^3*b*x+2/d*a^3*b*c+6/d*a^2*b^2*sin(d*x+c)+4*a*b^3*x+4/d*a*b^3*c+1/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
483,1,116,135,0.948000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{4 a^{3} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+6 a^{2} b^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+4 a \,b^{3} \sin \left(d x +c \right)+b^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4/3*a^3*b*(2+cos(d*x+c)^2)*sin(d*x+c)+6*a^2*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*a*b^3*sin(d*x+c)+b^4*(d*x+c))","A"
484,1,138,161,1.507000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+4 a^{3} b \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a^{2} b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 a \,b^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{4} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a^3*b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*a^2*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+4*a*b^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^4*sin(d*x+c))","A"
485,1,174,199,1.596000," ","int(cos(d*x+c)^6*(a+b*sec(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{4 a^{3} b \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+6 a^{2} b^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{4 a \,b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+b^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^4*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+4/5*a^3*b*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+6*a^2*b^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4/3*a*b^3*(2+cos(d*x+c)^2)*sin(d*x+c)+b^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
486,1,205,148,1.103000," ","int((a+b*sec(d*x+c))^5,x)","a^{5} x +\frac{a^{5} c}{d}+\frac{5 b \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{10 b^{2} a^{3} \tan \left(d x +c \right)}{d}+\frac{5 a^{2} b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{5 a^{2} b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{10 a \,b^{4} \tan \left(d x +c \right)}{3 d}+\frac{5 a \,b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{5} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{5} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"a^5*x+1/d*a^5*c+5/d*b*a^4*ln(sec(d*x+c)+tan(d*x+c))+10/d*b^2*a^3*tan(d*x+c)+5/d*a^2*b^3*sec(d*x+c)*tan(d*x+c)+5/d*a^2*b^3*ln(sec(d*x+c)+tan(d*x+c))+10/3/d*a*b^4*tan(d*x+c)+5/3/d*a*b^4*tan(d*x+c)*sec(d*x+c)^2+1/4/d*b^5*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^5*sec(d*x+c)*tan(d*x+c)+3/8/d*b^5*ln(sec(d*x+c)+tan(d*x+c))","A"
487,1,400,140,0.345000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c)),x)","\frac{2 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}-\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}-\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}"," ",0,"2/d*a^4/b^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/3/d/b/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a-1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a-1/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)-1)+1/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/b/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a-1/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)+1)-1/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
488,1,262,106,0.423000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c)),x)","-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{d \,b^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d b}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d b}"," ",0,"-2/d*a^3/b^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2+1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*a^2-1/2/d/b*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2+1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*a^2+1/2/d/b*ln(tan(1/2*d*x+1/2*c)+1)","B"
489,1,134,76,0.354000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c)),x)","\frac{2 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}"," ",0,"2/d/b^2*a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)-1/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
490,1,88,59,0.353000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c)),x)","-\frac{2 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d b}"," ",0,"-2/d/b*a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b*ln(tan(1/2*d*x+1/2*c)+1)","A"
491,1,44,40,0.385000," ","int(sec(d*x+c)/(a+b*sec(d*x+c)),x)","\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"2/d/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","A"
492,1,67,50,0.433000," ","int(1/(a+b*sec(d*x+c)),x)","-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-2/d/a*b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
493,1,102,67,0.638000," ","int(cos(d*x+c)/(a+b*sec(d*x+c)),x)","\frac{2 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"2/d*b^2/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/d/a^2*b*arctan(tan(1/2*d*x+1/2*c))","A"
494,1,222,97,0.639000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c)),x)","-\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}"," ",0,"-2/d*b^3/a^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b+1/d/a*arctan(tan(1/2*d*x+1/2*c))+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*b^2","B"
495,1,367,131,0.718000," ","int(cos(d*x+c)^3/(a+b*sec(d*x+c)),x)","\frac{2 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4}}"," ",0,"2/d/a^4*b^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b^2+4/3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*b^2+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b^2-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b-1/d/a^2*b*arctan(tan(1/2*d*x+1/2*c))-2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*b^3","B"
496,1,672,174,0.657000," ","int(cos(d*x+c)^4/(a+b*sec(d*x+c)),x)","-\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}"," ",0,"-2/d*b^5/a^5/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-5/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^2-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^3+3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-10/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^3-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^2-3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^2-10/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^3+5/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^2-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^3+3/4/d/a*arctan(tan(1/2*d*x+1/2*c))+1/d/a^3*arctan(tan(1/2*d*x+1/2*c))*b^2+2/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^4","B"
497,1,405,209,0.390000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^2,x)","\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{6 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{d \,b^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}-\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{d \,b^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}"," ",0,"2/d*a^4/b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-6/d*a^5/b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+8/d*a^3/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2+2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)-3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^2-1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2+2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)+3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^2+1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
498,1,275,155,0.451000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^2,x)","-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{4 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{3}}-\frac{1}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{3}}"," ",0,"-2/d*a^3/b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+4/d*a^4/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-6/d*a^2/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*a/b^3*ln(tan(1/2*d*x+1/2*c)-1)-1/d/b^2/(tan(1/2*d*x+1/2*c)-1)-1/d/b^2/(tan(1/2*d*x+1/2*c)+1)-2/d*a/b^3*ln(tan(1/2*d*x+1/2*c)+1)","A"
499,1,225,108,0.378000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}"," ",0,"2/d*a^2/b/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-2/d*a^3/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+4/d*a/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
500,1,118,76,0.397000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","\frac{-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \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)}}}{d}"," ",0,"1/d*(-2*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-2*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
501,1,118,77,0.339000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^2,x)","\frac{\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \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)}}}{d}"," ",0,"1/d*(2*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+2*a/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
502,1,204,100,0.486000," ","int(1/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{4 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d*b^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-4/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b^3/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
503,1,242,137,0.558000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^2,x)","\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{6 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"2/d*b^3/a^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+6/d*b^2/a/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-4/d*b^4/a^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^2*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^3*b*arctan(tan(1/2*d*x+1/2*c))","A"
504,1,362,195,0.734000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}"," ",0,"-2/d*b^4/a^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)-8/d*b^3/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+6/d*b^5/a^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b+1/d/a^2*arctan(tan(1/2*d*x+1/2*c))+6/d/a^4*arctan(tan(1/2*d*x+1/2*c))*b^2","A"
505,1,508,248,0.676000," ","int(cos(d*x+c)^3/(a+b*sec(d*x+c))^2,x)","\frac{2 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{10 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{5} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{5}}"," ",0,"2/d*b^5/a^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+10/d*b^4/a^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-8/d*b^6/a^5/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b^2+4/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+12/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*b^2+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b^2-2/d/a^3*b*arctan(tan(1/2*d*x+1/2*c))-8/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^3","B"
506,1,735,215,0.394000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^3,x)","-\frac{4 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{8 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{8 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{6 a^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}-\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}"," ",0,"-4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+6/d*a^6/b^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-15/d*a^4/b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+12/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)+3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)-1)-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)-3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
507,1,685,175,0.427000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^3,x)","\frac{2 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{6 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{3}}"," ",0,"2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-6/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+6/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2/d*a^5/b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+5/d*a^3/b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-6/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)","B"
508,1,184,136,0.401000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(a +4 b \right) a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{\left(a -4 b \right) a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2}}+\frac{\left(a^{2}+2 b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(a+4*b)*a/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(a-4*b)*a/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2+(a^2+2*b^2)/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
509,1,195,121,0.353000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^3,x)","\frac{\frac{-\frac{\left(2 a^{2}+a b +2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(2 a^{2}-a b +2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2}}-\frac{3 a b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(-1/2*(2*a^2+a*b+2*b^2)/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(2*a^2-a*b+2*b^2)/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2-3*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
510,1,186,120,0.377000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(4 a +b \right) b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(4 a -b \right) b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2}}+\frac{\left(2 a^{2}+b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(4*a+b)*b/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(4*a-b)*b/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2+(2*a^2+b^2)/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
511,1,664,160,0.422000," ","int(1/(a+b*sec(d*x+c))^3,x)","-\frac{6 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{6 a b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/d/a*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+2/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-1/d/a*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-6/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+5/d/a*b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d/a^3*b^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
512,1,702,208,0.683000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^3,x)","\frac{8 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{12 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"8/d/a*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-8/d/a*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+1/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+12/d*b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-15/d*b^4/a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+6/d*b^6/a^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^3*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-6/d/a^4*b*arctan(tan(1/2*d*x+1/2*c))","B"
513,1,827,277,0.608000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^3,x)","-\frac{10 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{6 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{10 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{6 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{20 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{29 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{12 b^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{5} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}"," ",0,"-10/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+6/d*b^6/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+10/d/a^2*b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-1/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-6/d*b^6/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-20/d/a*b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+29/d/a^3*b^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-12/d*b^7/a^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+1/d/a^3*arctan(tan(1/2*d*x+1/2*c))+12/d/a^5*arctan(tan(1/2*d*x+1/2*c))*b^2","B"
514,1,1481,299,0.432000," ","int(sec(d*x+c)^6/(a+b*sec(d*x+c))^4,x)","-\frac{6 a^{7} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 a^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{18 a^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{5 a^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{20 a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{12 a^{7} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{116 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{40 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{6 a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{18 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{5 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{20 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{8 a^{8} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{5} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{28 a^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{35 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d b \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{20 a^{2} b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{5}}-\frac{1}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{5}}"," ",0,"-6/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+18/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-5/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-20/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+12/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-116/3/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+40/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-6/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+18/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+5/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-20/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+8/d*a^8/b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-28/d*a^6/b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+35/d*a^4/b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-20/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^4/(tan(1/2*d*x+1/2*c)-1)+4/d*a/b^5*ln(tan(1/2*d*x+1/2*c)-1)-1/d/b^4/(tan(1/2*d*x+1/2*c)+1)-4/d*a/b^5*ln(tan(1/2*d*x+1/2*c)+1)","B"
515,1,1429,244,0.362000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^4,x)","\frac{2 a^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{a^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 a^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{4 a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{12 a^{2} b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{4 a^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{44 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{24 a^{2} b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{6 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{4 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{12 a^{2} b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 a^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{7 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,b^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 a \,b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}"," ",0,"2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+12/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-4/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+44/3/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-24/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+12/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-2/d*a^7/b^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+7/d*a^5/b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-8/d*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+8/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
516,1,285,207,0.406000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^4,x)","\frac{\frac{-\frac{\left(2 a^{2}+3 a b +6 b^{2}\right) a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{4 \left(a^{2}+9 b^{2}\right) a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(2 a^{2}-3 a b +6 b^{2}\right) a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}-\frac{b \left(3 a^{2}+2 b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(-1/2*(2*a^2+3*a*b+6*b^2)*a/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(a^2+9*b^2)*a/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(2*a^2-3*a*b+6*b^2)*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3-b*(3*a^2+2*b^2)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
517,1,294,191,0.347000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{\left(a^{3}+6 a^{2} b +2 b^{2} a +2 b^{3}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 \left(7 a^{2}+3 b^{2}\right) b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{\left(a^{3}-6 a^{2} b +2 b^{2} a -2 b^{3}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}+\frac{a \left(a^{2}+4 b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(a^3+6*a^2*b+2*a*b^2+2*b^3)/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(7*a^2+3*b^2)*b/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(a^3-6*a^2*b+2*a*b^2-2*b^3)/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3+a*(a^2+4*b^2)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
518,1,297,177,0.428000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^4,x)","\frac{\frac{-\frac{\left(2 a^{3}+2 a^{2} b +6 b^{2} a +b^{3}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{4 \left(3 a^{2}+7 b^{2}\right) a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(2 a^{3}-2 a^{2} b +6 b^{2} a -b^{3}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}-\frac{b \left(4 a^{2}+b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(-1/2*(2*a^3+2*a^2*b+6*a*b^2+b^3)/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(3*a^2+7*b^2)*a/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(2*a^3-2*a^2*b+6*a*b^2-b^3)/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3-b*(4*a^2+b^2)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
519,1,284,169,0.346000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{\left(6 a^{2}+3 a b +2 b^{2}\right) b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 \left(9 a^{2}+b^{2}\right) b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(6 a^{2}-3 a b +2 b^{2}\right) b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}+\frac{a \left(2 a^{2}+3 b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(6*a^2+3*a*b+2*b^2)*b/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(9*a^2+b^2)*b/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(6*a^2-3*a*b+2*b^2)*b/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3+a*(2*a^2+3*b^2)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
520,1,1408,227,0.527000," ","int(1/(a+b*sec(d*x+c))^4,x)","-\frac{12 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{4 b^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 b^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{b^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{24 b^{2} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{44 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{4 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{12 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{4 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{8 a^{2} b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{7 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"-12/d*b^2*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-4/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+6/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+1/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+24/d*b^2*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-44/3/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+4/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-12/d*b^2*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+4/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+6/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-1/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-8/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+8/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-7/d*b^5/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b^7/a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))","B"
521,1,1448,282,0.684000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^4,x)","\frac{20 b^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{5 b^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{18 b^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 b^{7} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{40 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{116 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{12 b^{7} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{20 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{5 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{18 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{20 a \,b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{35 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d a \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{28 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b^{8} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{5} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{8 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}"," ",0,"20/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+5/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-18/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-40/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+116/3/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-12/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+20/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-5/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-18/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+20/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-35/d*b^4/a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+28/d*b^6/a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-8/d*b^8/a^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/a^4*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-8/d/a^5*b*arctan(tan(1/2*d*x+1/2*c))","B"
522,1,1576,366,0.797000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^4,x)","-\frac{30 b^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 b^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{34 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{3 b^{7} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{12 b^{8} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{60 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{212 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{24 b^{8} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{30 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{34 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{3 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{12 b^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{40 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{84 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{69 b^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{20 b^{9} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \,a^{6} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{20 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{6}}"," ",0,"-30/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-6/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+34/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5-12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+60/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-212/3/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+24/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-30/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+6/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)+34/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)-40/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+84/d*b^5/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-69/d*b^7/a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+20/d*b^9/a^6/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*b+1/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*b+1/d/a^4*arctan(tan(1/2*d*x+1/2*c))+20/d/a^6*arctan(tan(1/2*d*x+1/2*c))*b^2","B"
523,1,34,27,0.399000," ","int(1/(3+5*sec(d*x+c)),x)","-\frac{5 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{6 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d}"," ",0,"-5/6/d*arctan(1/2*tan(1/2*d*x+1/2*c))+2/3/d*arctan(tan(1/2*d*x+1/2*c))","A"
524,1,63,50,0.500000," ","int(1/(3+5*sec(d*x+c))^2,x)","-\frac{25 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{48 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)}-\frac{35 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{288 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9 d}"," ",0,"-25/48/d*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+4)-35/288/d*arctan(1/2*tan(1/2*d*x+1/2*c))+2/9/d*arctan(tan(1/2*d*x+1/2*c))","A"
525,1,94,73,0.432000," ","int(1/(3+5*sec(d*x+c))^3,x)","\frac{475 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4608 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}-\frac{275 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{1152 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}-\frac{3055 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{27648 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{27 d}"," ",0,"475/4608/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)^3-275/1152/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)-3055/27648/d*arctan(1/2*tan(1/2*d*x+1/2*c))+2/27/d*arctan(tan(1/2*d*x+1/2*c))","A"
526,1,125,96,0.551000," ","int(1/(3+5*sec(d*x+c))^4,x)","-\frac{25925 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{221184 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{3575 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6912 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{17675 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{13824 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{11215 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{1327104 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{81 d}"," ",0,"-25925/221184/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^5-3575/6912/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^3-17675/13824/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)-11215/1327104/d*arctan(1/2*tan(1/2*d*x+1/2*c))+2/81/d*arctan(tan(1/2*d*x+1/2*c))","A"
527,1,51,60,0.423000," ","int(1/(5+3*sec(d*x+c)),x)","\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{20 d}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{20 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d}"," ",0,"3/20/d*ln(tan(1/2*d*x+1/2*c)-2)-3/20/d*ln(tan(1/2*d*x+1/2*c)+2)+2/5/d*arctan(tan(1/2*d*x+1/2*c))","A"
528,1,87,83,0.481000," ","int(1/(5+3*sec(d*x+c))^2,x)","-\frac{9}{160 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{123 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{1600 d}-\frac{9}{160 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{123 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{1600 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{25 d}"," ",0,"-9/160/d/(tan(1/2*d*x+1/2*c)-2)+123/1600/d*ln(tan(1/2*d*x+1/2*c)-2)-9/160/d/(tan(1/2*d*x+1/2*c)+2)-123/1600/d*ln(tan(1/2*d*x+1/2*c)+2)+2/25/d*arctan(tan(1/2*d*x+1/2*c))","A"
529,1,123,106,0.434000," ","int(1/(5+3*sec(d*x+c))^3,x)","-\frac{27}{2560 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}-\frac{1323}{25600 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{8361 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{256000 d}+\frac{27}{2560 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}-\frac{1323}{25600 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{8361 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{256000 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{125 d}"," ",0,"-27/2560/d/(tan(1/2*d*x+1/2*c)-2)^2-1323/25600/d/(tan(1/2*d*x+1/2*c)-2)+8361/256000/d*ln(tan(1/2*d*x+1/2*c)-2)+27/2560/d/(tan(1/2*d*x+1/2*c)+2)^2-1323/25600/d/(tan(1/2*d*x+1/2*c)+2)-8361/256000/d*ln(tan(1/2*d*x+1/2*c)+2)+2/125/d*arctan(tan(1/2*d*x+1/2*c))","A"
530,1,159,129,0.552000," ","int(1/(5+3*sec(d*x+c))^4,x)","-\frac{27}{10240 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{3}}-\frac{1431}{102400 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}-\frac{69093}{2048000 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{278151 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{20480000 d}-\frac{27}{10240 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{3}}+\frac{1431}{102400 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}-\frac{69093}{2048000 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{278151 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{20480000 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{625 d}"," ",0,"-27/10240/d/(tan(1/2*d*x+1/2*c)-2)^3-1431/102400/d/(tan(1/2*d*x+1/2*c)-2)^2-69093/2048000/d/(tan(1/2*d*x+1/2*c)-2)+278151/20480000/d*ln(tan(1/2*d*x+1/2*c)-2)-27/10240/d/(tan(1/2*d*x+1/2*c)+2)^3+1431/102400/d/(tan(1/2*d*x+1/2*c)+2)^2-69093/2048000/d/(tan(1/2*d*x+1/2*c)+2)-278151/20480000/d*ln(tan(1/2*d*x+1/2*c)+2)+2/625/d*arctan(tan(1/2*d*x+1/2*c))","A"
531,1,1584,262,1.793000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 b^{3}-9 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{4}\left(d x +c \right)\right) a^{2} b -\left(\cos^{2}\left(d x +c \right)\right) a^{2} b -9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}+9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}-2 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+2 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b +5 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)+4 \cos \left(d x +c \right) a \,b^{2}+2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -7 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) b^{3}+2 \left(\cos^{4}\left(d x +c \right)\right) a^{3}\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} b^{2}}"," ",0,"2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-cos(d*x+c)^2*a^2*b+3*b^3-9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+5*a*b^2*cos(d*x+c)^3-2*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-2*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+4*cos(d*x+c)*a*b^2+2*a^2*cos(d*x+c)^3*b-cos(d*x+c)^4*a^2*b-9*cos(d*x+c)^4*a*b^2+2*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-7*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-2*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+2*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-7*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-2*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-2*cos(d*x+c)^3*a^3+6*cos(d*x+c)^2*b^3-9*cos(d*x+c)^3*b^3+2*cos(d*x+c)^4*a^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b^2","B"
532,1,913,215,1.446000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\left(\cos^{3}\left(d x +c \right)\right) a^{2}+\left(\cos^{3}\left(d x +c \right)\right) a b -\left(\cos^{2}\left(d x +c \right)\right) a^{2}+\left(\cos^{2}\left(d x +c \right)\right) a b +\left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 a b \cos \left(d x +c \right)-b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} b}"," ",0,"-2/3/d*(-1+cos(d*x+c))^2*(sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+cos(d*x+c)^3*a^2+cos(d*x+c)^3*a*b-cos(d*x+c)^2*a^2+cos(d*x+c)^2*a*b+cos(d*x+c)^2*b^2-2*a*b*cos(d*x+c)-b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5/b","B"
533,1,814,191,1.360000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +a \left(\cos^{2}\left(d x +c \right)\right)-a \cos \left(d x +c \right)+b \cos \left(d x +c \right)-b \right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+a*cos(d*x+c)^2-a*cos(d*x+c)+b*cos(d*x+c)-b)/sin(d*x+c)^5/(b+a*cos(d*x+c))","B"
534,1,215,116,1.421000," ","int((a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 a \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1+cos(d*x+c))^2*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*a*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2)))*(-1+cos(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
535,1,826,301,1.657000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +a \left(\cos^{3}\left(d x +c \right)\right)-a \left(\cos^{2}\left(d x +c \right)\right)+\left(\cos^{2}\left(d x +c \right)\right) b -b \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+a*cos(d*x+c)^3-a*cos(d*x+c)^2+cos(d*x+c)^2*b-b*cos(d*x+c))*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
536,1,1254,355,1.433000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+2 \left(\cos^{4}\left(d x +c \right)\right) a^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) a^{2}-\left(\cos^{2}\left(d x +c \right)\right) a b +\left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 a b \cos \left(d x +c \right)-\cos \left(d x +c \right) b^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} a}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+2*cos(d*x+c)^4*a^2+3*cos(d*x+c)^3*a*b-2*cos(d*x+c)^2*a^2-cos(d*x+c)^2*a*b+cos(d*x+c)^2*b^2-2*a*b*cos(d*x+c)-cos(d*x+c)*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
537,1,2522,367,2.125000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-2/315/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-4*cos(d*x+c)^6*a^4*b-147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-53*cos(d*x+c)^2*a^2*b^3+8*cos(d*x+c)^6*a^5-8*cos(d*x+c)^5*a^5+147*cos(d*x+c)^5*b^5-98*cos(d*x+c)^4*b^5-14*cos(d*x+c)^2*b^5+cos(d*x+c)^3*a^3*b^2-52*cos(d*x+c)^3*a*b^4-35*b^5+33*cos(d*x+c)^6*a^3*b^2+88*cos(d*x+c)^6*a^2*b^3+147*cos(d*x+c)^6*a*b^4+8*cos(d*x+c)^5*a^4*b-34*cos(d*x+c)^5*a^3*b^2+33*cos(d*x+c)^5*a^2*b^3-10*cos(d*x+c)^5*a*b^4-4*cos(d*x+c)^4*a^4*b-68*cos(d*x+c)^4*a^2*b^3-85*cos(d*x+c)*a*b^4+8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+2*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+33*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+186*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-33*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-33*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+8*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+2*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+33*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+186*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-8*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-33*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-33*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-8*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5)/(b+a*cos(d*x+c))/cos(d*x+c)^4/sin(d*x+c)^5/b^3","B"
538,1,1852,308,1.675000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(27 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+15 b^{4}-25 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}-6 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}-6 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}-25 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}+39 \cos \left(d x +c \right) a \,b^{3}-82 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+6 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +68 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}-82 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}-3 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -25 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}+6 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b -51 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-82 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-6 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +82 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}+82 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}+6 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b -51 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-82 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-6 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +82 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}+82 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}+55 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}-3 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -25 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right) b^{4}+6 \left(\cos^{5}\left(d x +c \right)\right) a^{4}-6 \left(\cos^{4}\left(d x +c \right)\right) a^{4}\right)}{105 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{5} b^{2}}"," ",0,"2/105/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(27*cos(d*x+c)^2*a^2*b^2+55*cos(d*x+c)^4*a^2*b^2-25*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+15*b^4-6*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+6*cos(d*x+c)^4*a^3*b-82*cos(d*x+c)^4*a*b^3+68*cos(d*x+c)^3*a*b^3+39*cos(d*x+c)*a*b^3-3*cos(d*x+c)^5*a^3*b-82*cos(d*x+c)^5*a^2*b^2-25*cos(d*x+c)^5*a*b^3-3*cos(d*x+c)^3*a^3*b-6*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4-25*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+6*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-51*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-82*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-6*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+82*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+82*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+6*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-51*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-82*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-6*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+82*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+82*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-6*cos(d*x+c)^4*a^4-25*b^4*cos(d*x+c)^4+10*cos(d*x+c)^2*b^4+6*cos(d*x+c)^5*a^4)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b^2","B"
539,1,1566,252,1.453000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +4 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+\left(\cos^{4}\left(d x +c \right)\right) a^{3}+2 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +3 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{3}\left(d x +c \right)\right) a^{3}+a^{2} \left(\cos^{3}\left(d x +c \right)\right) b +3 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -2 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-3 \cos \left(d x +c \right) a \,b^{2}-b^{3}\right)}{5 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} b}"," ",0,"-2/5/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+4*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+4*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+3*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-3*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-3*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+cos(d*x+c)^4*a^3+2*cos(d*x+c)^4*a^2*b+3*cos(d*x+c)^4*a*b^2-cos(d*x+c)^3*a^3+a^2*cos(d*x+c)^3*b+3*cos(d*x+c)^3*b^3-3*cos(d*x+c)^2*a^2*b-2*cos(d*x+c)^2*b^3-3*cos(d*x+c)*a*b^2-b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b","B"
540,1,1106,223,1.269000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+4 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-4 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-4 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +4 \left(\cos^{3}\left(d x +c \right)\right) a^{2}+\left(\cos^{3}\left(d x +c \right)\right) a b -4 \left(\cos^{2}\left(d x +c \right)\right) a^{2}+4 \left(\cos^{2}\left(d x +c \right)\right) a b +\left(\cos^{2}\left(d x +c \right)\right) b^{2}-5 a b \cos \left(d x +c \right)-b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5}}"," ",0,"-2/3/d*(-1+cos(d*x+c))^2*(3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+4*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-4*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-4*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+4*cos(d*x+c)^3*a^2+cos(d*x+c)^3*a*b-4*cos(d*x+c)^2*a^2+4*cos(d*x+c)^2*a*b+cos(d*x+c)^2*b^2-5*a*b*cos(d*x+c)-b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5","B"
541,1,1199,282,1.351000," ","int((a+b*sec(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-\left(\cos^{2}\left(d x +c \right)\right) a b +a b \cos \left(d x +c \right)-\cos \left(d x +c \right) b^{2}+b^{2}\right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-cos(d*x+c)^2*a*b+a*b*cos(d*x+c)-cos(d*x+c)*b^2+b^2)/sin(d*x+c)^5/(b+a*cos(d*x+c))","B"
542,1,1026,305,1.263000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a b -4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-4 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) a^{2}-\left(\cos^{2}\left(d x +c \right)\right) a^{2}+\left(\cos^{2}\left(d x +c \right)\right) a b -a b \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+6*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-4*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^3*a^2-cos(d*x+c)^2*a^2+cos(d*x+c)^2*a*b-a*b*cos(d*x+c))*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
543,1,1440,349,1.233000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +5 \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+6 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+5 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+2 \left(\cos^{4}\left(d x +c \right)\right) a^{2}+7 \left(\cos^{3}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) a^{2}-5 \left(\cos^{2}\left(d x +c \right)\right) a b +5 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 a b \cos \left(d x +c \right)-5 \cos \left(d x +c \right) b^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(5*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+5*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+5*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+2*cos(d*x+c)^4*a^2+7*cos(d*x+c)^3*a*b-2*cos(d*x+c)^2*a^2-5*cos(d*x+c)^2*a*b+5*cos(d*x+c)^2*b^2-2*a*b*cos(d*x+c)-5*cos(d*x+c)*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
544,1,2807,421,2.301000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/693/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-135*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^6+8*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^6-8*cos(d*x+c)^6*a^5*b+63*b^6+307*cos(d*x+c)^6*a^2*b^4-51*cos(d*x+c)^6*a^3*b^3-741*cos(d*x+c)^6*a*b^5+4*cos(d*x+c)^5*a^5*b+140*cos(d*x+c)^5*a^3*b^3+566*cos(d*x+c)^5*a*b^5-cos(d*x+c)^4*a^4*b^2+160*cos(d*x+c)^4*a^2*b^4+116*cos(d*x+c)^3*a^3*b^3+86*cos(d*x+c)^3*a*b^5+274*cos(d*x+c)^2*a^2*b^4+224*cos(d*x+c)*a*b^5+4*cos(d*x+c)^7*a^5*b-51*cos(d*x+c)^7*a^4*b^2-205*cos(d*x+c)^7*a^3*b^3-741*cos(d*x+c)^7*a^2*b^4-135*cos(d*x+c)^7*a*b^5+52*cos(d*x+c)^6*a^4*b^2-135*cos(d*x+c)^6*b^6+54*cos(d*x+c)^4*b^6-8*cos(d*x+c)^7*a^6+8*cos(d*x+c)^6*a^6+18*cos(d*x+c)^2*b^6+8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^6-135*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^6-2*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2-51*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3-663*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4-741*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5+8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b+51*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2+51*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3+741*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4+741*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5-8*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b-2*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2-51*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3-663*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4-741*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5+8*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b+51*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2+51*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3+741*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4+741*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5-8*cos(d*x+c)^6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b)/(b+a*cos(d*x+c))/cos(d*x+c)^5/sin(d*x+c)^5/b^3","B"
545,1,2523,361,1.875000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"2/315/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-10*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-5*cos(d*x+c)^6*a^4*b+147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+170*cos(d*x+c)^2*a^2*b^3+10*cos(d*x+c)^6*a^5-10*cos(d*x+c)^5*a^5-147*cos(d*x+c)^5*b^5+98*cos(d*x+c)^4*b^5+14*cos(d*x+c)^2*b^5+80*cos(d*x+c)^3*a^3*b^2+82*cos(d*x+c)^3*a*b^4+35*b^5-279*cos(d*x+c)^6*a^3*b^2-163*cos(d*x+c)^6*a^2*b^3-147*cos(d*x+c)^6*a*b^4+10*cos(d*x+c)^5*a^4*b+199*cos(d*x+c)^5*a^3*b^2-279*cos(d*x+c)^5*a^2*b^3-65*cos(d*x+c)^5*a*b^4-5*cos(d*x+c)^4*a^4*b+272*cos(d*x+c)^4*a^2*b^3+130*cos(d*x+c)*a*b^4+10*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-155*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-279*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-261*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-10*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+279*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+279*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+10*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-155*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-279*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-261*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-10*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+279*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+279*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-10*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5+147*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-147*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5)/(b+a*cos(d*x+c))/cos(d*x+c)^4/sin(d*x+c)^5/b^2","B"
546,1,1852,299,1.528000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-18 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-3 b^{4}-3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}-3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}+5 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}-12 \cos \left(d x +c \right) a \,b^{3}-3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b -29 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-29 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-29 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}+9 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b +29 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b -22 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+29 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+5 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +27 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}+29 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-29 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +27 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}+29 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}-11 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}-12 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b +5 b^{4} \left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right) b^{4}+3 \left(\cos^{5}\left(d x +c \right)\right) a^{4}-3 \left(\cos^{4}\left(d x +c \right)\right) a^{4}\right)}{21 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{5} b}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-18*cos(d*x+c)^2*a^2*b^2-11*cos(d*x+c)^4*a^2*b^2+5*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4-3*b^4-3*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+3*cos(d*x+c)^4*a^3*b+29*cos(d*x+c)^4*a*b^3-22*cos(d*x+c)^3*a*b^3-12*cos(d*x+c)*a*b^3+9*cos(d*x+c)^5*a^3*b+29*cos(d*x+c)^5*a^2*b^2+5*cos(d*x+c)^5*a*b^3-12*cos(d*x+c)^3*a^3*b-3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+5*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+3*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+27*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+29*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-3*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-29*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-29*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+27*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+29*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-29*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-29*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-3*cos(d*x+c)^4*a^4+5*b^4*cos(d*x+c)^4-2*cos(d*x+c)^2*b^4+3*cos(d*x+c)^5*a^4)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b","B"
547,1,1775,266,1.353000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-3 b^{3}+9 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+11 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b -9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-23 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}-9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-23 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}-23 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+23 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b -6 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+5 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)-14 \cos \left(d x +c \right) a \,b^{2}+23 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -23 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +17 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-34 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +23 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+17 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-23 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+15 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+15 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) b^{3}+23 \left(\cos^{4}\left(d x +c \right)\right) a^{3}\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5}}"," ",0,"-2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-34*cos(d*x+c)^2*a^2*b-3*b^3+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+5*a*b^2*cos(d*x+c)^3-23*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-23*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-14*cos(d*x+c)*a*b^2+23*a^2*cos(d*x+c)^3*b+11*cos(d*x+c)^4*a^2*b+9*cos(d*x+c)^4*a*b^2+15*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+15*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+23*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+17*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-23*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+23*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+17*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-23*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-23*cos(d*x+c)^3*a^3-6*cos(d*x+c)^2*b^3+9*cos(d*x+c)^3*b^3+23*cos(d*x+c)^4*a^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5","B"
548,1,1514,317,1.281000," ","int((a+b*sec(d*x+c))^(5/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-6 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+7 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +7 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-9 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -7 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-7 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b -a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)+7 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -7 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{2}\left(d x +c \right)\right) b^{3}+8 \cos \left(d x +c \right) a \,b^{2}+b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5}}"," ",0,"2/3/d*(-1+cos(d*x+c))^2*(7*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+7*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-7*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-6*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3+7*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+7*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-7*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-6*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3-7*a^2*cos(d*x+c)^3*b-a*b^2*cos(d*x+c)^3+7*cos(d*x+c)^2*a^2*b-7*cos(d*x+c)^2*a*b^2-cos(d*x+c)^2*b^3+8*cos(d*x+c)*a*b^2+b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5","B"
549,1,1640,324,1.363000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+10 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \sin \left(d x +c \right)+a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sin \left(d x +c \right)-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)+2 b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)+10 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) a^{3}-\left(\cos^{2}\left(d x +c \right)\right) a^{3}+\left(\cos^{2}\left(d x +c \right)\right) a^{2} b +2 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-\cos \left(d x +c \right) a^{2} b -2 \cos \left(d x +c \right) a \,b^{2}+2 \cos \left(d x +c \right) b^{3}-2 b^{3}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-6*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+6*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+10*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+2*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+cos(d*x+c)^3*a^3-cos(d*x+c)^2*a^3+cos(d*x+c)^2*a^2*b+2*cos(d*x+c)^2*a*b^2-cos(d*x+c)*a^2*b-2*cos(d*x+c)*a*b^2+2*cos(d*x+c)*b^3-2*b^3)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
550,1,1646,358,1.233000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(9 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +9 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -24 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+30 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+9 a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +9 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -4 a^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)-24 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)+8 b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)+8 a^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)+30 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a +2 \left(\cos^{4}\left(d x +c \right)\right) a^{3}+11 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b -2 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-9 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +9 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-2 \cos \left(d x +c \right) a^{2} b -9 \cos \left(d x +c \right) a \,b^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(9*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+9*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-24*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3+30*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2+9*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+9*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-4*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-24*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+8*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+8*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))+30*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a+2*cos(d*x+c)^4*a^3+11*a^2*cos(d*x+c)^3*b-2*cos(d*x+c)^2*a^3-9*cos(d*x+c)^2*a^2*b+9*cos(d*x+c)^2*a*b^2-2*cos(d*x+c)*a^2*b-9*cos(d*x+c)*a*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
551,1,1881,415,1.278000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-30 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{3}-34 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b -8 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+48 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \sin \left(d x +c \right)-33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sin \left(d x +c \right)+48 b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)-33 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-59 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)+26 \cos \left(d x +c \right) a \,b^{2}-16 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -33 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+76 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -26 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+16 \cos \left(d x +c \right) a^{2} b -120 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +18 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -30 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-16 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-33 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-16 a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -33 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +76 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)-26 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)-120 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+33 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-8 \left(\cos^{5}\left(d x +c \right)\right) a^{3}+33 \cos \left(d x +c \right) b^{3}+16 \left(\cos^{2}\left(d x +c \right)\right) a^{3}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{24 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"1/24/d*(-1+cos(d*x+c))^2*(18*cos(d*x+c)^2*a^2*b-16*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-30*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3-33*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-59*a*b^2*cos(d*x+c)^3-8*cos(d*x+c)^5*a^3+48*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+48*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+33*cos(d*x+c)^2*a*b^2+26*cos(d*x+c)*a*b^2-34*cos(d*x+c)^4*a^2*b-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-16*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-33*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+76*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-26*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+16*cos(d*x+c)*a^2*b-120*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b-30*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-16*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-33*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+76*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-26*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-120*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-8*cos(d*x+c)^3*a^3-33*cos(d*x+c)^2*b^3+16*cos(d*x+c)^2*a^3+33*cos(d*x+c)*b^3)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
552,1,2330,481,1.467000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/192/d*(-1+cos(d*x+c))^2*(-30*cos(d*x+c)^2*a^2*b^2-254*cos(d*x+c)^4*a^2*b^2-288*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^4+30*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^4+284*cos(d*x+c)^2*a^3*b+15*cos(d*x+c)^2*a*b^3+284*cos(d*x+c)*a^2*b^2+72*cos(d*x+c)*a^3*b-133*cos(d*x+c)^3*a*b^3+118*cos(d*x+c)*a*b^3-184*cos(d*x+c)^5*a^3*b-172*cos(d*x+c)^3*a^3*b+144*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)-288*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)-48*cos(d*x+c)^6*a^4+72*cos(d*x+c)^2*a^4+15*cos(d*x+c)*b^4-72*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+644*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-118*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-284*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-284*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*a^2*sin(d*x+c)-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*a*sin(d*x+c)-720*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+144*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-72*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b+644*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2-118*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b^3-284*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-284*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-720*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-24*cos(d*x+c)^4*a^4-15*cos(d*x+c)^2*b^4)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
553,1,2185,364,1.501000," ","int((a+b*sec(d*x+c))^(7/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(74*cos(d*x+c)^2*a^2*b^2-16*cos(d*x+c)^4*a^2*b^2-9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+3*b^4+15*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-58*cos(d*x+c)^4*a^3*b-9*cos(d*x+c)^4*a*b^3-10*cos(d*x+c)^3*a*b^3+19*cos(d*x+c)*a*b^3+58*cos(d*x+c)^3*a^3*b-58*cos(d*x+c)^3*a^2*b^2-60*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-58*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-22*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+58*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+58*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+9*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+9*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-30*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4+15*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-9*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+9*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-30*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4-9*cos(d*x+c)^3*b^4-60*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-58*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-22*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+58*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+58*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+6*cos(d*x+c)^2*b^4)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5","B"
554,1,1852,325,1.761000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(6 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+15 b^{4}-48 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}-48 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{4}-25 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}-3 \cos \left(d x +c \right) a \,b^{3}-48 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b -44 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-44 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-24 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b +44 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+48 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b -16 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+44 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}-25 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}+48 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +44 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}+48 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b +12 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-48 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3} b -50 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}-24 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b +12 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-44 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-25 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{4}-25 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right) b^{4}+48 \left(\cos^{5}\left(d x +c \right)\right) a^{4}-48 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+44 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{3}-44 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b^{2}\right)}{105 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)^{5} b^{4}}"," ",0,"2/105/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(6*cos(d*x+c)^2*a^2*b^2-50*cos(d*x+c)^4*a^2*b^2-25*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+15*b^4-48*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+48*cos(d*x+c)^4*a^3*b+44*cos(d*x+c)^4*a*b^3-16*cos(d*x+c)^3*a*b^3-3*cos(d*x+c)*a*b^3-24*cos(d*x+c)^5*a^3*b+44*cos(d*x+c)^5*a^2*b^2-25*cos(d*x+c)^5*a*b^3-24*cos(d*x+c)^3*a^3*b-48*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4-25*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4+48*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+12*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+44*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-48*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-44*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-44*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+48*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+12*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+44*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-48*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-44*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-44*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3-48*cos(d*x+c)^4*a^4-25*b^4*cos(d*x+c)^4+10*cos(d*x+c)^2*b^4+48*cos(d*x+c)^5*a^4)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b^4","B"
555,1,1584,271,1.665000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 b^{3}-9 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+4 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +8 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}+9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}+8 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}+8 \left(\cos^{3}\left(d x +c \right)\right) a^{3}-8 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b +6 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+10 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)-\cos \left(d x +c \right) a \,b^{2}-8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{3}-8 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b +9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}-9 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-8 \left(\cos^{4}\left(d x +c \right)\right) a^{3}\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} b^{3}}"," ",0,"2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(4*cos(d*x+c)^2*a^2*b+3*b^3-9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+10*a*b^2*cos(d*x+c)^3+8*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3-9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+8*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-cos(d*x+c)*a*b^2-8*a^2*cos(d*x+c)^3*b+4*cos(d*x+c)^4*a^2*b-9*cos(d*x+c)^4*a*b^2-8*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-2*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+8*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2-8*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-2*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+8*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+9*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+8*cos(d*x+c)^3*a^3+6*cos(d*x+c)^2*b^3-9*cos(d*x+c)^3*b^3-8*cos(d*x+c)^4*a^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b^3","B"
556,1,919,218,1.607000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+2 \left(\cos^{3}\left(d x +c \right)\right) a^{2}-\left(\cos^{3}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) a^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) a b -\left(\cos^{2}\left(d x +c \right)\right) b^{2}-a b \cos \left(d x +c \right)+b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} b^{2}}"," ",0,"2/3/d*(-1+cos(d*x+c))^2*(-2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+2*cos(d*x+c)^3*a^2-cos(d*x+c)^3*a*b-2*cos(d*x+c)^2*a^2+2*cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2-a*b*cos(d*x+c)+b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5/b^2","B"
557,1,639,186,1.395000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +a \left(\cos^{2}\left(d x +c \right)\right)-a \cos \left(d x +c \right)+b \cos \left(d x +c \right)-b \right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right) b}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+a*cos(d*x+c)^2-a*cos(d*x+c)+b*cos(d*x+c)-b)/sin(d*x+c)^5/(b+a*cos(d*x+c))/b","B"
558,1,143,90,1.118000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"2/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
559,1,178,97,1.290000," ","int(1/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)\right) \left(-1+\cos \left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1+cos(d*x+c))^2*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2)))*(-1+cos(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
560,1,649,309,1.419000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+a \left(\cos^{3}\left(d x +c \right)\right)-a \left(\cos^{2}\left(d x +c \right)\right)+\left(\cos^{2}\left(d x +c \right)\right) b -b \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} a}"," ",0,"-1/d*(-1+cos(d*x+c))^2*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+a*cos(d*x+c)^3-a*cos(d*x+c)^2+cos(d*x+c)^2*b-b*cos(d*x+c))*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
561,1,1259,360,1.392000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+6 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +8 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-3 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+2 \left(\cos^{4}\left(d x +c \right)\right) a^{2}-\left(\cos^{3}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) a b -3 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 a b \cos \left(d x +c \right)+3 \cos \left(d x +c \right) b^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+8*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-3*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+2*cos(d*x+c)^4*a^2-cos(d*x+c)^3*a*b-2*cos(d*x+c)^2*a^2+3*cos(d*x+c)^2*a*b-3*cos(d*x+c)^2*b^2-2*a*b*cos(d*x+c)+3*cos(d*x+c)*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a^2","B"
562,1,2480,367,2.041000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/5/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(8*cos(d*x+c)^2*a^4*b+8*cos(d*x+c)^3*a^2*b^3+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^5-6*cos(d*x+c)^2*a^2*b^3-2*cos(d*x+c)*a^3*b^2-16*cos(d*x+c)^3*a^4*b+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^5-6*cos(d*x+c)^3*a^3*b^2-5*cos(d*x+c)^3*a*b^4-b^5+a^2*b^3+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^5+8*cos(d*x+c)^4*a^4*b-3*cos(d*x+c)^4*a^2*b^3+2*cos(d*x+c)*a*b^4+8*cos(d*x+c)^4*a^3*b^2+3*cos(d*x+c)^4*a*b^4-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^5+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^5-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^4-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^4+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^4*b-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3*b^2-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^4*b-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3*b^2-2*cos(d*x+c)^2*b^5-16*cos(d*x+c)^4*a^5+16*cos(d*x+c)^3*a^5+3*cos(d*x+c)^3*b^5-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^4+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b^3-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^4+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^2/(a-b)/(a+b)/b^4","B"
563,1,1792,297,1.655000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(4 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+b^{4}-a^{2} b^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3}+4 \cos \left(d x +c \right) a^{3} b +5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b^{2}+8 \left(\cos^{2}\left(d x +c \right)\right) a^{4}-4 \cos \left(d x +c \right) a \,b^{3}-8 \left(\cos^{2}\left(d x +c \right)\right) a^{3} b -\left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}-2 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{2} b^{2}-5 \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a -\sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{4}+8 \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{4}+8 \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{4}-\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}-8 \left(\cos^{3}\left(d x +c \right)\right) a^{4}-8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b -2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}-5 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{3}-\left(\cos^{2}\left(d x +c \right)\right) b^{4}-8 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{3} b +5 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a \,b^{3}+8 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{3} b -5 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a^{2} b^{2}+5 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{3}+8 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b -5 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \left(a -b \right) \left(a +b \right) b^{3}}"," ",0,"-1/3/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-4*cos(d*x+c)^2*a^2*b^2-sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+b^4-a^2*b^2-8*cos(d*x+c)^2*a^3*b+5*cos(d*x+c)^2*a*b^3+4*cos(d*x+c)*a^3*b+8*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-cos(d*x+c)^3*a*b^3-4*cos(d*x+c)*a*b^3+4*cos(d*x+c)^3*a^3*b-8*cos(d*x+c)^3*a^4+8*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4+5*cos(d*x+c)^3*a^2*b^2-8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-2*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+5*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+8*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-5*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-5*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+8*cos(d*x+c)^2*a^4-sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-8*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2+5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b^3+8*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2-5*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-cos(d*x+c)^2*b^4)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)/(a-b)/(a+b)/b^3","B"
564,1,1451,237,1.510000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \sin \left(d x +c \right)-2 a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)-b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)+2 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-\left(\cos^{2}\left(d x +c \right)\right) a^{2} b -\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-2 a^{3} \cos \left(d x +c \right)+2 \cos \left(d x +c \right) a^{2} b +\cos \left(d x +c \right) a \,b^{2}-\cos \left(d x +c \right) b^{3}-a^{2} b +b^{3}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b^{2} \left(a +b \right) \left(a -b \right)}"," ",0,"-1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-2*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+2*cos(d*x+c)^2*a^3-cos(d*x+c)^2*a^2*b-cos(d*x+c)^2*a*b^2-2*a^3*cos(d*x+c)+2*cos(d*x+c)*a^2*b+cos(d*x+c)*a*b^2-cos(d*x+c)*b^3-a^2*b+b^3)/(b+a*cos(d*x+c))/sin(d*x+c)/b^2/(a+b)/(a-b)","B"
565,1,837,217,1.213000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) a^{2}-\left(\cos^{2}\left(d x +c \right)\right) a b -a^{2} \cos \left(d x +c \right)+a b \cos \left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b \left(a +b \right) \left(a -b \right)}"," ",0,"1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+cos(d*x+c)^2*a^2-cos(d*x+c)^2*a*b-a^2*cos(d*x+c)+a*b*cos(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)/b/(a+b)/(a-b)","B"
566,1,817,216,1.258000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+a \left(\cos^{2}\left(d x +c \right)\right)-\left(\cos^{2}\left(d x +c \right)\right) b -a \cos \left(d x +c \right)+b \cos \left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \left(a -b \right) \left(a +b \right)}"," ",0,"-1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+a*cos(d*x+c)^2-cos(d*x+c)^2*b-a*cos(d*x+c)+b*cos(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)/(a-b)/(a+b)","B"
567,1,1209,318,1.331000," ","int(1/(a+b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -\EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) a b -\left(\cos^{2}\left(d x +c \right)\right) b^{2}-a b \cos \left(d x +c \right)+\cos \left(d x +c \right) b^{2}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \left(a +b \right) \left(a -b \right)}"," ",0,"1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2-a*b*cos(d*x+c)+cos(d*x+c)*b^2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a+b)/(a-b)","B"
568,1,1662,365,1.391000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\left(\cos^{3}\left(d x +c \right)\right) a^{3}-6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \sin \left(d x +c \right)+6 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{3}-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-\left(\cos^{2}\left(d x +c \right)\right) a^{3}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)-2 \cos \left(d x +c \right) a \,b^{2}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\cos \left(d x +c \right) a^{2} b +\left(\cos^{2}\left(d x +c \right)\right) a^{2} b -3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-3 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+6 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) b^{3}\right)}{2 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} \left(a +b \right) \left(a -b \right)}"," ",0,"-1/2/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)^2*a^2*b+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3-3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-a*b^2*cos(d*x+c)^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+3*cos(d*x+c)^2*a*b^2-2*cos(d*x+c)*a*b^2+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-cos(d*x+c)*a^2*b-6*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b+6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-3*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+cos(d*x+c)^3*a^3-3*cos(d*x+c)^2*b^3-cos(d*x+c)^2*a^3+3*cos(d*x+c)*b^3)/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/(a+b)/(a-b)","B"
569,1,2298,425,1.437000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/8/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-5*cos(d*x+c)^2*a^2*b^2-2*cos(d*x+c)^4*a^2*b^2+8*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^4-30*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^4+7*cos(d*x+c)^2*a^3*b-15*cos(d*x+c)^2*a*b^3+7*cos(d*x+c)*a^2*b^2-2*cos(d*x+c)*a^3*b+5*cos(d*x+c)^3*a*b^3+10*cos(d*x+c)*a*b^3-5*cos(d*x+c)^3*a^3*b-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)-30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)-2*cos(d*x+c)^2*a^4-15*cos(d*x+c)*b^4+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*a^2*sin(d*x+c)+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*a*sin(d*x+c)+22*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2-10*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b^3-7*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-7*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+22*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^4*a^4+15*cos(d*x+c)^2*b^4)/(b+a*cos(d*x+c))/sin(d*x+c)/a^3/(a+b)/(a-b)","B"
570,1,4176,393,2.040000," ","int(sec(d*x+c)^5/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"1/3/d*4^(1/2)*(-8*cos(d*x+c)^4*a^6*b+13*cos(d*x+c)^4*a^4*b^3+8*cos(d*x+c)^4*a^3*b^4-cos(d*x+c)^4*a^2*b^5+32*cos(d*x+c)^3*a^6*b+18*cos(d*x+c)^3*a^5*b^2-56*cos(d*x+c)^3*a^4*b^3+8*cos(d*x+c)^3*a^3*b^4+16*cos(d*x+c)^3*a^2*b^5-2*cos(d*x+c)^3*a*b^6-24*cos(d*x+c)^2*a^6*b+16*cos(d*x+c)^2*a^5*b^2+42*cos(d*x+c)^2*a^4*b^3-28*cos(d*x+c)^2*a^3*b^4-13*cos(d*x+c)^2*a^2*b^5+8*cos(d*x+c)^2*a*b^6-6*cos(d*x+c)*a^5*b^2+12*cos(d*x+c)*a^3*b^4-16*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^7-28*cos(d*x+c)^4*a^5*b^2-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^7-6*cos(d*x+c)*a*b^6-16*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^7-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^7-2*b^5*a^2+a^4*b^3-7*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b^4+28*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3+28*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^4-8*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5-8*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6-16*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b-16*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b^2+8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^5-cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^6-16*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^6*b+28*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b^2+28*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*b^3-8*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^4-8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^5+16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^6*b+20*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^5*b^2-24*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*b^3-35*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b^4+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^5+7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^6-32*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b+12*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b^2+56*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3+20*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^4-16*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5-8*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6+16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^5*b^2+4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*b^3-28*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b^4-7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^5+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^6+16*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^6*b+4*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^5*b^2-28*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*b^3+16*cos(d*x+c)^4*a^7-16*cos(d*x+c)^3*a^7-cos(d*x+c)^2*b^7+b^7)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/cos(d*x+c)/(a-b)^2/(a+b)^2/b^4","B"
571,1,3674,332,1.778000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"1/3/d*4^(1/2)*(8*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6-6*b^4*a^2+3*b^6+8*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6+8*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+8*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5-8*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+15*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+3*a^4*b^2+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^5+16*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^5*b-30*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b^3+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^5-8*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+15*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5-7*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-12*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-8*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-10*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+13*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-8*cos(d*x+c)^3*a^3*b^3-6*cos(d*x+c)^2*a^2*b^4+6*cos(d*x+c)*a*b^5+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6+4*cos(d*x+c)^3*a^5*b-16*cos(d*x+c)^2*a^5*b-10*cos(d*x+c)^2*a^4*b^2+12*cos(d*x+c)*a^5*b-8*cos(d*x+c)*a^4*b^2-22*cos(d*x+c)*a^3*b^3+30*cos(d*x+c)^2*a^3*b^3-6*cos(d*x+c)^2*a*b^5+15*cos(d*x+c)^3*a^4*b^2-3*cos(d*x+c)^3*a^2*b^4+15*cos(d*x+c)*a^2*b^4+21*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+8*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^5*b-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3*b^3-3*cos(d*x+c)*b^6-8*cos(d*x+c)^3*a^6+8*cos(d*x+c)^2*a^6)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/b^3","B"
572,1,2733,307,1.326000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/3/d*4^(1/2)*(4*cos(d*x+c)^2*a^4*b+5*cos(d*x+c)^3*a^2*b^3-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^5-12*cos(d*x+c)^2*a^2*b^3+2*cos(d*x+c)*a^3*b^2-cos(d*x+c)^3*a^4*b+4*cos(d*x+c)^2*a^3*b^2-3*cos(d*x+c)*a^4*b-6*cos(d*x+c)^3*a^3*b^2+6*cos(d*x+c)^2*a*b^4+7*cos(d*x+c)*a^2*b^3-2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2-2*cos(d*x+c)^2*a^5+EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2-7*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3-9*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4+4*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4*b+12*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^5-6*cos(d*x+c)*a*b^4+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4-3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^5-2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^5+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3-6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4-2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4*b+2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4*b+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^4+2*cos(d*x+c)^3*a^5-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/b^2","B"
573,1,2411,287,1.263000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/3/d*4^(1/2)*(-4*cos(d*x+c)^2*a^2*b^2+3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+2*cos(d*x+c)^2*a^3*b+6*cos(d*x+c)^2*a*b^3+cos(d*x+c)*a^2*b^2-sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-2*cos(d*x+c)^3*a*b^3-4*cos(d*x+c)*a*b^3-2*cos(d*x+c)^3*a^3*b+cos(d*x+c)^3*a^4-sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4+3*cos(d*x+c)^3*a^2*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)+sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+4*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-cos(d*x+c)^2*a^4+3*cos(d*x+c)*b^4+3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*a^2*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*a*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b+5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2+7*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b^3-2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*b-4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*b^2-6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-3*cos(d*x+c)^2*b^4)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/b","B"
574,1,1781,274,1.224000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{4}\, \left(-4 a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{3}+4 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+b^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)-5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) b +3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-4 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+4 \cos \left(d x +c \right) a \,b^{2}+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2} b -8 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -4 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+7 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +5 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-3 \cos \left(d x +c \right) a^{2} b +8 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +\left(\cos^{3}\left(d x +c \right)\right) b^{3}-4 b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b \sin \left(d x +c \right)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2} \sin \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a \,b^{2}+3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-\cos \left(d x +c \right) b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right)^{2} \left(a -b \right)^{2} \left(a +b \right)^{2}}"," ",0,"-1/3/d*4^(1/2)*(3*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+8*cos(d*x+c)^2*a^2*b-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-4*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+3*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3+sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-4*cos(d*x+c)^2*a*b^2+4*cos(d*x+c)*a*b^2-5*a^2*cos(d*x+c)^3*b-8*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-4*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+7*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+5*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-3*cos(d*x+c)*a^2*b-4*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-4*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-4*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+4*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+4*cos(d*x+c)^3*a^3+cos(d*x+c)^3*b^3-4*cos(d*x+c)^2*a^3-cos(d*x+c)*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2","B"
575,1,3888,409,1.239000," ","int(1/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"1/3/d*4^(1/2)*(-7*cos(d*x+c)^2*a^4*b-3*cos(d*x+c)^3*a^2*b^3-6*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-4*cos(d*x+c)^2*a^2*b^3-6*cos(d*x+c)*a^3*b^2+7*cos(d*x+c)^3*a^4*b+14*cos(d*x+c)^2*a^3*b^2-8*cos(d*x+c)^3*a^3*b^2+4*cos(d*x+c)^3*a*b^4-6*cos(d*x+c)^2*a*b^4+7*cos(d*x+c)*a^2*b^3-7*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2-6*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5+3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5+3*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5+3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-6*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+7*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2-EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3-2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4-14*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4*b-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^3-3*cos(d*x+c)*b^5+12*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2-6*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4-6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+12*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2+12*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3-6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4+2*cos(d*x+c)*a*b^4-7*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4+6*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b^2+EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^3-2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^4+12*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3+3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+9*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4*b+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^4+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3+3*cos(d*x+c)^2*b^5-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^4*b-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/a^2","B"
576,1,4580,469,1.849000," ","int(cos(d*x+c)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-1/6/d*4^(1/2)*(3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-26*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-26*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+12*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+18*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-10*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^5+6*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^5*b-52*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b^3+30*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^5+12*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+18*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-4*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-10*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-23*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-11*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+12*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+30*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+14*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-6*cos(d*x+c)^4*a^4*b^2+3*cos(d*x+c)^4*a^2*b^4-34*cos(d*x+c)^3*a^3*b^3+20*cos(d*x+c)^3*a*b^5-14*cos(d*x+c)^2*a^2*b^4+10*cos(d*x+c)*a*b^5-30*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b+60*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3-30*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5-30*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5*b-30*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2+60*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^3+60*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6+6*cos(d*x+c)^3*a^5*b-6*cos(d*x+c)^2*a^5*b-17*cos(d*x+c)^2*a^4*b^2-3*cos(d*x+c)*a^4*b^2-18*cos(d*x+c)*a^3*b^3+52*cos(d*x+c)^2*a^3*b^3-30*cos(d*x+c)^2*a*b^5+26*cos(d*x+c)^3*a^4*b^2-15*cos(d*x+c)^3*a^2*b^4+26*cos(d*x+c)*a^2*b^4-30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^6-30*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^6-30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b^2+60*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^4+3*cos(d*x+c)^4*a^6-14*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-10*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+15*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^5*b-26*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-26*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3*b^3-15*cos(d*x+c)*b^6-3*cos(d*x+c)^3*a^6-30*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^5+15*cos(d*x+c)^2*b^6)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/a^3","B"
577,1,5638,513,1.838000," ","int(cos(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
578,1,7838,492,1.566000," ","int(1/(a+b*sec(d*x+c))^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
579,1,502,179,9.102000," ","int(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
580,1,397,159,8.109000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b*sin(1/2*d*x+1/2*c)^2+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*sin(1/2*d*x+1/2*c)^2-12*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+6*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2*a+2*b*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
581,1,148,139,3.888000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-2*b*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
582,1,152,119,3.225000," ","int((a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-a \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
583,1,228,139,3.146000," ","int((a+b*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
584,1,262,159,3.792000," ","int((a+b*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a +20 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a -10 b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*a+20*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*a-10*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
585,1,290,179,3.623000," ","int((a+b*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a -168 b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a +168 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a -42 b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -63 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a-168*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a+168*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a-42*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a-63*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
586,1,689,224,10.770000," ","int(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 a^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{4 a b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^2*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*a^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-4/5*a*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
587,1,660,203,10.226000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 a^{2} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 b^{2} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*a^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*b^2/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
588,1,514,171,8.635000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(6 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}-\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-6 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b +12 a b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(6*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*sin(1/2*d*x+1/2*c)^2+2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^2+12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b*sin(1/2*d*x+1/2*c)^2-24*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2-(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2-6*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b+12*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
589,1,202,150,4.451000," ","int((a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x)","-\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2-2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
590,1,283,150,3.734000," ","int((a+b*sec(d*x+c))^2/sec(d*x+c)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}+3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-6 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b -2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2+3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2-6*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b-2*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
591,1,321,173,4.089000," ","int((a+b*sec(d*x+c))^2/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a^{2}+40 a b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a^{2}-20 a b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b -9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}-15 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*a^2+40*a*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*a^2-20*a*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b-9*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2-15*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
592,1,362,203,4.144000," ","int((a+b*sec(d*x+c))^2/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{2}-336 a b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{2}+336 a b +140 b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{2}-84 a b -70 b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}+35 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-126 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a^2-336*a*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a^2+336*a*b+140*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a^2-84*a*b-70*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2+35*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2-126*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
593,1,847,258,12.798000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{3} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+6 a^{2} b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{6 b^{2} a \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 a^{3} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^3*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+6*a^2*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-6/5*b^2*a/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
594,1,738,219,11.117000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+6 b^{2} a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b^{3} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{6 a^{2} b \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*b^2*a*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+6*a^2*b*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
595,1,631,192,8.744000," ","int((a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(18 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-9 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+18 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(18*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b*sin(1/2*d*x+1/2*c)^2+2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^3*sin(1/2*d*x+1/2*c)^2-6*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*sin(1/2*d*x+1/2*c)^2+18*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2*sin(1/2*d*x+1/2*c)^2-36*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-9*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^3+3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-9*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+18*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
596,1,303,200,3.982000," ","int((a+b*sec(d*x+c))^3/sec(d*x+c)^(3/2),x)","-\frac{2 \left(4 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-2 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*(4*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3-2*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-6*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
597,1,376,190,3.860000," ","int((a+b*sec(d*x+c))^3/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(8 a^{3}+20 a^{2} b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2 a^{3}-10 a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +5 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-15 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/5*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(8*a^3+20*a^2*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-2*a^3-10*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+5*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^3-3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-15*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
598,1,421,227,3.756000," ","int((a+b*sec(d*x+c))^3/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{3}-504 a^{2} b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{3}+504 a^{2} b +420 b^{2} a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{3}-126 a^{2} b -210 b^{2} a \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-105 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a^3-504*a^2*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a^3+504*a^2*b+420*a*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a^3-126*a^2*b-210*a*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
599,1,470,258,3.532000," ","int((a+b*sec(d*x+c))^3/sec(d*x+c)^(9/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a^{3}+2160 a^{2} b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a^{3}-3240 a^{2} b -1512 b^{2} a \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a^{3}+2520 a^{2} b +1512 b^{2} a +420 b^{3}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a^{3}-720 a^{2} b -378 b^{2} a -210 b^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+225 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +105 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-147 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-567 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*a^3+2160*a^2*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*a^3-3240*a^2*b-1512*a*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*a^3+2520*a^2*b+1512*a*b^2+420*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*a^3-720*a^2*b-378*a*b^2-210*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+225*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+105*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^3-147*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-567*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
600,1,1174,307,15.926000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(8 a \,b^{3} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{12 a^{2} b^{2} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 a^{4} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+8 a^{3} b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 b^{4} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{144 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{180 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*a*b^3*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-12/5*a^2*b^2/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a^4*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+8*a^3*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*b^4*(-1/144*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
601,1,925,271,12.663000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+2 b^{4} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{8 a \,b^{3} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{8 a^{3} b \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+12 a^{2} b^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*b^4*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-8/5*a*b^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+8*a^3*b*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+12*a^2*b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
602,1,907,237,10.298000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{8 a^{3} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{4} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{12 a^{2} b^{2} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+8 a \,b^{3} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+8*a^3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2/5*b^4/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+12*a^2*b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+8*a*b^3*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
603,1,777,238,5.015000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(3/2),x)","-\frac{2 \left(-8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a \left(a^{3}+6 b^{3}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(a^{4}+12 a \,b^{3}+b^{4}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+18 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+18 a^{2} b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/3*(-8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(a^3+6*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(a^4+12*a*b^3+b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+18*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3)*sin(1/2*d*x+1/2*c)^2+a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+18*a^2*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
604,1,619,235,4.591000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-24 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a^{3} \left(3 a +10 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 a^{4}+20 a^{3} b +15 b^{4}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+20 a^{3} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+60 a \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-9 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-90 a^{2} b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*(-24*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(3*a+10*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*a^4+20*a^3*b+15*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+20*a^3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+60*a*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-9*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-90*a^2*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+15*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
605,1,476,239,3.728000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{4}-672 a^{3} b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{4}+672 a^{3} b +840 a^{2} b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{4}-168 a^{3} b -420 a^{2} b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+210 a^{2} b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 b^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-252 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -420 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a^4-672*a^3*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a^4+672*a^3*b+840*a^2*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a^4-168*a^3*b-420*a^2*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+210*a^2*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-252*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-420*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
606,1,529,269,4.096000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(9/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a^{4}+2880 a^{3} b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a^{4}-4320 a^{3} b -3024 a^{2} b^{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a^{4}+3360 a^{3} b +3024 a^{2} b^{2}+1680 a \,b^{3}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a^{4}-960 a^{3} b -756 a^{2} b^{2}-840 a \,b^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+300 a^{3} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+420 a \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}-1134 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-315 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*a^4+2880*a^3*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*a^4-4320*a^3*b-3024*a^2*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*a^4+3360*a^3*b+3024*a^2*b^2+1680*a*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*a^4-960*a^3*b-756*a^2*b^2-840*a*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+300*a^3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+420*a*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4-1134*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-315*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
607,1,586,309,4.105000," ","int((a+b*sec(d*x+c))^4/sec(d*x+c)^(11/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(20160 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-50400 a^{4}-49280 a^{3} b \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(56880 a^{4}+98560 a^{3} b +47520 a^{2} b^{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-34920 a^{4}-91168 a^{3} b -71280 a^{2} b^{2}-22176 a \,b^{3}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(13860 a^{4}+41888 a^{3} b +55440 a^{2} b^{2}+22176 a \,b^{3}+4620 b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2790 a^{4}-7392 a^{3} b -15840 a^{2} b^{2}-5544 a \,b^{3}-2310 b^{4}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-6468 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -8316 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}+675 a^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4950 a^{2} b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+1155 b^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(20160*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-50400*a^4-49280*a^3*b)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(56880*a^4+98560*a^3*b+47520*a^2*b^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-34920*a^4-91168*a^3*b-71280*a^2*b^2-22176*a*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(13860*a^4+41888*a^3*b+55440*a^2*b^2+22176*a*b^3+4620*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-2790*a^4-7392*a^3*b-15840*a^2*b^2-5544*a*b^3-2310*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-6468*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-8316*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3+675*a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4950*a^2*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1155*b^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
608,1,450,246,9.504000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}}{b}-\frac{2 a \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/b^2*a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2*a/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
609,1,353,159,4.223000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \left(-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(a -b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b \right)}{b \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(a-b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b)/b/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
610,1,150,71,3.234000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
611,1,187,137,3.863000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+b \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{a \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+b*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
612,1,226,201,3.829000," ","int(1/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +b^{2} \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{a^{2} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+b^2*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a^2/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
613,1,516,232,4.481000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(4 a^{3}-4 a^{2} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 a^{3}+2 a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +3 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+3 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+3 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{3 a^{3} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((4*a^3-4*a^2*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*a^3+2*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+3*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^3+3*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+3*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a^3/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
614,1,1002,398,14.653000," ","int(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{4 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}}{b^{2}}-\frac{4 a \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 a^{2} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*a^3/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-4/b^3*a*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2/b^2*a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
615,1,868,341,11.059000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/b*a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
616,1,608,278,7.158000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
617,1,707,272,8.325000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a*b*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
618,1,788,291,8.391000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{4 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4*b/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^2/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
619,1,809,308,10.325000," ","int(1/(a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+a \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{6 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{3} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{3}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-6*b^2/a^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^3*b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
620,1,1064,362,11.489000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\frac{8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}+\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3}-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\frac{4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{3}}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{4 \left(a +b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(a^{2}+2 a b +3 b^{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{8 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{4} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{4}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4/3/a^2*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-4*(a+b)/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(a^2+2*a*b+3*b^2)/a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+8*b^3/a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/a^4*b^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
621,1,2014,436,16.754000," ","int(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/b*a*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/b^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2*a/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
622,1,1203,367,7.985000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{2 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/2*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/4/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/2/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/4/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/4*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/4*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/4*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/4*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/4/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/4/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
623,1,1760,365,13.495000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}+\frac{\frac{2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a*b*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
624,1,1858,358,13.654000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}-\frac{4 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^2/a^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-4*b/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
625,1,1936,375,13.740000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6/a^2*b/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^3*b^3*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+6*b^2/a^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
626,1,1957,394,15.081000," ","int(1/(a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-12*b^2/a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/a^4*b^4*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-8/a^4*b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
627,1,2216,454,16.279000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4/3/a^3*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-2/a^4*(2*a+3*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(a^2+3*a*b+6*b^2)/a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+20*b^3/a^4/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^5*b^5*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+10/a^5*b^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
628,1,789,302,1.818000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*(2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b+2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
629,1,283,184,1.490000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \left(-1+\cos \left(d x +c \right)\right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b+2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
630,1,925,90,1.750000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{2 \left(\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +\sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+((a-b)/(a+b))^(1/2)*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","B"
631,1,1021,228,1.838000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}-b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)-b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a/((a-b)/(a+b))^(1/2)","B"
632,1,1736,274,1.817000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-9 a^{2} b \sqrt{\frac{a -b}{a +b}}-a \,b^{2} \sqrt{\frac{a -b}{a +b}}+4 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+2 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/15/d*(-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-9*a^2*b*((a-b)/(a+b))^(1/2)-a*b^2*((a-b)/(a+b))^(1/2)-9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3+4*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+5*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+2*b^3*((a-b)/(a+b))^(1/2)+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
633,1,2050,329,1.902000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(10 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+15 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+26 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-25 a^{3} b \sqrt{\frac{a -b}{a +b}}-19 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}+4 a \,b^{3} \sqrt{\frac{a -b}{a +b}}+18 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -19 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +20 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}+8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-25 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-19 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 b^{4} \sqrt{\frac{a -b}{a +b}}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+25 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-19 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+19 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+25 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+19 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -19 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}-19 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{105 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}}"," ",0,"-2/105/d*(-8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+25*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-25*a^3*b*((a-b)/(a+b))^(1/2)-19*a^2*b^2*((a-b)/(a+b))^(1/2)+4*a*b^3*((a-b)/(a+b))^(1/2)-cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+26*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-19*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+20*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+18*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+15*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+25*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*b^4*((a-b)/(a+b))^(1/2)-19*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+19*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-19*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-19*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+2*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-8*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+19*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-19*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a^3","B"
634,1,1744,350,1.737000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x)","\frac{\left(5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}-5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"1/4/d*(5*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-5*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-6*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+5*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-5*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-5*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b+5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
635,1,1207,314,1.599000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{\left(6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*(6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b+2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^2+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
636,1,1367,278,1.838000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{2 \left(-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -a b \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/d*(-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+2*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-a*b*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
637,1,1219,223,1.894000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}-4 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2+4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)-4*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","B"
638,1,1707,270,1.800000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(\left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-3 a^{2} b \sqrt{\frac{a -b}{a +b}}-2 a \,b^{2} \sqrt{\frac{a -b}{a +b}}-b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{5 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/5/d*(cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+4*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-3*a^2*b*((a-b)/(a+b))^(1/2)-2*a*b^2*((a-b)/(a+b))^(1/2)-b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a/((a-b)/(a+b))^(1/2)","B"
639,1,2050,327,1.967000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(25 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+10 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+15 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+27 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+68 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-25 a^{3} b \sqrt{\frac{a -b}{a +b}}-82 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-3 a \,b^{3} \sqrt{\frac{a -b}{a +b}}+39 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -82 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +55 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-25 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-82 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 b^{4} \sqrt{\frac{a -b}{a +b}}+25 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-82 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+51 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+82 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-82 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b +51 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+82 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -82 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{105 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/105/d*(6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+25*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-25*a^3*b*((a-b)/(a+b))^(1/2)-82*a^2*b^2*((a-b)/(a+b))^(1/2)-3*a*b^3*((a-b)/(a+b))^(1/2)+27*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+68*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-82*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+55*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+39*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+15*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+25*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*b^4*((a-b)/(a+b))^(1/2)-82*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+51*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+82*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+51*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2+6*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+82*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-82*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
640,1,2295,414,1.811000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/24/d*(30*cos(d*x+c)^4*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3+26*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^2*b+16*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a*b^2+18*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a*b^2-59*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+33*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-33*cos(d*x+c)^4*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+33*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-34*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-33*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+16*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*b^3-8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*b^3+16*cos(d*x+c)^4*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+18*cos(d*x+c)^4*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+30*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3-33*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+16*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+18*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-8*b^3*((a-b)/(a+b))^(1/2)+120*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^2+33*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-16*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+26*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-44*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+120*cos(d*x+c)^4*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^2+33*cos(d*x+c)^4*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-16*cos(d*x+c)^4*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+26*cos(d*x+c)^4*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-44*cos(d*x+c)^4*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
641,1,1982,365,1.536000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x)","\frac{\left(9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+4 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-30 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}-8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+4 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-30 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+9 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) b^{3}+11 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+2 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"1/4/d*(9*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-9*cos(d*x+c)^3*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2-8*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-2*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*sin(d*x+c)*b^3-30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*sin(d*x+c)*a^2*b-8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*sin(d*x+c)*b^3+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^2*b-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2-8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3-30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3-9*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a*b^2+9*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-9*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*b^3+11*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+2*b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
642,1,1949,328,1.789000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -4 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+10 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+10 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a \,b^{2}+2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*(2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^2*b-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*b^3-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+10*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-4*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+10*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2+2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
643,1,1661,321,1.789000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b^{3}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) b^{3}+7 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -7 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{3} \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sin \left(d x +c \right)+7 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-a^{2} b \sqrt{\frac{a -b}{a +b}}-7 a \,b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b^3+cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3+7*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-7*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*sin(d*x+c)+7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-a^2*b*((a-b)/(a+b))^(1/2)-7*a*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
644,1,1931,269,1.916000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-23 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+23 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+17 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-23 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-9 a^{2} b \sqrt{\frac{a -b}{a +b}}-11 a \,b^{2} \sqrt{\frac{a -b}{a +b}}+14 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +34 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+23 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-5 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -23 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+15 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) b^{3}-23 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +23 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+17 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -23 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+15 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sin \left(d x +c \right)-23 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/15/d*(-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+23*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+17*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-23*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-23*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-9*a^2*b*((a-b)/(a+b))^(1/2)-11*a*b^2*((a-b)/(a+b))^(1/2)-9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+23*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3+14*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+34*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-5*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-23*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+15*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+23*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+17*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-23*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-23*b^3*((a-b)/(a+b))^(1/2)+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-23*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","B"
645,1,2050,327,1.968000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(5 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+3 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+18 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+22 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +12 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-5 a^{3} b \sqrt{\frac{a -b}{a +b}}-29 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-9 a \,b^{3} \sqrt{\frac{a -b}{a +b}}+12 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -29 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +11 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}+3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-5 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-29 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 b^{4} \sqrt{\frac{a -b}{a +b}}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-29 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+27 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+29 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-29 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b +27 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+29 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -29 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{21 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/21/d*(-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-5*a^3*b*((a-b)/(a+b))^(1/2)-29*a^2*b^2*((a-b)/(a+b))^(1/2)-9*a*b^3*((a-b)/(a+b))^(1/2)+18*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+22*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+12*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-29*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+11*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+12*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-5*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+5*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*b^4*((a-b)/(a+b))^(1/2)-29*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+27*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+29*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-29*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-29*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+27*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+29*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-29*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a/((a-b)/(a+b))^(1/2)","B"
646,1,2788,381,2.093000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x)","\text{Expression too large to display}"," ",0,"-2/315/d*(35*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^5+14*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5+98*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5-147*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5-10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5+147*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+10*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5-147*a^4*b*((a-b)/(a+b))^(1/2)-163*a^3*b^2*((a-b)/(a+b))^(1/2)-279*a^2*b^3*((a-b)/(a+b))^(1/2)-5*a*b^4*((a-b)/(a+b))^(1/2)+130*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b+170*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^2+82*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b-279*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2+199*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4+80*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3+272*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2-5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4-65*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-147*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-147*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+279*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-279*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+261*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-279*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+155*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*b^5*((a-b)/(a+b))^(1/2)-279*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+155*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+10*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-147*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b+279*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-279*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-10*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4+261*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
647,1,1755,363,1.712000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{\left(6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2}}"," ",0,"1/4/d*(6*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-3*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+3*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-6*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+6*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/b^2","C"
648,1,996,311,1.749000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b}"," ",0,"-1/d*(-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b-2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/b","C"
649,1,216,91,1.692000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))-2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2)))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/((a-b)/(a+b))^(1/2)","C"
650,1,171,90,1.596000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)}{d \left(-1+\cos \left(d x +c \right)\right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))/(-1+cos(d*x+c))/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","A"
651,1,736,188,1.827000," ","int(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b -\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a}"," ",0,"-2/d*(-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a","B"
652,1,1024,231,1.983000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}+2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)+2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
653,1,1736,279,2.114000," ","int(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-9 a^{2} b \sqrt{\frac{a -b}{a +b}}+4 a \,b^{2} \sqrt{\frac{a -b}{a +b}}-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+10 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-8 b^{3} \sqrt{\frac{a -b}{a +b}}-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{3} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/15/d*(-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-9*a^2*b*((a-b)/(a+b))^(1/2)+4*a*b^2*((a-b)/(a+b))^(1/2)-9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-8*b^3*((a-b)/(a+b))^(1/2)+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^3/((a-b)/(a+b))^(1/2)","B"
654,1,1501,406,1.857000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\left(6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a b +3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -3 \sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}-b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right) b^{2}}"," ",0,"-1/d*(6*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^2-6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b+6*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-3*((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)-b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(7/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)/b^2","C"
655,1,1144,248,1.574000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a -2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)-2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a \sin \left(d x +c \right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a -a \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"2/d*(2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a-2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-2*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a-a*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/(b+a*cos(d*x+c))/sin(d*x+c)/b/((a-b)/(a+b))^(1/2)/(a+b)","C"
656,1,501,145,1.922000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}-\sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-2/d*(EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)-((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)","B"
657,1,510,242,1.728000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b -\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \cos \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"2/d*(-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*cos(d*x+c)*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/((a-b)/(a+b))^(1/2)/(a+b)","B"
658,1,999,256,1.794000," ","int(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+a b \sqrt{\frac{a -b}{a +b}}+2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \left(a +b \right) \sqrt{\frac{a -b}{a +b}}\, a^{2}}"," ",0,"2/d*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+a*b*((a-b)/(a+b))^(1/2)+2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/(a+b)/((a-b)/(a+b))^(1/2)/a^2","B"
659,1,1315,321,2.137000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -5 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-a^{2} b \sqrt{\frac{a -b}{a +b}}+4 a \,b^{2} \sqrt{\frac{a -b}{a +b}}+8 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{3} \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-2/3/d*(-5*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-5*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-a^2*b*((a-b)/(a+b))^(1/2)+4*a*b^2*((a-b)/(a+b))^(1/2)+8*b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))/a^3/((a-b)/(a+b))^(1/2)/(a+b)","B"
660,1,1861,386,1.891000," ","int(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3} b +8 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-12 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{4}-3 a^{3} b \sqrt{\frac{a -b}{a +b}}-8 a \,b^{3} \sqrt{\frac{a -b}{a +b}}+\left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{4}+16 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-3 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 b^{4} \sqrt{\frac{a -b}{a +b}}+3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a^{4}-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-12 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-16 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{5 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{4} \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-2/5/d*(-16*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4-3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4+((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4+2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4-2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b+8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2-3*a^3*b*((a-b)/(a+b))^(1/2)-8*a*b^3*((a-b)/(a+b))^(1/2)-2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+8*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+16*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-3*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*b^4*((a-b)/(a+b))^(1/2)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-12*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b-12*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-16*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^4/((a-b)/(a+b))^(1/2)/(a+b)","B"
661,1,4591,505,1.773000," ","int(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"1/3/d*(15*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5+30*cos(d*x+c)^3*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5-30*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+30*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+15*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5-30*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+15*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5-15*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5+3*a^3*b^2*((a-b)/(a+b))^(1/2)+3*a^2*b^3*((a-b)/(a+b))^(1/2)-3*a*b^4*((a-b)/(a+b))^(1/2)+21*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2-15*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b+23*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3-5*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b+5*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2-29*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3-29*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4+20*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-30*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-30*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4-3*b^5*((a-b)/(a+b))^(1/2)+30*cos(d*x+c)^3*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-30*cos(d*x+c)^3*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-30*cos(d*x+c)^3*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-26*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+3*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-20*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+36*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+18*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+60*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-60*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-30*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4+15*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-26*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-26*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-50*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+16*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+54*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+18*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+30*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b+30*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-20*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+36*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+18*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+15*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-26*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-30*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/b^3/((a-b)/(a+b))^(1/2)/(a+b)^2/(a-b)","C"
662,1,3854,423,1.563000," ","int(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(-6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4+6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-3*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4+12*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b-12*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^3-6*cos(d*x+c)^2*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2+6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3*b-6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^3-7*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-4*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b+9*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3+6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2+4*a^3*b*((a-b)/(a+b))^(1/2)+a^2*b^2*((a-b)/(a+b))^(1/2)-7*a*b^3*((a-b)/(a+b))^(1/2)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+3*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4-6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4+6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-6*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^4+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2+12*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)/b^2","C"
663,1,1343,307,1.701000," ","int(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-\sqrt{\frac{a -b}{a +b}}\, a^{2}-a b \sqrt{\frac{a -b}{a +b}}+4 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right)^{2} \left(a -b \right) \left(a +b \right)^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(4*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-3*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2+4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-((a-b)/(a+b))^(1/2)*a^2-a*b*((a-b)/(a+b))^(1/2)+4*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)","B"
664,1,1822,311,1.561000," ","int(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-2 a^{2} b \sqrt{\frac{a -b}{a +b}}+a \,b^{2} \sqrt{\frac{a -b}{a +b}}-b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right)^{2} \left(a -b \right) \left(a +b \right)^{2} a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-2*a^2*b*((a-b)/(a+b))^(1/2)+a*b^2*((a-b)/(a+b))^(1/2)-b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/a/((a-b)/(a+b))^(1/2)","B"
665,1,2070,332,1.519000," ","int(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+5 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-a \,b^{3} \sqrt{\frac{a -b}{a +b}}+6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}+2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}+6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 b^{4} \sqrt{\frac{a -b}{a +b}}+3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}+6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4}-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}\right) \cos \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right)^{2} \left(a -b \right) \left(a +b \right)^{2} \sqrt{\frac{a -b}{a +b}}\, a^{2}}"," ",0,"-2/3/d*(-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-2*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2+5*a^2*b^2*((a-b)/(a+b))^(1/2)-a*b^3*((a-b)/(a+b))^(1/2)-6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4-2*b^4*((a-b)/(a+b))^(1/2)+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3*b-2*cos(d*x+c)^2*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3-5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-2*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*cos(d*x+c)*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)/a^2","B"
666,1,3103,347,1.873000," ","int(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5-3*a^3*b^2*((a-b)/(a+b))^(1/2)-11*a^2*b^3*((a-b)/(a+b))^(1/2)+4*a*b^4*((a-b)/(a+b))^(1/2)-3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b-4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b-12*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2+18*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4-3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3+18*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2-12*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*b^5*((a-b)/(a+b))^(1/2)-15*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-9*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+14*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-15*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-15*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4-12*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))^2/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/a^3/((a-b)/(a+b))^(1/2)/(a+b)^2/(a-b)","B"
667,1,3615,415,2.042000," ","int(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(a^4*b^2*((a-b)/(a+b))^(1/2)-7*a^3*b^3*((a-b)/(a+b))^(1/2)-20*a^2*b^4*((a-b)/(a+b))^(1/2)+8*a*b^5*((a-b)/(a+b))^(1/2)+28*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+16*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5+16*cos(d*x+c)^2*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5-9*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b-16*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2+12*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3+16*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-28*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+16*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^6-cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6+16*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^5-6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^3-6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^4-7*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5*b+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b^2+34*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^3-8*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^4-24*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^5+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b-14*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^2-22*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^3+34*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^4-cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5*b+cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b^2+cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^3+6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5*b+6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-28*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+12*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+16*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^6*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-16*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^6-cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^6+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^6+16*b^6*((a-b)/(a+b))^(1/2)-28*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+16*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5-10*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b-25*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3+8*cos(d*x+c)^2*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-28*cos(d*x+c)^2*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)*cos(d*x+c)^2/sin(d*x+c)/(b+a*cos(d*x+c))^2/a^4/((a-b)/(a+b))^(1/2)/(a+b)^2/(a-b)","B"
668,1,4586,492,2.073000," ","int(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/15/d*(3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^7+6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^7+9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^7-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^7-9*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^7-128*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^7+5*a^4*b^3*((a-b)/(a+b))^(1/2)-50*a^3*b^4*((a-b)/(a+b))^(1/2)-148*a^2*b^5*((a-b)/(a+b))^(1/2)+64*a*b^6*((a-b)/(a+b))^(1/2)-9*a^5*b^2*((a-b)/(a+b))^(1/2)+17*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^6*b-38*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5*b^2+42*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b^3+254*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^4-64*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^5-192*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^6+3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^6*b-3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^5*b^2-3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b^3-8*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^6*b-8*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5*b^2+6*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^6*b+42*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5*b^2+42*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b^3-48*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^4-48*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^5+8*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b^3+8*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^4-18*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^6*b+16*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b^2-94*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^3-164*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^4+260*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^5+128*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^6+128*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^7*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+55*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^5*b^2-212*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3*b^4+128*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^6-17*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^6*b-72*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^5*b^2-116*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^4*b^3+96*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3*b^4+128*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^2*b^5+9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^6*b+55*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^5*b^2+55*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4*b^3-212*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^3*b^4-212*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^5+128*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^6-26*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^6*b-89*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^5*b^2-188*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^4*b^3-20*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b^4+224*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^2*b^5+128*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^6+128*b^7*((a-b)/(a+b))^(1/2)+9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^7+128*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b^7-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^7+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+55*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-212*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-17*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-72*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-116*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+96*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+128*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/a^5/((a-b)/(a+b))^(1/2)/(a+b)^2/(a-b)","B"
669,1,405,158,1.770000," ","int(1/sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x)","-\frac{\left(2 i \sin \left(d x +c \right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{5}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}+i \sin \left(d x +c \right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{5}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}+2 i \sqrt{5}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+i \sqrt{5}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+20 \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right)-30\right) \sqrt{\frac{3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{10 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(3+2 \cos \left(d x +c \right)\right)}"," ",0,"-1/10/d*(2*I*sin(d*x+c)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*5^(1/2)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5^(1/2))*2^(1/2)+I*sin(d*x+c)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*5^(1/2)*EllipticE(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5^(1/2))*2^(1/2)+2*I*5^(1/2)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5^(1/2))*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+I*5^(1/2)*EllipticE(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5^(1/2))*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+20*cos(d*x+c)^2+10*cos(d*x+c)-30)*((3+2*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(3+2*cos(d*x+c))","C"
670,1,374,147,1.883000," ","int(1/sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x)","\frac{\left(-2 i \cos \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \cos \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right)-10 \cos \left(d x +c \right)+6\right) \sqrt{-\frac{-3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(-3+2 \cos \left(d x +c \right)\right)}"," ",0,"1/2/d*(-2*I*cos(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-I*cos(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*cos(d*x+c)^2-10*cos(d*x+c)+6)*(-(-3+2*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(-3+2*cos(d*x+c))","B"
671,1,405,146,1.849000," ","int(1/(2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(2 i \sqrt{5}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)-5 i \sqrt{5}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+2 i \sqrt{5}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-5 i \sqrt{5}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+20 \left(\cos^{2}\left(d x +c \right)\right)-50 \cos \left(d x +c \right)+30\right) \sqrt{\frac{-3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{10 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(-3+2 \cos \left(d x +c \right)\right)}"," ",0,"-1/10/d*(2*I*5^(1/2)*cos(d*x+c)*sin(d*x+c)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*5^(1/2))-5*I*5^(1/2)*cos(d*x+c)*sin(d*x+c)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*5^(1/2))+2*I*5^(1/2)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*5^(1/2))*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*I*5^(1/2)*EllipticE(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*5^(1/2))*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+20*cos(d*x+c)^2-50*cos(d*x+c)+30)*((-3+2*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(-3+2*cos(d*x+c))","B"
672,1,390,159,1.863000," ","int(1/(-2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(2 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)-5 i \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+2 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-5 i \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-20 \left(\cos^{2}\left(d x +c \right)\right)-10 \cos \left(d x +c \right)+30\right) \sqrt{-\frac{3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{10 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(3+2 \cos \left(d x +c \right)\right)}"," ",0,"-1/10/d*(2*I*cos(d*x+c)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))-5*I*cos(d*x+c)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+2*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-20*cos(d*x+c)^2-10*cos(d*x+c)+30)*(-(3+2*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(3+2*cos(d*x+c))","C"
673,1,409,159,1.803000," ","int(1/sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x)","\frac{\left(3 \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{5}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-\sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{5}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+3 \sqrt{5}\, \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{5}\, \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-30 \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right)+20\right) \sqrt{\frac{2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{15 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(2+3 \cos \left(d x +c \right)\right)}"," ",0,"1/15/d*(3*sin(d*x+c)*cos(d*x+c)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*5^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*2^(1/2)-sin(d*x+c)*cos(d*x+c)*EllipticE(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*5^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*2^(1/2)+3*5^(1/2)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5^(1/2)*EllipticE(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-30*cos(d*x+c)^2+10*cos(d*x+c)+20)*((2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(2+3*cos(d*x+c))","C"
674,1,381,149,1.909000," ","int(1/(3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{2 \left(3 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{5}-5 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{5}+3 \sqrt{5}\, \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-5 \sqrt{5}\, \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 \left(\cos^{2}\left(d x +c \right)\right)+25 \cos \left(d x +c \right)-10\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{15 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(-2+3 \cos \left(d x +c \right)\right)}"," ",0,"2/15/d*(3*sin(d*x+c)*cos(d*x+c)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF(5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*5^(1/2)-5*sin(d*x+c)*cos(d*x+c)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE(5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*5^(1/2)+3*5^(1/2)*EllipticF(5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*5^(1/2)*EllipticE(5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*cos(d*x+c)^2+25*cos(d*x+c)-10)*((-2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(-2+3*cos(d*x+c))","C"
675,1,370,159,1.785000," ","int(1/sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x)","-\frac{2 \left(3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right)-i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right)+3 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-i \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)-2\right) \sqrt{-\frac{-2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(-2+3 \cos \left(d x +c \right)\right)}"," ",0,"-2/3/d*(3*I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))-I*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))+3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*cos(d*x+c)^2+5*cos(d*x+c)-2)*(-(-2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(-2+3*cos(d*x+c))","C"
676,1,394,149,1.877000," ","int(1/(-3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{\left(-3 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)+5 i \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)-3 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+5 i \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+30 \left(\cos^{2}\left(d x +c \right)\right)-10 \cos \left(d x +c \right)-20\right) \sqrt{-\frac{2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{15 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(2+3 \cos \left(d x +c \right)\right)}"," ",0,"1/15/d*(-3*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))+5*I*cos(d*x+c)*sin(d*x+c)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-3*I*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+5*I*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+30*cos(d*x+c)^2-10*cos(d*x+c)-20)*(-(2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(2+3*cos(d*x+c))","C"
677,1,142,79,1.494000," ","int(sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x)","-\frac{i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{5}}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)-3\right)}"," ",0,"-1/5*I/d*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5^(1/2))*10^(1/2)*(1/cos(d*x+c))^(1/2)*((3+2*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)^2*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/(2*cos(d*x+c)^2+cos(d*x+c)-3)*5^(1/2)","C"
678,1,137,73,1.583000," ","int(sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x)","\frac{i \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{-3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}}{d \left(2 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+3\right)}"," ",0,"I/d*(1/cos(d*x+c))^(1/2)*(-(-3+2*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(2*cos(d*x+c)^2-5*cos(d*x+c)+3)","A"
679,1,144,73,1.533000," ","int(sec(d*x+c)^(1/2)/(2-3*sec(d*x+c))^(1/2),x)","-\frac{i \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{-3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{5}}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+3\right)}"," ",0,"-1/5*I/d*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*5^(1/2))*(1/cos(d*x+c))^(1/2)*((-3+2*cos(d*x+c))/cos(d*x+c))^(1/2)/(2*cos(d*x+c)^2-5*cos(d*x+c)+3)*5^(1/2)","A"
680,1,139,79,1.651000," ","int(sec(d*x+c)^(1/2)/(-2-3*sec(d*x+c))^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{3+2 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right) \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)-3\right)}"," ",0,"1/5*I/d*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(1/2)*(-(3+2*cos(d*x+c))/cos(d*x+c))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))*sin(d*x+c)^2*cos(d*x+c)/(2*cos(d*x+c)^2+cos(d*x+c)-3)","C"
681,1,145,79,1.464000," ","int(sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x)","\frac{\cos \left(d x +c \right) \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{5}}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-2\right)}"," ",0,"1/5/d*cos(d*x+c)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2*(1/cos(d*x+c))^(1/2)*((2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(3*cos(d*x+c)^2-cos(d*x+c)-2)*5^(1/2)","C"
682,1,138,74,1.564000," ","int(sec(d*x+c)^(1/2)/(3-2*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{5}}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+2\right)}"," ",0,"2/5/d*(1/cos(d*x+c))^(1/2)*((-2+3*cos(d*x+c))/cos(d*x+c))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2*cos(d*x+c)*EllipticF(5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))/(3*cos(d*x+c)^2-5*cos(d*x+c)+2)*5^(1/2)","C"
683,1,136,79,1.608000," ","int(sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x)","\frac{2 i \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{-2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+2\right)}"," ",0,"2*I/d*(1/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*cos(d*x+c)*sin(d*x+c)^2*(1/cos(d*x+c))^(1/2)*(-(-2+3*cos(d*x+c))/cos(d*x+c))^(1/2)/(3*cos(d*x+c)^2-5*cos(d*x+c)+2)","C"
684,1,142,74,1.678000," ","int(sec(d*x+c)^(1/2)/(-3-2*sec(d*x+c))^(1/2),x)","\frac{i \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2+3 \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{10}}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-2\right)}"," ",0,"1/5*I/d*(1/cos(d*x+c))^(1/2)*(-(2+3*cos(d*x+c))/cos(d*x+c))^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)^2*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*10^(1/2)/(3*cos(d*x+c)^2-cos(d*x+c)-2)","C"
685,0,0,85,0.718000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(1/3),x)","\int \sec \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+b*sec(d*x+c))^(1/3),x)","F"
686,0,0,14,0.959000," ","int((a+b*sec(d*x+c))^(1/3),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/3),x)","F"
687,0,0,306,0.892000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(2/3),x)","\int \left(\sec^{4}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(2/3),x)","F"
688,0,0,253,0.800000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(2/3),x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(2/3),x)","F"
689,0,0,212,0.737000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(2/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(2/3),x)","F"
690,0,0,85,0.708000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(2/3),x)","\int \sec \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+b*sec(d*x+c))^(2/3),x)","F"
691,0,0,14,0.825000," ","int((a+b*sec(d*x+c))^(2/3),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(2/3),x)","F"
692,0,0,88,0.728000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(4/3),x)","\int \sec \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+b*sec(d*x+c))^(4/3),x)","F"
693,0,0,14,0.737000," ","int((a+b*sec(d*x+c))^(4/3),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(4/3),x)","F"
694,0,0,352,0.810000," ","int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/3),x)","\int \left(\sec^{4}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/3),x)","F"
695,0,0,300,0.891000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/3),x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/3),x)","F"
696,0,0,247,0.749000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/3),x)","F"
697,0,0,88,0.684000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(5/3),x)","\int \sec \left(d x +c \right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(d*x+c)*(a+b*sec(d*x+c))^(5/3),x)","F"
698,0,0,14,0.732000," ","int((a+b*sec(d*x+c))^(5/3),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/3),x)","F"
699,0,0,261,0.817000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{4}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/3),x)","F"
700,0,0,217,0.820000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/3),x)","F"
701,0,0,179,0.714000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/3),x)","F"
702,0,0,85,0.818000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+b*sec(d*x+c))^(1/3),x)","F"
703,0,0,14,0.793000," ","int(1/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{1}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+b*sec(d*x+c))^(1/3),x)","F"
704,0,0,85,0.802000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(2/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+b*sec(d*x+c))^(2/3),x)","F"
705,0,0,14,0.732000," ","int(1/(a+b*sec(d*x+c))^(2/3),x)","\int \frac{1}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(a+b*sec(d*x+c))^(2/3),x)","F"
706,0,0,90,0.740000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(4/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+b*sec(d*x+c))^(4/3),x)","F"
707,0,0,14,0.751000," ","int(1/(a+b*sec(d*x+c))^(4/3),x)","\int \frac{1}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+b*sec(d*x+c))^(4/3),x)","F"
708,0,0,326,0.895000," ","int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{4}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/3),x)","F"
709,0,0,264,0.891000," ","int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/3),x)","F"
710,0,0,246,0.769000," ","int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/3),x)","F"
711,0,0,90,0.746000," ","int(sec(d*x+c)/(a+b*sec(d*x+c))^(5/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(a+b*sec(d*x+c))^(5/3),x)","F"
712,0,0,14,0.758000," ","int(1/(a+b*sec(d*x+c))^(5/3),x)","\int \frac{1}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(1/(a+b*sec(d*x+c))^(5/3),x)","F"
713,0,0,154,0.949000," ","int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x)","\int \frac{\sec^{\frac{2}{3}}\left(d x +c \right)}{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x)","F"
714,0,0,154,0.916000," ","int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x)","\int \frac{\sec^{\frac{1}{3}}\left(d x +c \right)}{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x)","F"
715,0,0,154,0.914000," ","int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{1}{3}} \left(a +b \sec \left(d x +c \right)\right)}\, dx"," ",0,"int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x)","F"
716,0,0,154,0.951000," ","int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{2}{3}} \left(a +b \sec \left(d x +c \right)\right)}\, dx"," ",0,"int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x)","F"
717,0,0,23,1.660000," ","int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(1/2),x)","\int \left(\sec^{\frac{7}{3}}\left(d x +c \right)\right) \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(1/2),x)","F"
718,0,0,23,1.703000," ","int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(1/2),x)","\int \left(\sec^{\frac{5}{3}}\left(d x +c \right)\right) \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(1/2),x)","F"
719,0,0,23,1.648000," ","int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(1/2),x)","\int \left(\sec^{\frac{4}{3}}\left(d x +c \right)\right) \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(1/2),x)","F"
720,0,0,23,1.477000," ","int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(1/2),x)","\int \left(\sec^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(1/2),x)","F"
721,0,0,23,1.994000," ","int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(1/2),x)","\int \left(\sec^{\frac{1}{3}}\left(d x +c \right)\right) \sqrt{a +b \sec \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(1/2),x)","F"
722,0,0,23,1.503000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/3),x)","\int \frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sec \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/3),x)","F"
723,0,0,23,1.772000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(2/3),x)","\int \frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sec \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(2/3),x)","F"
724,0,0,23,1.774000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(4/3),x)","\int \frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sec \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(4/3),x)","F"
725,0,0,23,1.486000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/3),x)","\int \frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sec \left(d x +c \right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/3),x)","F"
726,0,0,23,1.509000," ","int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/3),x)","\int \frac{\sqrt{a +b \sec \left(d x +c \right)}}{\sec \left(d x +c \right)^{\frac{7}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/3),x)","F"
727,0,0,23,1.444000," ","int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(3/2),x)","\int \left(\sec^{\frac{7}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(3/2),x)","F"
728,0,0,23,1.556000," ","int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(3/2),x)","\int \left(\sec^{\frac{5}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(3/2),x)","F"
729,0,0,23,1.532000," ","int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(3/2),x)","\int \left(\sec^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(3/2),x)","F"
730,0,0,23,1.598000," ","int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(3/2),x)","\int \left(\sec^{\frac{2}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(3/2),x)","F"
731,0,0,23,1.495000," ","int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(3/2),x)","\int \left(\sec^{\frac{1}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(3/2),x)","F"
732,0,0,23,1.421000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/3),x)","F"
733,0,0,23,1.505000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(2/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(2/3),x)","F"
734,0,0,23,1.355000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(4/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(4/3),x)","F"
735,0,0,23,1.303000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/3),x)","F"
736,0,0,23,1.331000," ","int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}{\sec \left(d x +c \right)^{\frac{7}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/3),x)","F"
737,0,0,23,1.572000," ","int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(5/2),x)","\int \left(\sec^{\frac{7}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(5/2),x)","F"
738,0,0,23,1.492000," ","int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(5/2),x)","\int \left(\sec^{\frac{5}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(5/2),x)","F"
739,0,0,23,1.370000," ","int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(5/2),x)","\int \left(\sec^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(5/2),x)","F"
740,0,0,23,1.288000," ","int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(5/2),x)","\int \left(\sec^{\frac{2}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(5/2),x)","F"
741,0,0,23,1.315000," ","int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(5/2),x)","\int \left(\sec^{\frac{1}{3}}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(5/2),x)","F"
742,0,0,23,1.282000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{\sec \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/3),x)","F"
743,0,0,23,1.418000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(2/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{\sec \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(2/3),x)","F"
744,0,0,23,1.432000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(4/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{\sec \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(4/3),x)","F"
745,0,0,23,1.470000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{\sec \left(d x +c \right)^{\frac{5}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/3),x)","F"
746,0,0,23,1.389000," ","int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/3),x)","\int \frac{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}{\sec \left(d x +c \right)^{\frac{7}{3}}}\, dx"," ",0,"int((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/3),x)","F"
747,0,0,23,1.450000," ","int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\sec^{\frac{7}{3}}\left(d x +c \right)}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
748,0,0,23,1.348000," ","int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\sec^{\frac{5}{3}}\left(d x +c \right)}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
749,0,0,23,1.471000," ","int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\sec^{\frac{4}{3}}\left(d x +c \right)}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
750,0,0,23,1.531000," ","int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\sec^{\frac{2}{3}}\left(d x +c \right)}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
751,0,0,23,1.598000," ","int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{\sec^{\frac{1}{3}}\left(d x +c \right)}{\sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
752,0,0,23,1.589000," ","int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{1}{3}} \sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
753,0,0,23,1.754000," ","int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{2}{3}} \sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
754,0,0,23,1.660000," ","int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{4}{3}} \sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
755,0,0,23,1.611000," ","int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{5}{3}} \sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
756,0,0,23,1.560000," ","int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{7}{3}} \sqrt{a +b \sec \left(d x +c \right)}}\, dx"," ",0,"int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x)","F"
757,0,0,23,1.484000," ","int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\sec^{\frac{7}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
758,0,0,23,1.384000," ","int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\sec^{\frac{5}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
759,0,0,23,1.325000," ","int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\sec^{\frac{4}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
760,0,0,23,1.335000," ","int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\sec^{\frac{2}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
761,0,0,23,1.250000," ","int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{\sec^{\frac{1}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
762,0,0,23,1.401000," ","int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{1}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
763,0,0,23,1.445000," ","int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{2}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
764,0,0,23,1.374000," ","int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{4}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
765,0,0,23,1.716000," ","int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{5}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
766,0,0,23,1.600000," ","int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{7}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x)","F"
767,0,0,23,1.432000," ","int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{\sec^{\frac{7}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
768,0,0,23,1.441000," ","int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{\sec^{\frac{5}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
769,0,0,23,1.503000," ","int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{\sec^{\frac{4}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
770,0,0,23,1.318000," ","int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{\sec^{\frac{2}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
771,0,0,23,1.356000," ","int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{\sec^{\frac{1}{3}}\left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
772,0,0,23,1.560000," ","int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{1}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
773,0,0,23,1.577000," ","int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{2}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
774,0,0,23,1.575000," ","int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{4}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
775,0,0,23,1.618000," ","int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{5}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
776,0,0,23,1.647000," ","int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x)","\int \frac{1}{\sec \left(d x +c \right)^{\frac{7}{3}} \left(a +b \sec \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x)","F"
777,0,0,233,11.293000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^3,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^3,x)","F"
778,0,0,163,8.194000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^2,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^2,x)","F"
779,0,0,119,2.598000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e)),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e)),x)","F"
780,0,0,176,2.829000," ","int((d*sec(f*x+e))^n/(a+b*sec(f*x+e)),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+b*sec(f*x+e)),x)","F"
781,0,0,275,0.865000," ","int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^2,x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^2,x)","F"
782,0,0,25,1.241000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(3/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(3/2),x)","F"
783,0,0,25,1.252000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(1/2),x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \sqrt{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(1/2),x)","F"
784,0,0,25,1.071000," ","int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(1/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\sqrt{a +b \sec \left(f x +e \right)}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(1/2),x)","F"
785,0,0,25,1.117000," ","int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(3/2),x)","\int \frac{\left(d \sec \left(f x +e \right)\right)^{n}}{\left(a +b \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(3/2),x)","F"
786,0,0,23,2.995000," ","int(sec(f*x+e)^n*(a+b*sec(f*x+e))^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^n*(a+b*sec(f*x+e))^m,x)","F"
787,0,0,25,2.530000," ","int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^m,x)","\int \left(d \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^m,x)","F"
788,0,0,245,1.143000," ","int(sec(f*x+e)^3*(a+b*sec(f*x+e))^m,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*sec(f*x+e))^m,x)","F"
789,0,0,192,0.808000," ","int(sec(f*x+e)^2*(a+b*sec(f*x+e))^m,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*sec(f*x+e))^m,x)","F"
790,0,0,89,0.921000," ","int(sec(f*x+e)*(a+b*sec(f*x+e))^m,x)","\int \sec \left(f x +e \right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)*(a+b*sec(f*x+e))^m,x)","F"
791,0,0,14,0.783000," ","int((a+b*sec(f*x+e))^m,x)","\int \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*sec(f*x+e))^m,x)","F"
792,0,0,21,1.278000," ","int(cos(f*x+e)*(a+b*sec(f*x+e))^m,x)","\int \cos \left(f x +e \right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cos(f*x+e)*(a+b*sec(f*x+e))^m,x)","F"
793,0,0,23,1.941000," ","int(cos(f*x+e)^2*(a+b*sec(f*x+e))^m,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sec(f*x+e))^m,x)","F"
794,1,318,167,4.016000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a +720 b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a -1080 b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a +840 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a -240 b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+75 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*a+720*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*a-1080*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*a+840*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*a-240*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+75*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
795,1,290,147,3.384000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a -168 b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a +168 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a -42 b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -63 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a-168*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a+168*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a-42*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a-63*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
796,1,262,127,3.640000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a +20 b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a -10 b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*a+20*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*a-10*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
797,1,228,107,3.513000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
798,1,152,87,2.958000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-a \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
799,1,148,107,3.959000," ","int((a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{2 \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-2*b*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
800,1,397,127,7.964000," ","int((a+b*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a +6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b*sin(1/2*d*x+1/2*c)^2+6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*sin(1/2*d*x+1/2*c)^2-12*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a+6*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2*a+2*b*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
801,1,502,147,8.999000," ","int((a+b*sec(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
802,1,398,192,3.952000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a^{2}+1440 a b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a^{2}-2160 a b -504 b^{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a^{2}+1680 a b +504 b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a^{2}-480 a b -126 b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+150 a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-189 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*a^2+1440*a*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*a^2-2160*a*b-504*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*a^2+1680*a*b+504*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*a^2-480*a*b-126*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+150*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-189*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
803,1,362,171,3.899000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{2}-336 a b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{2}+336 a b +140 b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{2}-84 a b -70 b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}+35 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-126 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a^2-336*a*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a^2+336*a*b+140*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a^2-84*a*b-70*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+35*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-126*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
804,1,321,141,3.680000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a^{2}+40 a b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a^{2}-20 a b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*a^2+40*a*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*a^2-20*a*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
805,1,283,118,4.243000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}+3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}-6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
806,1,202,118,4.142000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x)","-\frac{2 \left(2 a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(2*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
807,1,514,139,8.343000," ","int((a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2}-\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2}+12 a b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b*sin(1/2*d*x+1/2*c)^2+6*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*sin(1/2*d*x+1/2*c)^2+2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^2-24*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-3*a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+12*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
808,1,660,171,10.707000," ","int((a+b*sec(d*x+c))^2/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 b^{2} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+4 a b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*b^2/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+4*a*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
809,1,689,192,10.986000," ","int((a+b*sec(d*x+c))^2/cos(d*x+c)^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 a^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{4 a b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-4/5*a*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b^2*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
810,1,470,226,3.875000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a^{3}+2160 a^{2} b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a^{3}-3240 a^{2} b -1512 b^{2} a \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a^{3}+2520 a^{2} b +1512 b^{2} a +420 b^{3}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a^{3}-720 a^{2} b -378 b^{2} a -210 b^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+225 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +105 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-147 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-567 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*a^3+2160*a^2*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*a^3-3240*a^2*b-1512*a*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*a^3+2520*a^2*b+1512*a*b^2+420*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*a^3-720*a^2*b-378*a*b^2-210*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+225*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-567*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
811,1,421,195,4.124000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{3}-504 a^{2} b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{3}+504 a^{2} b +420 b^{2} a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{3}-126 a^{2} b -210 b^{2} a \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-105 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*a^3-504*a^2*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*a^3+504*a^2*b+420*a*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*a^3-126*a^2*b-210*a*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
812,1,376,158,3.699000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3,x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(8 a^{3}+20 a^{2} b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2 a^{3}-10 a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +5 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-15 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/5*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(8*a^3+20*a^2*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-2*a^3-10*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+5*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
813,1,303,168,4.556000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x)","-\frac{2 \left(4 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-2 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*(4*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3-2*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-6*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
814,1,630,160,8.455000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x)","-\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(6 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+36 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+9 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+9 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}-18 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(6*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2-18*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-18*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2-2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2+36*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+9*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-18*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
815,1,738,187,10.750000," ","int((a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+6 b^{2} a \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b^{3} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{6 a^{2} b \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*b^2*a*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+6*a^2*b*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
816,1,847,226,12.604000," ","int((a+b*sec(d*x+c))^3/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{3} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+6 a^{2} b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{6 b^{2} a \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 a^{3} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^3*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+6*a^2*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-6/5*b^2*a/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
817,1,668,218,4.520000," ","int(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(-24 a^{4}+24 a^{3} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a^{4}-44 a^{3} b +20 a^{2} b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a^{4}+16 a^{3} b -10 a^{2} b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 a^{3} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-15 a \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}-15 b^{4} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{15 a^{4} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((-24*a^4+24*a^3*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*a^4-44*a^3*b+20*a^2*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*a^4+16*a^3*b-10*a^2*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-5*a^3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-15*a*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3-15*b^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a^4/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
818,1,516,184,4.552000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(4 a^{3}-4 a^{2} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 a^{3}+2 a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +3 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+3 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+3 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{3 a^{3} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((4*a^3-4*a^2*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*a^3+2*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+3*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a^3/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
819,1,226,153,3.685000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +b^{2} \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)+\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}\right)}{a^{2} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+b^2*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2)/a^2/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
820,1,187,105,3.864000," ","int(1/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+b \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)\right)}{a \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+b*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/a/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
821,1,150,55,3.071000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
822,1,353,127,4.956000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \left(-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(a -b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a -\sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b \right)}{b \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(a-b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a-(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b)/b/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
823,1,450,198,10.055000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 a \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/b^2*a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*a/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2/b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
824,1,1063,314,11.366000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{4 \left(-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{4 \left(a +b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(a^{2}+2 a b +3 b^{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{8 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{4} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{4}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4/3/a^2/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))-4*(a+b)/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(a^2+2*a*b+3*b^2)/a^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+8*b^3/a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/a^4*b^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
825,1,809,260,10.569000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+a \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{6 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{3} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{3}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-6*b^2/a^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^3*b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
826,1,788,243,8.365000," ","int(1/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{4 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4*b/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^2/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
827,1,707,224,8.278000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a*b*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
828,1,608,230,6.375000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
829,1,868,293,10.828000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/b*a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
830,1,2216,406,17.272000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4/3/a^3*(2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-2/a^4*(2*a+3*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(a^2+3*a*b+6*b^2)/a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+20*b^3/a^4/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^5*b^5*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+10/a^5*b^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
831,1,1957,346,15.624000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*b*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+a*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-12*b^2/a^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2/a^4*b^4*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-8/a^4*b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
832,1,1936,327,13.445000," ","int(1/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6/a^2*b/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/a^3*b^3*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+6*b^2/a^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
833,1,1858,310,13.896000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}-\frac{4 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^2/a^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-4*b/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
834,1,1760,317,13.650000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}+\frac{\frac{2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a*b*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
835,1,1203,319,8.638000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{2 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/2*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/4/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/2/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/4/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/4*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/4*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/4*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/4*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/4/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/4/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
836,1,2014,388,17.374000," ","int(1/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/b*a*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/b^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2*a/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
837,1,1724,274,1.450000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-4 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+9 a^{2} b \sqrt{\frac{a -b}{a +b}}+a \,b^{2} \sqrt{\frac{a -b}{a +b}}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-5 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-2 b^{3} \sqrt{\frac{a -b}{a +b}}-2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/15/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+9*a^2*b*((a-b)/(a+b))^(1/2)+a*b^2*((a-b)/(a+b))^(1/2)+9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-4*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-5*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2-7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-2*b^3*((a-b)/(a+b))^(1/2)-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/((a-b)/(a+b))^(1/2)","B"
838,1,1011,228,1.487000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}-b^{2} \sqrt{\frac{a -b}{a +b}}\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)-b^2*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/a/((a-b)/(a+b))^(1/2)","B"
839,1,923,90,1.286000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +\sqrt{\frac{a -b}{a +b}}\, b \right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+((a-b)/(a+b))^(1/2)*b)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","B"
840,1,275,184,1.219000," ","int((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{2 \left(\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b +2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}}{d \left(-1+\cos \left(d x +c \right)\right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b+2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b)*cos(d*x+c)^(1/2)*sin(d*x+c)^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)/(-1+cos(d*x+c))/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
841,1,780,302,1.267000," ","int((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","\frac{\left(\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b -2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +\sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"1/d*(sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-2*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+((a-b)/(a+b))^(1/2)*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
842,1,2040,327,1.416000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(10 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+27 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+68 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}+6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+39 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -25 a^{3} b \sqrt{\frac{a -b}{a +b}}-82 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-3 a \,b^{3} \sqrt{\frac{a -b}{a +b}}-82 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +55 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}+51 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+82 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}+15 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}-6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-25 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+25 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-82 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+82 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-82 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+25 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 b^{4} \sqrt{\frac{a -b}{a +b}}+51 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-82 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b -82 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}\right)}{105 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/105/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+25*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-25*a^3*b*((a-b)/(a+b))^(1/2)-82*a^2*b^2*((a-b)/(a+b))^(1/2)-3*a*b^3*((a-b)/(a+b))^(1/2)+27*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+68*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-82*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+55*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+39*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+15*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+25*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*b^4*((a-b)/(a+b))^(1/2)-82*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+51*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+82*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+51*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2+6*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+82*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-82*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/((a-b)/(a+b))^(1/2)","B"
843,1,1695,270,1.490000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-\left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+3 a^{2} b \sqrt{\frac{a -b}{a +b}}+2 a \,b^{2} \sqrt{\frac{a -b}{a +b}}+b^{3} \sqrt{\frac{a -b}{a +b}}\right)}{5 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/5/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-4*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+3*a^2*b*((a-b)/(a+b))^(1/2)+2*a*b^2*((a-b)/(a+b))^(1/2)+b^3*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/a/((a-b)/(a+b))^(1/2)","B"
844,1,1209,223,1.474000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}-4 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(4*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2+4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)-4*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","B"
845,1,1365,278,1.317000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2} \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -a b \sqrt{\frac{a -b}{a +b}}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-a*b*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
846,1,1205,314,1.286000," ","int((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","-\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*(2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b-cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b-sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
847,1,1742,350,1.180000," ","int((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}+8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}-5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}-5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/4/d*(6*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2+8*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-5*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+5*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-4*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2+6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2+8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-5*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+5*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2+5*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2-7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
848,1,2778,381,1.525000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"2/315/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-35*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^5-14*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5-98*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5+147*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5+10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5-147*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5-10*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5+147*a^4*b*((a-b)/(a+b))^(1/2)+163*a^3*b^2*((a-b)/(a+b))^(1/2)+279*a^2*b^3*((a-b)/(a+b))^(1/2)+5*a*b^4*((a-b)/(a+b))^(1/2)-130*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b-170*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^2-82*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b+279*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2-199*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3-10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4-80*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3-272*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2+5*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4+65*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b+147*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+147*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-279*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+279*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-261*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+279*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-155*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*b^5*((a-b)/(a+b))^(1/2)+279*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-155*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3-10*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+147*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-279*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2+279*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3+10*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4-261*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b)/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/((a-b)/(a+b))^(1/2)","B"
849,1,2040,327,1.276000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(-29 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-29 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+12 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+18 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+22 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +12 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-5 a^{3} b \sqrt{\frac{a -b}{a +b}}-29 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-9 a \,b^{3} \sqrt{\frac{a -b}{a +b}}-29 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +11 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+29 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b +3 \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4}+3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-5 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}+29 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+5 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 b^{4} \sqrt{\frac{a -b}{a +b}}+27 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-29 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b -29 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}+27 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{21 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/21/d*(-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-5*a^3*b*((a-b)/(a+b))^(1/2)-29*a^2*b^2*((a-b)/(a+b))^(1/2)-9*a*b^3*((a-b)/(a+b))^(1/2)+18*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+22*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+12*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-29*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+11*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+12*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+3*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-5*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+5*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*b^4*((a-b)/(a+b))^(1/2)-29*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+27*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+29*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-29*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-29*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b+27*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+29*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-29*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/((a-b)/(a+b))^(1/2)","B"
850,1,1921,269,1.337000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-23 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-17 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-14 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+9 a^{2} b \sqrt{\frac{a -b}{a +b}}+11 a \,b^{2} \sqrt{\frac{a -b}{a +b}}-34 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-23 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+5 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +23 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -23 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+23 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-17 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -15 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) b^{3}+23 b^{3} \sqrt{\frac{a -b}{a +b}}+23 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+23 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+23 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sin \left(d x +c \right)\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/15/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-23*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-17*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+23*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+23*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+9*a^2*b*((a-b)/(a+b))^(1/2)+11*a*b^2*((a-b)/(a+b))^(1/2)+9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-23*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-14*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-34*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+5*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+23*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-15*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-23*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2-17*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+23*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+23*b^3*((a-b)/(a+b))^(1/2)-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+23*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*sin(d*x+c))/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","B"
851,1,1651,321,1.262000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) b^{3}+7 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -7 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+6 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{3}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sin \left(d x +c \right)+7 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+8 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +7 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-a^{2} b \sqrt{\frac{a -b}{a +b}}-7 a \,b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*b^3+7*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-7*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+6*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*sin(d*x+c)+7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3+8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-a^2*b*((a-b)/(a+b))^(1/2)-7*a*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
852,1,1947,328,1.273000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+10 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b -\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+10 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a \,b^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}+2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-b^{3} \sqrt{\frac{a -b}{a +b}}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b^2+10*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^2+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^3-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-4*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+10*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-2*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3+2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3-b^3*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^(1/2)/((a-b)/(a+b))^(1/2)","C"
853,1,1972,365,1.305000," ","int((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","-\frac{\left(30 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) b^{3}-9 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +9 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a^{3}-6 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) b^{3}+30 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{3}-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b +9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}+8 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}-6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b +2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{3}-11 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-2 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/4/d*(30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3-9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^3-6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*b^3+30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b+8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^3-9*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2+8*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b^2-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^3+9*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2-9*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+9*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3-11*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-2*b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
854,1,2285,414,1.169000," ","int((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/24/d*(59*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+33*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3-16*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*b^3-26*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b-16*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2-33*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+16*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2-26*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b+44*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-33*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-18*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^3+8*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3+33*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3-18*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2-33*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+34*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-18*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3-30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3+33*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3-16*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3-30*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3-16*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3+44*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2-120*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2-120*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2-33*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b+16*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2-26*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b+8*b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^(5/2)/((a-b)/(a+b))^(1/2)","C"
855,1,1726,279,1.292000," ","int(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}+9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-9 a^{2} b \sqrt{\frac{a -b}{a +b}}+4 a \,b^{2} \sqrt{\frac{a -b}{a +b}}+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-9 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+3 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+10 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b -8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-9 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -8 b^{3} \sqrt{\frac{a -b}{a +b}}-8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-9 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-9 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{15 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/15/d*(-9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3-8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-9*a^2*b*((a-b)/(a+b))^(1/2)+4*a*b^2*((a-b)/(a+b))^(1/2)-9*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3-9*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+3*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+10*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-9*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-8*b^3*((a-b)/(a+b))^(1/2)+9*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a^3/((a-b)/(a+b))^(1/2)","B"
856,1,1014,231,1.469000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-a b \sqrt{\frac{a -b}{a +b}}+2 b^{2} \sqrt{\frac{a -b}{a +b}}\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-2*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-a*b*((a-b)/(a+b))^(1/2)+2*b^2*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/((a-b)/(a+b))^(1/2)","B"
857,1,732,188,1.415000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +\sqrt{\frac{a -b}{a +b}}\, b \right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a}"," ",0,"2/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+((a-b)/(a+b))^(1/2)*b)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/a","B"
858,1,163,90,1.344000," ","int(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(-1+\cos \left(d x +c \right)\right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*sin(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","A"
859,1,206,91,1.298000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)-2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))-2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2)))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/((a-b)/(a+b))^(1/2)","C"
860,1,986,311,1.457000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b -2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b}"," ",0,"-1/d*(-sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a+sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-2*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a+2*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)/b","C"
861,1,1745,363,1.339000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{\left(6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+3 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +2 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}}"," ",0,"1/4/d*(6*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-3*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+3*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-6*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^3*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+6*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+2*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)/((a-b)/(a+b))^(1/2)/b^2","C"
862,1,1851,386,1.431000," ","int(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-4 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3} b +8 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+2 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{4}-2 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}+2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +8 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}+3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a^{4}-16 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{4}+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 a^{3} b \sqrt{\frac{a -b}{a +b}}-8 a \,b^{3} \sqrt{\frac{a -b}{a +b}}-12 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+16 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}-3 a^{4} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-16 b^{4} \sqrt{\frac{a -b}{a +b}}-12 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}\right)}{5 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{4} \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/5/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-16*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4-3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4+((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4+2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4-2*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b+8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*a^3*b*((a-b)/(a+b))^(1/2)-8*a*b^3*((a-b)/(a+b))^(1/2)-2*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+2*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+8*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+16*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-3*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*b^4*((a-b)/(a+b))^(1/2)-4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-12*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b-12*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-16*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2)/(b+a*cos(d*x+c))/sin(d*x+c)/a^4/(a+b)/((a-b)/(a+b))^(1/2)","B"
863,1,1307,321,1.543000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b -8 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+5 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-8 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-\left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +4 \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +8 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+a^{2} b \sqrt{\frac{a -b}{a +b}}-4 a \,b^{2} \sqrt{\frac{a -b}{a +b}}-8 b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/3/d*(5*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b-8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+5*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3-cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+4*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+a^2*b*((a-b)/(a+b))^(1/2)-4*a*b^2*((a-b)/(a+b))^(1/2)-8*b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a^3/(a+b)/((a-b)/(a+b))^(1/2)","B"
864,1,997,256,1.486000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)+2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +\sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+a b \sqrt{\frac{a -b}{a +b}}+2 b^{2} \sqrt{\frac{a -b}{a +b}}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right) a^{2}}"," ",0,"2/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+a*b*((a-b)/(a+b))^(1/2)+2*b^2*((a-b)/(a+b))^(1/2))/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)/a^2","B"
865,1,502,242,1.409000," ","int(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) b -\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -\sqrt{\frac{a -b}{a +b}}\, b \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-((a-b)/(a+b))^(1/2)*b)*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a+b)/((a-b)/(a+b))^(1/2)","B"
866,1,491,145,1.255000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}-\sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right)}"," ",0,"-2/d*(((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)*((a-b)/(a+b))^(1/2)-((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)","B"
867,1,1134,248,1.350000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b +\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a +2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a \sin \left(d x +c \right)+2 \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +a \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/d*(2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+2*cos(d*x+c)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b-2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a+2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)-cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+a*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/b/(a+b)/((a-b)/(a+b))^(1/2)","C"
868,1,1492,406,1.423000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{\left(6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a^{2}+6 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) a b +3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +3 \sqrt{\frac{a -b}{a +b}}\, a^{2} \cos \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+a b \sqrt{\frac{a -b}{a +b}}+b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right) b^{2}}"," ",0,"1/d*(6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b+3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^2-6*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-4*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2+6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b+3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-6*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*((a-b)/(a+b))^(1/2)*a^2*cos(d*x+c)-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+a*b*((a-b)/(a+b))^(1/2)+b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^(1/2)/((a-b)/(a+b))^(1/2)/(a+b)/b^2","C"
869,1,3604,415,1.523000," ","int(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6+sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6-a^4*b^2*((a-b)/(a+b))^(1/2)+7*a^3*b^3*((a-b)/(a+b))^(1/2)+20*a^2*b^4*((a-b)/(a+b))^(1/2)-8*a*b^5*((a-b)/(a+b))^(1/2)-16*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^5+((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^5*b-((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*b^2-((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b^3-6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^5*b-6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*b^2+6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b^3+6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^4+7*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^5*b-6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*b^2-34*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b^3+8*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^4+24*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^5-2*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^5*b+14*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b^2+22*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^3-34*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^4-16*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^6+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-12*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+28*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+16*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^6+((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^6-((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^6-16*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^6*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-16*b^6*((a-b)/(a+b))^(1/2)-16*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^5+28*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^3+28*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^4+9*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b+16*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2-12*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3-16*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4-8*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5*b+28*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^3-16*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^5+10*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b+25*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2+4*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3-28*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4-16*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5-8*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5*b-8*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/a^4/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)","B"
870,1,3101,347,1.505000," ","int(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-3*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5-8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5-3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b-4*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5-3*a^3*b^2*((a-b)/(a+b))^(1/2)-11*a^2*b^3*((a-b)/(a+b))^(1/2)+4*a*b^4*((a-b)/(a+b))^(1/2)+3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b-12*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2+18*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+8*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4-3*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3+18*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2-12*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-9*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+6*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+8*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+8*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*b^5*((a-b)/(a+b))^(1/2)-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+14*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+8*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-15*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-15*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3+8*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4-12*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b)/sin(d*x+c)/(b+a*cos(d*x+c))^2/a^3/((a-b)/(a+b))^(1/2)/(a+b)^2/(a-b)","B"
871,1,2062,332,1.528000," ","int(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b +3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4}-2 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{4} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+5 a^{2} b^{2} \sqrt{\frac{a -b}{a +b}}-a \,b^{3} \sqrt{\frac{a -b}{a +b}}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}+6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b -6 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2}-2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{3}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b +2 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{4}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}-2 b^{4} \sqrt{\frac{a -b}{a +b}}-3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3} b -2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b^{2}+6 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3} b -2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{3}-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b^{2}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \left(b +a \cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) \left(a -b \right) \left(a +b \right)^{2} \sqrt{\frac{a -b}{a +b}}\, a^{2}}"," ",0,"-2/3/d*(-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4+3*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+3*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2-3*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b-2*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2+6*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b-2*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3+5*a^2*b^2*((a-b)/(a+b))^(1/2)-a*b^3*((a-b)/(a+b))^(1/2)-6*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-6*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+2*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-2*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*b^4*((a-b)/(a+b))^(1/2)+3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-2*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b+6*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3)*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)/a^2","B"
872,1,1804,311,1.312000," ","int(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","\frac{2 \left(3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{2}-3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}+\sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b +3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{3}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a \,b^{2}+\cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{3}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+3 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}+\sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-3 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b +\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2}-\cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3}+2 a^{2} b \sqrt{\frac{a -b}{a +b}}-a \,b^{2} \sqrt{\frac{a -b}{a +b}}+b^{3} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \left(b +a \cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) \left(a -b \right) \left(a +b \right)^{2} a \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/3/d*(3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a^3+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)*a*b^2-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3+3*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^2+cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^3-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-2*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3+((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3-3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b+cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^2-cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3+2*a^2*b*((a-b)/(a+b))^(1/2)-a*b^2*((a-b)/(a+b))^(1/2)+b^3*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/(a-b)/(a+b)^2/a/((a-b)/(a+b))^(1/2)","B"
873,1,1333,307,1.512000," ","int(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -3 \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}+4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+4 \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -4 \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-\sqrt{\frac{a -b}{a +b}}\, a^{2}-a b \sqrt{\frac{a -b}{a +b}}+4 b^{2} \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \left(b +a \cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) \left(a -b \right) \left(a +b \right)^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-3*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+4*cos(d*x+c)^2*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2+4*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+4*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+4*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-3*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-4*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-((a-b)/(a+b))^(1/2)*a^2-a*b*((a-b)/(a+b))^(1/2)+4*b^2*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)","B"
874,1,3844,423,1.385000," ","int(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+6*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4+6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4-6*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2+4*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b-9*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-4*a^3*b*((a-b)/(a+b))^(1/2)-a^2*b^2*((a-b)/(a+b))^(1/2)+7*a*b^3*((a-b)/(a+b))^(1/2)+cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+3*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-7*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3-3*a^4*((a-b)/(a+b))^(1/2)*cos(d*x+c)+6*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4-6*sin(d*x+c)*cos(d*x+c)^2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4-6*sin(d*x+c)*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+6*sin(d*x+c)*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^4-3*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^4-6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b-5*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2-12*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3-3*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b+7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2+7*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3-12*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3*b+12*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^3-3*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^3+7*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2-6*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^3*b+6*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^3+6*sin(d*x+c)*cos(d*x+c)^2*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/(b+a*cos(d*x+c))^2/sin(d*x+c)/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)/b^2","C"
875,0,0,247,11.273000," ","int((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^3,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^3,x)","F"
876,0,0,171,8.810000," ","int((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^2,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^2,x)","F"
877,0,0,120,3.038000," ","int((d*cos(f*x+e))^n*(a+b*sec(f*x+e)),x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)\, dx"," ",0,"int((d*cos(f*x+e))^n*(a+b*sec(f*x+e)),x)","F"
878,0,0,178,2.541000," ","int((d*cos(f*x+e))^n/(a+b*sec(f*x+e)),x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{n}}{a +b \sec \left(f x +e \right)}\, dx"," ",0,"int((d*cos(f*x+e))^n/(a+b*sec(f*x+e)),x)","F"
879,0,0,277,1.104000," ","int((d*cos(f*x+e))^n/(a+b*sec(f*x+e))^2,x)","\int \frac{\left(d \cos \left(f x +e \right)\right)^{n}}{\left(a +b \sec \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*cos(f*x+e))^n/(a+b*sec(f*x+e))^2,x)","F"